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Chapter 1 Resource Masters
Bothell, WA • Chicago, IL • Columbus, OH • New York, NY
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Copyright © by The McGraw-Hill Companies, Inc.
All rights reserved. The contents, or parts thereof, may be reproduced in print form for non-profit educational use with Glencoe Algebra 1, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning.
Send all inquiries to:McGraw-Hill Education8787 Orion PlaceColumbus, OH 43240
ISBN: 978-0-07-660498-2MHID: 0-07-660498-5
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11
CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9
Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0
Answers For Workbooks The answers for Chapter 1 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.
Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 1 Test Form 2A and Form 2C.
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Teacher’s Guide to Using the Chapter 1 Resource Masters .........................................iv
Chapter Resources Chapter 1 Student-Built Glossary ...................... 1Chapter 1 Anticipation Guide (English) ............. 3Chapter 1 Anticipation Guide (Spanish) ............ 4
Lesson 1-1Variables and ExpressionsStudy Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice ............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10
Lesson 1-2Order of OperationsStudy Guide and Intervention ...........................11Skills Practice .................................................. 13Practice ........................................................... 14Word Problem Practice .................................... 15Enrichment ...................................................... 16TI-Nspire® Activity ............................................ 17
Lesson 1-3Properties of NumbersStudy Guide and Intervention .......................... 18Skills Practice .................................................. 20Practice ........................................................... 21Word Problem Practice .................................... 22Enrichment ...................................................... 23
Lesson 1-4The Distributive PropertyStudy Guide and Intervention .......................... 24Skills Practice .................................................. 26Practice ........................................................... 27Word Problem Practice .................................... 28Enrichment ...................................................... 29
Lesson 1-5EquationsStudy Guide and Intervention .......................... 30Skills Practice .................................................. 32Practice ........................................................... 33Word Problem Practice .................................... 34Enrichment ...................................................... 35Spreadsheet Activity ........................................ 36
Lesson 1-6RelationsStudy Guide and Intervention .......................... 37Skills Practice .................................................. 39Practice ........................................................... 40Word Problem Practice .................................... 41Enrichment ...................................................... 42
Lesson 1-7FunctionsStudy Guide and Intervention .......................... 43Skills Practice .................................................. 45Practice ........................................................... 46Word Problem Practice .................................... 47Enrichment ...................................................... 48
Lesson 1-8Interpreting Graphs of Functions
Study Guide and Intervention .......................... 49Skills Practice .................................................. 51Practice ........................................................... 52Word Problem Practice .................................... 53Enrichment ...................................................... 54
AssessmentStudent Recording Sheet ................................ 55Rubric for Scoring Extended Response .......... 56Chapter 1 Quizzes 1 and 2 ............................. 57Chapter 1 Quizzes 3 and 4 ............................. 58Chapter 1 Mid-Chapter Test ............................ 59Chapter 1 Vocabulary Test ............................... 60Chapter 1 Test, Form 1 .................................... 61Chapter 1 Test, Form 2A ................................. 63Chapter 1 Test, Form 2B ................................. 65
Chapter 1 Test, Form 2C ................................. 67Chapter 1 Test, Form 2D ................................. 69Chapter 1 Test, Form 3 .................................... 71Chapter 1 Extended Response Test ................ 73Standardized Test Practice ...............................74
Answers ........................................... A1–A36
Contents
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iv
Teacher’s Guide to Using the Chapter 1 Resource Masters
Chapter ResourcesStudent-Built Glossary (pages 1–2) These masters are a student study tool that pres-ents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students high-light or star the terms with which they are not familiar. Give this to students before beginning Lesson 1-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.
Anticipation Guide (pages 3–4) This mas-ter, presented in both English and Spanish, is a survey used before beginning the chap-ter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their percep-tions have changed.
Lesson ResourcesStudy Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteach-ing activity. It can also be used in conjunc-tion with the Student Edition as an instruc-tional tool for students who have been absent.
Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.
Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional prac-tice option or as homework for second-day teaching of the lesson.
Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.
Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathe-matics they are learning. They are written for use with all levels of students.
Graphing Calculator, TI-Nspire or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.
The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.
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Assessment OptionsThe assessment masters in the Chapter 1 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.
Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.
Extended Response Rubric This master provides information for teachers and stu-dents on how to assess performance on open-ended questions.
Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.
Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 11 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.
Leveled Chapter Tests• Form 1 contains multiple-choice
questions and is intended for use with below grade level students.
• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.
• Form 3 is a free-response test for use with above grade level students.
All of the above mentioned tests include a free-response Bonus question.
Extended-Response Test Performance assessment tasks are suitable for all stu-dents. Sample answers and a scoring rubric are included for evaluation.
Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided as reduced pages.
• Full-size answer keys are provided for the assessment masters.
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Chapter 1 1 Glencoe Algebra 1
This is an alphabetical list of the key vocabulary terms you will learn in Chapter 1. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.
(continued on the next page)
Vocabulary TermFound
on PageDefi nition/Description/Example
coefficient(koh·uh·FIH·shuhnt)
continuous function
coordinate system
dependent variable
domain
end behavior
function
identity
independent variable
intercept
Student-Built Glossary1
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Chapter 1 2 Glencoe Algebra 1
Vocabulary TermFound
on PageDefi nition/Description/Example
like terms
line symmetry
open sentence
order of operations
power
range
relative maximum
relative minimum
replacement set
solution set
variable
Student-Built Glossary (continued)1
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Chapter 1 3 Glencoe Algebra 1
Before you begin Chapter 1
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
After you complete Chapter 1
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
1 Anticipation GuideExpressions, Equations, and Functions
Step 1
Step 2
STEP 1A, D, or NS
StatementSTEP 2A or D
1. An algebraic expression contains one or more numbers, variables, and arithmetic operations.
2. The expression x4 means x + x + x + x.
3. According to the order of operations, all multiplication and division should be done before anything else.
4. Since 2 makes the equation 3t - 1 = 5 true, {2} is the solution set for the equation.
5. Because of the Reflexive Property of Equality, if a + b = c then c = a + b.
6. The multiplicative inverse of 23 is 1 − 23
.
7. The Distributive Property states that a(b + c) will equal ab + c.
8. The order in which you add or multiply numbers does not change their sum or product.
9. A graph has symmetry in a line if each half of the graph on either side of the line matches exactly.
10. In the coordinate plane, the x-axis is horizontal and the y-axis is vertical.
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Antes de comenzar el Capítulo 1
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).
Después de completar el Capítulo 1
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.
1 Ejercicios preparatoriosExpressions, Equations, and Functions
Paso 1
Paso 2
PASO 1A, D o NS
EnunciadoPASO 2A o D
1. Una expresión matemática contiene uno o más números, variables y operaciones aritméticas.
2. La expresión x4 significa x + x + x + x.
3. Según el orden de las operaciones, se debe realizar toda multi-plicación y división antes que cualquier otra operación.
4. Puesto que 2 hace verdadera la ecuación 3t - 1 = 5 , {2} es el conjunto solución para la ecuación.
5. Debido a la propiedad reflexiva de la igualdad, si a + b = c entonces c = a + b.
6. El inverso multiplicativo de 23 es 1 − 23
.
7. La propiedad distributiva dice que a(b + c) es igual a ab + c.
8. El orden en el cual sumas o multiplicas números no altera su suma o su producto.
9. Una gráfica tiene simetría en una línea si cada uno la mitad de la gráfica a cada lado de la línea corresponde exactamente.
10. En el plano de coordenadas, el eje x es horizontal y el eje y es vertical.
Capítulo 1 4 Álgebra 1 de Glencoe
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Chapter 1 5 Glencoe Algebra 1
Write Verbal Expressions An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. In algebra, variables are symbols used to represent unspecified numbers or values. Any letter may be used as a variable.
Write a verbal expression for each algebraic expression.
a. 6n2
the product of 6 and n squaredb. n3 - 12m
the difference of n cubed and twelve times m
ExercisesWrite a verbal expression for each algebraic expression.
1. w - 1 2. 1 − 3 a3
3. 81 + 2x 4. 12d
5. 84 6. 62
7. 2n2 + 4 8. a3 ․ b3
9. 2x3 - 3 10. 6k3 −
5
11. 1 − 4 b2 12. 7n5
13. 3x + 4 14. 2 − 3 k5
15. 3b2 + 2a3 16. 4(n2 + 1)
1-1 Study Guide and InterventionVariables and Expressions
Example
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Chapter 1 6 Glencoe Algebra 1
Write Algrebraic Expressions Translating verbal expressions into algebraic expressions is an important algebraic skill.
Write an algebraic expression for each verbal expression.
a. four more than a number nThe words more than imply addition.four more than a number n4 + nThe algebraic expression is 4 + n.
b. the difference of a number squared and 8The expression difference of implies subtraction.the difference of a number squared and 8n2 - 8The algebraic expression is n2 - 8.
ExercisesWrite an algebraic expression for each verbal expression.
1. a number decreased by 8
2. a number divided by 8
3. a number squared
4. four times a number
5. a number divided by 6
6. a number multiplied by 37
7. the sum of 9 and a number
8. 3 less than 5 times a number
9. twice the sum of 15 and a number
10. one-half the square of b
11. 7 more than the product of 6 and a number
12. 30 increased by 3 times the square of a number
1-1 Study Guide and Intervention (continued)
Variables and Expressions
Example
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Chapter 1 7 Glencoe Algebra 1
Write a verbal expression for each algebraic expression.
1. 9a2 2. 52
3. c + 2d 4. 4 - 5h
5. 2b2 6. 7x3 - 1
7. p4 + 6r 8. 3n2 - x
Write an algebraic expression for each verbal expression.
9. the sum of a number and 10
10. 15 less than k
11. the product of 18 and q
12. 6 more than twice m
13. 8 increased by three times a number
14. the difference of 17 and 5 times a number
15. the product of 2 and the second power of y
16. 9 less than g to the fourth power
1-1 Skills PracticeVariables and Expressions
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Chapter 1 8 Glencoe Algebra 1
Write a verbal expression for each algebraic expression.
1. 23f 2. 73
3. 5m2 + 2 4. 4d3 - 10
5. x3 ․ y4 6. b2 - 3c3
7. k5 −
6 8. 4n2
− 7
Write an algebraic expression for each verbal expression.
9. the difference of 10 and u
10. the sum of 18 and a number
11. the product of 33 and j
12. 74 increased by 3 times y
13. 15 decreased by twice a number
14. 91 more than the square of a number
15. three fourths the square of b
16. two fifths the cube of a number
17. BOOKS A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying x excellent-condition paperbacks and f fair-condition paperbacks.
18. GEOMETRY The surface area of the side of a right cylinder can be found by multiplying twice the number π by the radius times the height. If a circular cylinder has radius r and height h, write an expression that represents the surface area of its side.
1-1 PracticeVariables and Expressions
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Chapter 1 9 Glencoe Algebra 1
1. SOLAR SYSTEM It takes Earth about 365 days to orbit the Sun. It takes Uranus about 85 times as long. Write a numerical expression to describe the number of days it takes Uranus to orbit the Sun.
2. TECHNOLOGY There are 1024 bytes in a kilobyte. Write an expression that describes the number of bytes in a computer chip with n kilobytes.
3. THEATER H. Howard Hughes, Professor Emeritus of Texas Wesleyan College and his wife Erin Connor Hughes attended a record 6136 theatrical shows. Write an expression for the average number of shows they attended per year if they accumulated the record over y years.
4. TIDES The difference between high and low tides along the Maine coast in November is 19 feet on Monday and x feet on Tuesday. Write an expression to show the average rise and fall of the tide for Monday and Tuesday.
5. BLOCKS A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge.
a. Write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge.
b. The packaging team decides to take one layer of blocks off the top of this package. Write an expression representing the number of blocks in the top layer of the package.
c. The team finally decides that their favorite package arrangement is to take 2 layers of blocks off the top of a cube measuring b blocks along one edge. Write an expression representing the number of blocks left behind after the top two layers are removed.
b
b
b
1-1 Word Problem Practice Variables and Expressions
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Chapter 1 10 Glencoe Algebra 1
Toothpick TrianglesVariable expressions can be used to represent patterns and help solve problems. Consider the problem of creating triangles out of toothpicks shown below.
Figure 3Figure 2Figure 1
1. How many toothpicks does it take to create each figure?
2. How many toothpicks does it take to make up the perimeter of each image?
3. Sketch the next three figures in the pattern.
4. Continue the pattern to complete the table.
5. Let the variable n represent the figure number. Write an expression that can be used to find the number of toothpicks needed to create figure n.
6. Let the variable n represent the figure number. Write an expression that can be used to find the number of toothpicks in the perimeter of figure n.
1-1 Enrichment
Image Number 1 2 3 4 5 6 7 8 9 10
Number of toothpicks 3 5 7
Number of toothpicks in
Perimeter3 4 5
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Chapter 1 11 Glencoe Algebra 1
Evaluate Numerical Expressions Numerical expressions often contain more than one operation. To evaluate them, use the rules for order of operations shown below.
Order ofOperations
Step 1 Evaluate expressions inside grouping symbols.
Step 2 Evaluate all powers.
Step 3 Do all multiplication and/or division from left to right.
Step 4 Do all addition and/or subtraction from left to right.
Evaluate each expression.
a. 34
34 = 3 ․ 3 ․ 3 ․ 3 Use 3 as a factor 4 times.
= 81 Multiply.
b. 63
63 = 6 ․ 6 ․ 6 Use 6 as a factor 3 times.
= 216 Multiply.
Evaluate each expression.
a. 3[2 + (12 ÷ 3)2]3[2 + (12 ÷ 3)2] = 3(2 + 42) Divide 12 by 3.
= 3(2 + 16) Find 4 squared.
= 3(18) Add 2 and 16.
= 54 Multiply 3 and 18.
b. 3 + 23
−
42 · 3
3 + 23
− 42
· 3 =
3 + 8 − 42
· 3 Evaluate power in numerator.
= 11 − 42
· 3 Add 3 and 8 in the numerator.
= 11 − 16 · 3
Evaluate power in denominator.
= 11 − 48
Multiply.
ExercisesEvaluate each expression.
1. 52 2. 33 3. 104
4. 122 5. 83 6. 28
7. (8 - 4) ․ 2 8. (12 + 4) ․ 6 9. 10 + 8 ․ 1
10. 15 - 12 ÷ 4 11. 12(20 - 17) - 3 ․ 6 12. 24 ÷ 3 ․ 2 - 32
13. 32 ÷ 3 + 22 ․ 7 - 20 ÷ 5 14. 4 + 32
− 12 + 1
15. 250 ÷ [5(3 ․ 7 + 4)]
16. 2 · 42 - 8 ÷ 2 − (5 + 2) · 2
17. 4(52) - 4 · 3 −
4(4 · 5 + 2) 18. 52
- 3 − 20(3) + 2(3)
1-2 Study Guide and InterventionOrder of Operations
Example 1 Example 2
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Chapter 1 12 Glencoe Algebra 1
Evaluate Algebraic Expressions Algebraic expressions may contain more than one operation. Algebraic expressions can be evaluated if the values of the variables are known. First, replace the variables with their values. Then use the order of operations to calculate the value of the resulting numerical expression.
Evaluate x3 + 5(y - 3) if x = 2 and y = 12.x3 + 5(y - 3) = 23 + 5(12 - 3) Replace x with 2 and y with 12.
= 8 + 5(12 - 3) Evaluate 23.
= 8 + 5(9) Subtract 3 from 12.
= 8 + 45 Multiply 5 and 9.
= 53 Add 8 and 45.
The solution is 53.
ExercisesEvaluate each expression if x = 2, y = 3, z = 4, a = 4 −
5 , and b = 3 −
5 .
1. x + 7 2. 3x - 5 3. x + y2
4. x3 + y + z2 5. 6a + 8b 6. 23 - (a + b)
7. y2
− x2
8. 2xyz + 5 9. x(2y + 3z)
10. (10x)2 + 100a 11. 3xy - 4
− 7x
12. a2 + 2b
13. z2
- y2
− x2
14. 6xz + 5xy 15. (z - y) 2
− x
16. 25ab + y
− xz 17. 5 a 2 b − y 18. (z ÷ x)2 + ax
19. ( x − z ) 2 + (
y − z )
2 20. x + z
− y + 2z
21. ( z ÷ x − y ) + (
y ÷ x − z )
1-2 Study Guide and Intervention (continued)
Order of Operations
Example
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Chapter 1 13 Glencoe Algebra 1
Evaluate each expression.
1. 82 2. 34
3. 53 4. 33
5. (5 + 4) � 7 6. (9 - 2) � 3
7. 4 + 6 � 3 8. 12 + 2 � 2
9. (3 + 5) � 5 + 1 10. 9 + 4(3 + 1)
11. 30 - 5 � 4 + 2 12. 10 + 2 � 6 + 4
13. 14 ÷ 7 � 5 - 32 14. 4[30 - (10 - 2) � 3]
15. 5 + [30 - (6 - 1)2] 16. 2[12 + (5 - 2)2]
Evaluate each expression if x = 6, y = 8, and z = 3.
17. xy + z 18. yz - x
19. 2x + 3y - z 20. 2(x + z) - y
21. 5z + ( y - x) 22. 5x - ( y + 2z)
23. x2 + y2 - 10z 24. z3 + ( y2 - 4x)
25. y + xz
− 2 26.
3y + x2
− z
1-2 Skills PracticeOrder of Operations
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Chapter 1 14 Glencoe Algebra 1
Evaluate each expression.
1. 112 2. 83 3. 54
4. (15 - 5) ․ 2 5. 9 ․ (3 + 4) 6. 5 + 7 ․ 4
7. 4(3 + 5) - 5 ․ 4 8. 22 ÷ 11 ․ 9 - 32 9. 62 + 3 ․ 7 - 9
10. 3[10 - (27 ÷ 9)] 11. 2[52 + (36 ÷ 6)] 12. 162 ÷ [6(7 - 4)2]
13. 52 ․ 4 - 5 ․ 42
− 5(4)
14. (2 ․ 5)2 + 4 −
32 - 5
15. 7 + 32
− 42
· 2
Evaluate each expression if a = 12, b = 9, and c = 4.
16. a2 + b - c2 17. b2 + 2a - c2
18. 2c(a + b) 19. 4a + 2b - c2
20. (a2 ÷ 4b) + c 21. c2 · (2b - a)
22. bc2 + a − c 23. 2c3 - ab − 4
24. 2(a - b)2 - 5c 25. b
2 - 2c2 −
a + c - b
26. CAR RENTAL Ann Carlyle is planning a business trip for which she needs to rent a car. The car rental company charges $36 per day plus $0.50 per mile over 100 miles. Suppose Ms. Carlyle rents the car for 5 days and drives 180 miles.
a. Write an expression for how much it will cost Ms. Carlyle to rent the car.
b. Evaluate the expression to determine how much Ms. Carlyle must pay the car rental company.
27. GEOMETRY The length of a rectangle is 3n + 2 and its width is n - 1. The perimeter of the rectangle is twice the sum of its length and its width.
a. Write an expression that represents the perimeter of the rectangle.
b. Find the perimeter of the rectangle when n = 4 inches.
1-2 Practice Order of Operations
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Chapter 1 15 Glencoe Algebra 1
1. SCHOOLS Jefferson High School has 100 less than 5 times as many students as Taft High School. Write and evaluate an expression to find the number of students at Jefferson High School if Taft High School has 300 students.
2. GEOGRAPHY Guadalupe Peak in Texas has an altitude that is 671 feet more than double the altitude of Mount Sunflower in Kansas. Write and evaluate an expression for the altitude of Guadalupe Peak if Mount Sunflower has an altitude of 4039 feet.
3. TRANSPORTATION The Plaid Taxi Cab Company charges $1.75 per passenger plus $3.45 per mile for trips less than 10 miles. Write and evaluate an expression to find the cost for Max to take a Plaid taxi 8 miles to the airport.
4. GEOMETRY The area of a circle is related to the radius of the circle such that the product of the square of the radius and a number π gives the area. Write and evaluate an expression for the area of a circular pizza below. Approximate π as 3.14.
7 in.
5. BIOLOGY Lavania is studying the growth of a population of fruit flies in her laboratory. She notices that the number of fruit flies in her experiment is five times as large after any six-day period. She observes 20 fruit flies on October 1. Write and evaluate an expression to predict the population of fruit flies Lavania will observe on October 31.
6. CONSUMER SPENDING During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 4 days at a rate of $36 per day. There was an additional charge of $0.20 per mile after the first 200 miles driven.
a. Write an algebraic expression to represent the amount Devon paid for additional mileage only.
b. Write an algebraic expression to represent the number of miles over 200 miles that Devon drove the rented car.
c. How many miles did Devon drive overall if he paid a total of $174 for the car rental?
1-2 Word Problem PracticeOrder of Operations
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Chapter 1 16 Glencoe Algebra 1
The Four Digits ProblemOne well-known mathematics problem is to write expressions for consecutive numbers beginning with 1. On this page, you will use the digits 1, 2, 3, and 4. Each digit is used only once. You may use addition, subtraction, multiplication (not division), exponents, and parentheses in any way you wish. Also, you can use two digits to make one number, such as 12 or 34.
Express each number as a combination of the digits 1, 2, 3, and 4.
1 = (3 × 1) - (4 - 2) 18 = 35 = 2(4+1) + 3
2 = 19 = 3(2 + 4) + 1 36 =
3 = 20 = 37 =
4 = 21 = 38 =
5 = 22 = 39 =
6 = 23 = 31 - (4 × 2) 40 =
7 = 24 = 41 =
8 = 25 = 42 =
9 = 26 = 43 = 42 + 13
10 = 27 = 44 =
11 = 28 = 45 =
12 = 29 = 46 =
13 = 30 = 47 =
14 = 31 = 48 =
15 = 32 = 49 =
16 = 33 = 50 =
17 = 34 =
Does a calculator help in solving these types of puzzles? Give reasons for your opinion.
1-2 Enrichment
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Chapter 1 17 Glencoe Algebra 1
When evaluating algebraic expressions, it is sometimes helpful to use the store keyon the calculator, especially to check solutions, evaluate several expressions for the same values of variables, or evaluate the same expression for multiple values of the variables.
Evaluate a2 - 4a + 6 if a = 8.
First, open a new Calculator page on the TI-Nspire.
Then, delete any instances of stored variables by entering CLEARAZ.
Store 8 as the value for a.
Finally enter the expression, including the variables, to evaluate.
The answer is 38.
Exercises
Evaluate each expression if a = 4, b = 6, x = 8, and y = 12. Express answers as integers or fractions.
1. bx - ay ÷ b 2. a[ x + (y ÷ a)2] 3. a3 - (y - b)2 + x2
4. b + a2
− x2
- b2 5. 2a(x - b)
− xy - 9b 6. b3 - [3(a + b2
) + 5b] −−
y ÷ a(x - 1)
Evaluate xy - 4y
− 5x
if x = 4 and y = 12.
Enter 4 as the value for x and 12 as the value for y.
Evaluate the expression. The TI-Nspire will display the answer as a fraction.
The answer is 228 − 5 .
1-2 TI-Nspire® ActivityUsing the Store Key
Example 1
Example 2
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Chapter 1 18 Glencoe Algebra 1
Evaluate 24 � 1 - 8 + 5(9 ÷ 3 - 3). Name the property used in each step.24 ․ 1 - 8 + 5(9 ÷ 3 - 3) = 24 ․ 1 - 8 + 5(3 - 3) Substitution; 9 ÷ 3 = 3
= 24 ․ 1 - 8 + 5(0) Substitution; 3 - 3 = 0
= 24 - 8 + 5(0) Multiplicative Identity; 24 ․ 1 = 24
= 24 - 8 + 0 Multiplicative Property of Zero; 5(0) = 0
= 16 + 0 Substitution; 24 - 8 = 16
= 16 Additive Identity; 16 + 0 = 16
ExercisesEvaluate each expression. Name the property used in each step.
1. 2 [ 1 − 4 + ( 1 −
2 )
2 ] 2. 15 ․ 1 - 9 + 2(15 ÷ 3 - 5)
3. 2(3 ․ 5 ․ 1 - 14) - 4 ․ 1 − 4 4. 18 ․ 1 - 3 ․ 2 + 2(6 ÷ 3 - 2)
1-3 Study Guide and InterventionProperties of Numbers
Identity and Equality Properties The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions.
Additive Identity For any number a, a + 0 = a.
Additive Inverse For any number a, a + (-a) = 0.
Multiplicative Identity For any number a, a . 1 = a.
Multiplicative Property of 0 For any number a, a . 0 = 0.
Multiplicative Inverse
Property
For every number a − b , where a, b ≠ 0, there is exactly one number b − a such that
a − b . b −
a = 1.
Refl exive Property For any number a, a = a.
Symmetric Property For any numbers a and b, if a = b, then b = a.
Transitive Property For any numbers a, b, and c, if a = b and b = c, then a = c.
Substitution Property If a = b, then a may be replaced by b in any expression.
Example
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Chapter 1 19 Glencoe Algebra 1
Study Guide and Intervention (continued)
Properties of Numbers
1-3
Commutative and Associative Properties The Commutative and Associative Properties can be used to simplify expressions. The Commutative Properties state that the order in which you add or multiply numbers does not change their sum or product. The Associative Properties state that the way you group three or more numbers when adding or multiplying does not change their sum or product.
Evaluate 6 � 2 � 3 � 5 using properties of numbers. Name the property used in each step.6 ․ 2 ․ 3 ․ 5 = 6 ․ 3 ․ 2 ․ 5 Commutative Property
= (6 ․ 3)(2 ․ 5) Associative Property
= 18 ․ 10 Multiply.
= 180 Multiply.
The product is 180.
Evaluate 8.2 + 2.5 + 2.5 + 1.8 using properties of numbers. Name the property used in each step.8.2 + 2.5 + 2.5 + 1.8
= 8.2 + 1.8 + 2.5 + 2.5 Commutative Prop.
= (8.2 + 1.8) + (2.5 + 2.5) Associative Prop.
= 10 + 5 Add.
= 15 Add.
The sum is 15.
ExercisesEvaluate each expression using properties of numbers. Name the property used in each step.
1. 12 + 10 + 8 + 5 2. 16 + 8 + 22 + 12 3. 10 ․ 7 ․ 2.5
4. 4 ․ 8 ․ 5 ․ 3 5. 12 + 20 + 10 + 5 6. 26 + 8 + 4 + 22
7. 3 1 − 2 + 4 + 2 1 −
2 + 3 8. 3 −
4 ․ 12 ․ 4 ․ 2 9. 3.5 + 2.4 + 3.6 + 4.2
10. 4 1 − 2 + 5 + 1 −
2 + 3 11. 0.5 ․ 2.8 ․ 4 12. 2.5 + 2.4 + 2.5 + 3.6
13. 4 − 5 ․ 18 ․ 25 ․
2 − 9 14. 32 ․ 1 −
5 ․ 1 −
2 ․ 10 15. 1 −
4 ․ 7 ․ 16 ․ 1 −
7
16. 3.5 + 8 + 2.5 + 2 17. 18 ․ 8 ․ 1 − 2 ․ 1 −
9 18. 3 −
4 ․ 10 ․ 16 ․ 1 −
2
Example 1 Example 2
Commutative Properties For any numbers a and b, a + b = b + a and a � b = b � a.
Associative Properties For any numbers a, b, and c, (a + b) + c = a + (b + c ) and (ab)c = a(bc).
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Chapter 1 20 Glencoe Algebra 1
Evaluate each expression. Name the property used in each step.
1. 7(16 ÷ 42) 2. 2[5 - (15 ÷ 3)]
3. 4 - 3[7 - (2 ․ 3)] 4. 4[8 - (4 ․ 2)] + 1
5. 6 + 9[10 - 2(2 + 3)] 6. 2(6 ÷ 3 - 1) ․ 1 − 2
7. 16 + 8 + 14 + 12 8. 36 + 23 + 14 + 7
9. 5 ․ 3 ․ 4 ․ 3 10. 2 ․ 4 ․ 5 ․ 3
1-3 Skills PracticeProperties of Numbers
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Chapter 1 21 Glencoe Algebra 1
Evaluate each expression. Name the property used in each step.
1. 2 + 6(9 - 32) - 2 2. 5(14 - 39 ÷ 3) + 4 ․ 1 − 4
Evaluate each expression using properties of numbers. Name the property used in each step.
3. 13 + 23 + 12 + 7 4. 6 ․ 0.7 ․ 5
5. SALES Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets and sold each of them for $9.00.
a. Write an expression that represents the profit Althea made.
b. Evaluate the expression. Name the property used in each step.
6. SCHOOL SUPPLIES Kristen purchased two binders that cost $1.25 each, two binders that cost $4.75 each, two packages of paper that cost $1.50 per package, four blue pens that cost $1.15 each, and four pencils that cost $0.35 each.
a. Write an expression to represent the total cost of supplies before tax.
b. What was the total cost of supplies before tax?
1-3 PracticeProperties of Numbers
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1. EXERCISE Annika goes on a walk every day in order to get the exercise her doctor recommends. If she walks at a
rate of 3 miles per hour for 1−3
of an hour, then she will have walked 3 × 1
−3
miles. Evaluate the expression and name the
property used.
2. SCHOOL SUPPLIES At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Use mental math and the Associative Property of Addition to find the total cost if one of each item is purchased.
3. MENTAL MATH The triangular banner has a base of 9 centimeters and a height of 6 centimeters. Using the formula for area of a triangle, the banner’s area can
be expressed as 1 − 2 × 9 × 6. Gabrielle
finds it easier to write and evaluate
( 1 − 2 × 6) × 9 to find the area. Is
Gabrielle’s expression equivalent to the area formula? Explain.
b
h
4. ANATOMY The human body has 60 bones in the arms and hands, 84 bones in the upper body and head, and 62 bones in the legs and feet. Use the Associative Property to write and evaluate an expression that represents the total number of bones in the human body.
5. TOLL ROADS Some toll highways assess tolls based on where a car entered and exited. The table below shows the highway tolls for a car entering and exiting at a variety of exits. Assume that the toll for the reverse direction is the same.
Entered Exited Toll
Exit 5 Exit 8 $0.50
Exit 8 Exit 10 $0.25
Exit 10 Exit 15 $1.00
Exit 15 Exit 18 $0.50
Exit 18 Exit 22 $0.75
a. Running an errand, Julio travels from Exit 8 to Exit 5. What property would you use to determine the toll?
b. Gordon travels from home to work and back each day. He lives at Exit 15 on the toll road and works at Exit 22. Write and evaluate an expression to find his daily toll cost. What property or properties did you use?
Word Problem PracticeProperties of Numbers
1-3
Chapter 1 22 Glencoe Algebra 1
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Chapter 1 23 Glencoe Algebra 1
Properties of Operations
Let’s make up a new operation and denote it by �, so that a � b means ba.
2 � 3 = 32 = 9(1 � 2) � 3 = 21 � 3 = 32 = 9
1. What number is represented by 2 � 3?
2. What number is represented by 3 � 2?
3. Does the operation � appear to be commutative?
4. What number is represented by (2 � 1) � 3?
5. What number is represented by 2 � (1 � 3)?
6. Does the operation � appear to be associative?
Let’s make up another operation and denote it by ⊕, so that
a ⊕ b = (a + 1)(b + 1).
3 ⊕ 2 = (3 + 1)(2 + 1) = 4 ․ 3 = 12(1 ⊕ 2) ⊕ 3 = (2 ․ 3) ⊕ 3 = 6 ⊕ 3 = 7 ․ 4 = 28
7. What number is represented by 2 ⊕ 3?
8. What number is represented by 3 ⊕ 2?
9. Does the operation ⊕ appear to be commutative?
10. What number is represented by (2 ⊕ 3) ⊕ 4?
11. What number is represented by 2 ⊕ (3 ⊕ 4)?
12. Does the operation ⊕ appear to be associative?
13. What number is represented by 1 � (3 ⊕ 2)?
14. What number is represented by (1 � 3) ⊕ (1 � 2)?
15. Does the operation � appear to be distributive over the operation ⊕?
16. Let’s explore these operations a little further. What number is represented by 3 � (4 ⊕ 2)?
17. What number is represented by (3 � 4) ⊕ (3 � 2)?
18. Is the operation � actually distributive over the operation ⊕?
1-3 Enrichment
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Chapter 1 24 Glencoe Algebra 1
Evaluate Expressions The Distributive Property can be used to help evaluate expressions.
Distributive PropertyFor any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + ca and
a(b - c) = ab - ac and (b - c)a = ba - ca.
Use the Distributive Property to rewrite 6(8 + 10). Then evaluate.
6(8 + 10) = 6 ․ 8 + 6 ․ 10 Distributive Property
= 48 + 60 Multiply.
= 108 Add.
Use the Distributive Property to rewrite -2(3x2 + 5x + 1). Then simplify.
-2(3x2 + 5x + 1) = -2(3x2) + (-2)(5x) + (-2)(1) Distributive Property
= -6x2 + (-10x) + (-2) Multiply.
= -6x2 - 10x - 2 Simplify.
ExercisesUse the Distributive Property to rewrite each expression. Then evaluate.
1. 20(31) 2. 12 � 4 1 − 2 3. 5(311)
4. 5(4x - 9) 5. 3(8 - 2x) 6. 12 (6 - 1 − 2 x)
7. 12 (2 + 1 − 2 x) 8. 1 −
4 (12 - 4t) 9. 3(2x - y)
10. 2(3x + 2y - z) 11. (x - 2)y 12. 2(3a - 2b + c)
13. 1 − 4 (16x - 12y + 4z) 14. (2 - 3x + x2)3 15. -2(2x2 + 3x + 1)
1-4 Study Guide and InterventionThe Distributive Property
Example 1
Example 2
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Chapter 1 25 Glencoe Algebra 1
Simplify Expressions A term is a number, a variable, or a product or quotient of numbers and variables. Like terms are terms that contain the same variables, with corresponding variables having the same powers. The Distributive Property and properties of equalities can be used to simplify expressions. An expression is in simplest form if it is replaced by an equivalent expression with no like terms or parentheses.
Simplify 4(a2 + 3ab) - ab.
4(a2 + 3ab) - ab = 4(a2 + 3ab) - 1ab Multiplicative Identity
= 4a2 + 12ab - 1ab Distributive Property
= 4a2 + (12 - 1)ab Distributive Property
= 4a2 + 11ab Substitution
ExercisesSimplify each expression. If not possible, write simplified.
1. 12a - a 2. 3x + 6x 3. 3x - 1
4. 20a + 12a - 8 5. 3x2 + 2x2 6. -6x + 3x2 + 10x2
7. 2p + 1 − 2 q 8. 10xy - 4(xy + xy) 9. 21a + 18a + 31b - 3b
10. 4x + 1 − 4 (16x - 20y) 11. 2 - 1 - 6x + x2 12. 4x2 + 3x2 + 2x
Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.
13. six times the difference of 2a and b, increased by 4b
14. two times the sum of x squared and y squared, increased by three times the sum of x squared and y squared
1-4 Study Guide and Intervention (continued)
The Distributive Property
Example
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Chapter 1 26 Glencoe Algebra 1
Use the Distributive Property to rewrite each expression. Then evaluate.
1. 4(3 + 5) 2. 2(6 + 10)
3. 5(7 - 4) 4. (6 - 2)8
5. 5 ․ 89 6. 9 ․ 99
7. 15 ․ 104 8. 15 (2 1 − 3 )
Use the Distributive Property to rewrite each expression. Then evaluate.
9. (a + 7)2 10. 7(h - 10)
11. 3(m + n) 12. 2(x - y + 1)
Simplify each expression. If not possible, write simplified.
13. 2x + 8x 14. 17g + g
15. 2x2 + 6x2 16. 7a2 - 2a2
17. 3y2 - 2y 18. 2(n + 2n)
19. 4(2b - b) 20. 3q2 + q - q2
Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.
21. The product of 9 and t squared, increased by the sum of the square of t and 2
22. 3 times the sum of r and d squared minus 2 times the sum of r and d squared
Skills PracticeThe Distributive Property
1-4
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Chapter 1 27 Glencoe Algebra 1
Use the Distributive Property to rewrite each expression. Then evaluate.
1. 9(7 + 8) 2. 7(6 - 4) 3. (4 + 6)11
4. 9 ․ 499 5. 7 ․ 110 6. 16 (4 1 − 4 )
Use the Distributive property to rewrite each expression. Then simplify.
7. (9 - p)3 8. (5y - 3)7 9. 15 ( f + 1 − 3 )
10. 16(3b - 0.25) 11. m(n + 4) 12. (c - 4)d
Simplify each expression. If not possible, write simplified.
13. w + 14w - 6w 14. 3(5 + 6h) 15. 12b2 + 9b2
16. 25t3 - 17t3 17. 3a2 + 6a + 2b2 18. 4(6p + 2q - 2p)
Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.
19. 4 times the difference of f squared and g, increased by the sum of f squared and 2g
20. 3 times the sum of x and y squared plus 5 times the difference of 2x and y
21. DINING OUT The Ross family recently dined at an Italian restaurant. Each of the four family members ordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75.
a. Write an expression that could be used to calculate the cost of the Ross’ dinner before adding tax and a tip.
b. What was the cost of dining out for the Ross family?
1-4 Practice The Distributive Property
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Chapter 1 28 Glencoe Algebra 1
1. OPERA Mr. Delong’s drama class is planning a field trip to see Mozart’s famous opera Don Giovanni. Tickets cost $39 each, and there are 23 students and 2 teachers going on the field trip. Write and evaluate an expression to find the group’s total ticket cost.
2. SALARY In a recent year, the median salary for an engineer in the United States was $55,000 and the median salary for a computer programmer was $52,000. Write and evaluate an expression to estimate the total cost for a business to employ an engineer and a programmer for 5 years.
3. COSTUMES Isabella’s ballet class is performing a spring recital for which they need butterfly costumes. Each
butterfly costume is made from 3 3 − 5 yards
of fabric. Use the Distributive Property to find the number of yards of fabric needed for 5 costumes. (Hint: A mixed number can be written as the sum of an integer and a fraction.)
4. FENCES Demonstrate the Distributive Property by writing two equivalent expressions to represent the perimeter of the fenced dog pen below.
5. MENTAL MATH During a math facts speed contest, Jamal calculated the following expression faster than anyone else in his class.
197 × 4 When classmates asked him how he was
able to answer so quickly, he told them he used the Distributive Property to think of the problem differently. Write and evaluate an expression using the Distributive Property that would help Jamal perform the calculation quickly.
6. INVESTMENTS Letisha and Noel each opened a checking account, a savings account, and a college fund. The chart below shows the amounts that they deposited into each account.
Checking Savings College
Letisha $125 $75 $50
Noel $250 $50 $50
a. If Noel used only $50 bills when he deposited the money to open his accounts, how many $50 bills did he deposit?
b. If all accounts earn 1.5% interest per year and no further deposits are made, how much interest will Letisha have earned one year after her accounts were opened?
m
nDog Pen
Word Problem Practice The Distributive Property
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Chapter 1 29 Glencoe Algebra 1
The Maya The Maya were a Native American people who lived from about 1500 B.C. to about 1500 A.D. in the region that today encompasses much of Central America and southern Mexico. Their many accomplishments include exceptional architecture, pottery, painting, and sculpture, as well as significant advances in the fields of astronomy and mathematics. The Maya developed a system of numeration that was based on the number twenty. The basic symbols of this system are shown in the table at the right. The places in a Mayan numeral are written vertically—the bottom place represents ones, the place above represents twenties, the place above that represents 20 × 20, or four hundreds, and so on. For instance, this is how to write the number 997 in Mayan numerals.
← 2 × 400 = 800
← 9 × 20 = 180
← 17 × 1 = 17 997
Evaluate each expression when v = •_____, w = • • • _______________, x = • • • • , y = � , and z = • •__________. Then write the answer in Mayan numerals. Exercise 5 is done for you.
1. z − w 2. v + w + z − x 3. xv
4. vxy 5. wx - z 6. vz + xy
7. w(v + x + z) 8. vwz 9. z(wx - x)
Tell whether each statement is true or false.
10. • • •__________ + •_____ = •_____ + • • •__________ 11. • • •__________
•_____ =
•_____
• • •__________ 12.
• • •_______________ =
• • •____________________
13. (• • • + _____) + __________ = • • • + (_____ + __________)
14. How are Exercises 10 and 11 alike? How are they different?
• •_______________
• • • •_____
• •
0 10
1 11
2 12
3 13
4 14
5 15
6 16
7 17
8 18
9 19
�
•
• •
• • •
• • • •
_____
•_____
• •_____
• • •_____
• • • •_____
__________
•__________
• •__________
• • •__________
• • • •_______________
• • • •__________
_______________
•_______________
• •_______________
• • • _______________
Enrichment1-4
• • •
�
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Chapter 1 30 Glencoe Algebra 1
Solve Equations A mathematical sentence with one or more variables is called an open sentence. Open sentences are solved by finding replacements for the variables that result in true sentences. The set of numbers from which replacements for a variable may be chosen is called the replacement set. The set of all replacements for the variable that result in true statements is called the solution set for the variable. A sentence that contains an equal sign, =, is called an equation.
Find the solution set of 3a + 12 = 39 if the replacement set is {6, 7, 8, 9, 10}.
Replace a in 3a + 12 = 39 with each value in the replacement set.3(6) + 12 � 39 → 30 ≠ 39 false
3(7) + 12 � 39 → 33 ≠ 39 false
3(8) + 12 � 39 → 36 ≠ 39 false
3(9) + 12 � 39 → 39 = 39 true
3(10) + 12 � 39 → 42 ≠ 39 false
Since a = 9 makes the equation 3a + 12 = 39 true, the solution is 9.The solution set is {9}.
Solve 2(3 + 1) −
3(7 - 4) = b.
2(3 + 1)
− 3(7 - 4)
= b Original equation
2(4) −
3(3) = b Add in the numerator; subtract in the denominator.
8 − 9 = b Simplify.
The solution is 8 − 9 .
ExercisesFind the solution of each equation if the replacement sets are x =
{
1 −
4 , 1 −
2 , 1, 2, 3
}
and y = {2, 4, 6, 8}.
1. x + 1 − 2 = 5 −
2 2. x + 8 = 11 3. y - 2 = 6
4. x2 - 1 = 8 5. y2 - 2 = 34 6. x2 + 5 = 5 1 − 16
7. 2(x + 3) = 7 8. ( y + 1)2 = 9 9. y2 + y = 20
Solve each equation.
10. a = 23 - 1 11. n = 62 - 42 12. w = 62 ․ 32
13. 1 − 4 + 5 −
8 = k 14. 18 - 3 −
2 + 3 = p 15. t = 15 - 6 −
27 - 24
16. 18.4 - 3.2 = m 17. k = 9.8 + 5.7 18. c = 3 1 − 2 + 2 1 −
4
Study Guide and InterventionEquations
1-5
Example 1 Example 2
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Chapter 1 31 Glencoe Algebra 1
Study Guide and Intervention (continued)
Equations
1-5
Solve Equations with Two Variables Some equations contain two variables. It is often useful to make a table of values in which you can use substitution to find the corresponding values of the second variable.
MUSIC DOWNLOADS Emily belongs to an Internet music service that charges $5.99 per month and $0.89 per song. Write and solve an equation to find the total amount Emily spends if she downloads 10 songs this month.
The cost of the music service is a flat rate. The variable is the number of songs she downloads. The total cost is the price of the service plus $0.89 times the number of songs.
C = 0.89n + 5.99
To find the total cost for the month, substitute 10 for n in the equation.C = 0.89n + 5.99 Original equation
= 0.89(10) + 5.99 Substitute 10 for n.
= 8.90 + 5.99 Multiply.
= 14.89 Add.
Emily spent $14.89 on music downloads in one month.
Exercises 1. AUTO REPAIR A mechanic repairs Mr. Estes’ car. The amount for parts is $48.00 and
the rate for the mechanic is $40.00 per hour. Write and solve an equation to find the total cost of repairs to Mr. Estes’ car if the mechanic works for 1.5 hours.
2. SHIPPING FEES Mr. Moore purchases an inflatable kayak weighing 30 pounds from an online company. The standard rate to ship his purchase is $2.99 plus $0.85 per pound. Write and solve an equation to find the total amount Mr. Moore will pay to have the kayak shipped to his home.
3. SOUND The speed of sound is 1088 feet per second at sea level at 32° F. Write and solve an equation to find the distance sound travels in 8 seconds under these conditions.
4. VOLLEYBALL Your town decides to build a volleyball court. If the court is approximately 40 by 70 feet and its surface is of sand, one foot deep, the court will require about 166 tons of sand. A local sand pit sells sand for $11.00 per ton with a delivery charge of $3.00 per ton. Write and solve an equation to find the total cost of the sand for this court.
Example
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Chapter 1 32 Glencoe Algebra 1
Find the solution of each equation if the replacement sets are A = {4, 5, 6, 7, 8} and B = {9, 10, 11, 12, 13}.
1. 5a - 9 = 26 2. 4a - 8 = 16
3. 7a + 21 = 56 4. 3b + 15 = 48
5. 4b - 12 = 28 6. 36 − b - 3 = 0
Find the solution of each equation using the given replacement set.
7. 1 − 2 + x = 5 −
4 ; { 1 −
2 , 3 −
4 , 1, 5 −
4 } 8. x + 2 −
3 = 13 −
9 ; { 5 −
9 , 2 −
3 , 7 −
9 }
9. 1 − 4 (x + 2) = 5 −
6 ; { 2 −
3 , 3 −
4 , 5 −
4 , 4 −
3 } 10. 0.8(x + 5) = 5.2; {1.2, 1.3, 1.4, 1.5}
Solve each equation.
11. 10.4 - 6.8 = x 12. y = 20.1 - 11.9
13. 46 - 15 − 3 + 28
= a 14. c = 6 + 18 − 31 - 25
15. 2(4) + 4 −
3(3 - 1) = b 16. 6(7 - 2)
− 3(8) + 6
= n
17. SHOPPING ONLINE Jennifer is purchasing CDs and a new CD player from an online store. She pays $10 for each CD, as well as $50 for the CD player. Write and solve an equation to find the total amount Jennifer spent if she buys 4 CDs and a CD player from the store.
18. TRAVEL An airplane can travel at a speed of 550 miles per hour. Write and solve an equation to find the time it will take to fly from London to Montreal, a distance of approximately 3300 miles.
Skills PracticeEquations
1-5
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Chapter 1 33 Glencoe Algebra 1
Find the solution of each equation if the replacement sets are a = {0, 1 − 2 , 1, 3 −
2 , 2}
and b = {3, 3.5, 4, 4.5, 5}.
1. a + 1 − 2 = 1 2. 4b - 8 = 6 3. 6a + 18 = 27
4. 7b - 8 = 16.5 5. 120 - 28a = 78 6. 28 − b + 9 = 16
Solve each equation.
7. x = 18.3 - 4.8 8. w = 20.2 - 8.95 9. 37 - 9 − 18 - 11
= d
10. 97 - 25 − 41 - 23
= k 11. y = 4(22 - 4)
− 3(6) + 6
12. 5( 2 2 ) + 4(3)
− 4( 2 3 - 4)
= p
13. TEACHING A teacher has 15 weeks in which to teach six chapters. Write and then solve an equation that represents the number of lessons the teacher must teach per week if there is an average of 8.5 lessons per chapter.
14. CELL PHONES Gabriel pays $40 a month for basic cell phone service. In addition, Gabriel can send text messages for $0.20 each. Write and solve an equation to find the total amount Gabriel spent this month if he sends 40 text messages.
1-5 Practice Equations
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Chapter 1 34 Glencoe Algebra 1
1. TIME There are 6 time zones in the United States. The eastern part of the U.S., including New York City, is in the Eastern Time Zone. The central part of the U.S., including Dallas, is in the Central Time Zone, which is one hour behind Eastern Time. San Diego is in the Pacific Time Zone, which is 3 hours behind Eastern Time. Write and solve an equation to determine what time it is in California if it is noon in New York.
2. FOOD Part of the Nutrition Facts label from a box of macaroni and cheese is shown below.
Nutrition FactsServing Size 1 cup (228g)Servings Per Container 2
Amount Per Serving
Calories 250 Calories from Fat 110
Total Fat 12g
Saturated Fat 3g
Trans Fat 3g
Cholesterol 30mg
% Daily Value *
18 %
15 %
10 %
Write and solve an equation to determine how many servings of this item Alisa can eat each day if she wants to consume exactly 45 grams of cholesterol.
3. CRAFTS You need 30 yards of yarn to crochet a small scarf. Cheryl bought a 100-yard ball of yarn and has already used 10 yards. Write and solve an equation to find how many scarves she can crochet if she plans on using up the entire ball.
4. POOLS There are approximately 202 gallons per cubic yard of water. Write and solve an equation for the number of gallons of water that fill a pool with a volume of 1161 cubic feet. (Hint: There are 27 cubic feet per cubic yard.)
5. VEHICLES Recently developed hybrid cars contain both an electric and a gasoline engine. Hybrid car batteries store extra energy, such as the energy produced by braking. Since the car can use this stored energy to power the car, the hybrid uses less gasoline per mile than cars powered only by gasoline. Suppose a new hybrid car is rated to drive 45 miles per gallon of gasoline.
a. It costs $40 to fill the gasoline tank with gas that costs $3.00 per gallon. Write and solve an equation to find the distance the hybrid car can go using one tank of gas.
b. Write and solve an equation to find the cost of gasoline per mile for this hybrid car. Round to the nearest cent.
1-5 Word Problem PracticeEquations
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Chapter 1 35 Glencoe Algebra 1
Solution Sets
Consider the following open sentence.
It is the name of a month between March and July.
You know that a replacement for the variable It must be found in order to determine if the sentence is true or false. If It is replaced by either April, May, or June, the sentence is true.The set {April, May, June} is called the solution set of the open sentence given above. This set includes all replacements for the variable that make the sentence true.
Write the solution set for each open sentence.
1. It is the name of a state beginning with the letter A.
2. It is a primary color.
3. Its capital is Harrisburg.
4. It is a New England state.
5. x + 4 = 10
6. It is the name of a month that contains the letter r.
7. She was the wife of a U.S. President who served in the years 2000-2010.
8. It is an even number between 1 and 13.
9. 31 = 72 - k
10. It is the square of 2, 3, or 4.
Write an open sentence for each solution set.
11. {A, E, I, O, U}
12. {1, 3, 5, 7, 9}
13. {June, July, August}
14. {Atlantic, Pacific, Indian, Arctic}
Enrichment1-5
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A spreadsheet is a tool for working with and analyzing numerical data. The data is entered into a table in which each row is numbered and each column is labeled by a letter. You can use a spreadsheet to find solutions of open sentences.
Exercises
Use a spreadsheet to find the solution of each equation using the given replacement set.
1. x + 7.5 = 18.3; {8.8, 9.8, 10.8, 11.8} 2. 6(x + 2) = 18; {0, 1, 2, 3, 4, 5}
3. 4x + 1 = 17; {0, 1, 2, 3, 4, 5} 4. 4.9 - x = 2.2; {2.6, 2.7, 2.8, 2.9, 3.0}
5. 2.6x = 16.9; {6.1, 6.3, 6.5, 6.7, 6.9} 6. 12x - 8 = 22; {2.1, 2.2, 2.3, 2.4, 2.5, 2.6}
Use a spreadsheet to find the solution for 4(x - 3) = 32 if the replacement set is {7, 8, 9, 10, 11, 12}.
You can solve the open sentence by replacing x with each value in the replacement set.
Step 1 Use the first column of the spreadsheet for the replacement set. Enter the numbers using the formula bar. Click on a cell of the spreadsheet, type the number and press ENTER.
Step 2 The second column contains the formula for the left side of the open sentence. To enter a formula, enter an equals sign followed by the formula. Use the name of the cell containing each replacement value to evaluate the formula for that value. For example, in cell B2, the formula contains A2 in place of x.
The solution is the value of x for which the formula in column B returns 32. The solution is 11.
A 1
4 5 6 7 8
2 3
B C 4(x - 3) =4*(A2-3) =4*(A3-3) =4*(A4-3) =4*(A5-3) =4*(A6-3) =4*(A7-3)
x 7 8 9
10 11 12
Sheet 1 Sheet 2 Sheet 3
A 1
4 5 6 7 8
2 3
B C 4(x - 3) x
7 8 9
10 11 12
16 20 24 28 32 36
Sheet 1 Sheet 2 Sheet 3
1-5 Spreadsheet ActivitySolving Open Sentences
Example
Chapter 1 36 Glencoe Algebra 1
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Chapter 1 37 Glencoe Algebra 1
Study Guide and InterventionRelations
1-6
Represent a Relation A relation is a set of ordered pairs. A relation can be represented by a set of ordered pairs, a table, a graph, or a mapping. A mapping illustrates how each element of the domain is paired with an element in the range. The set of first numbers of the ordered pairs is the domain. The set of second numbers of the ordered pairs is the range of the relation.
a. Express the relation {(1, 1), (0, 2), (3, -2)} as a table, a graph, and a mapping.
x y
1 1
0 2
3 -2
x
y
O
X Y
103
12
-2
b. Determine the domain and the range of the relation. The domain for this relation is {0, 1, 3}. The range for this relation is {-2, 1, 2}.
Exercises 1A. Express the relation
{(-2, -1), (3, 3), (4, 3)} asa table, a graph, and a
mapping.
1B. Determine the domain and the range of the relation.
Example
x
y
O
X Yx y
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Chapter 1 38 Glencoe Algebra 1
Graphs of a Relation The value of the variable in a relation that is subject to choice is called the independent variable. The variable with a value that is dependent on the value of the independent variable is called the dependent variable. These relations can be graphed without a scale on either axis, and interpreted by analyzing the shape.
The graph below represents the height of a football after it is kicked downfield. Identify the independent and the dependent variable for the relation. Then describe what happens in the graph.
The independent variable is time, and the dependent variable is height. The football starts on the ground when it is kicked. It gains altitude until it reaches a maximum height, then it loses altitude until it falls to the ground.
Time
Height
The graph below represents the price of stock over time. Identify the independent and dependent variable for the relation. Then describe what happens in the graph.
The independent variable is time and the dependent variable is price. The price increases steadily, then it falls, then increases, then falls again.
Time
Price
ExercisesIdentify the independent and dependent variables for each relation. Then describe what is happening in each graph.
1. The graph represents the speed of a car as it travels to the grocery store.
2. The graph represents the balance of a savings account over time.
3. The graph represents the height of a baseball after it is hit.
Time
Height
Time
AccountBalance(dollars)
Time
Speed
Study Guide and Intervention (continued)
Relations
1-6
Example 1 Example 2
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Chapter 1 39 Glencoe Algebra 1
Skills PracticeRelations
1-6
Express each relation as a table, a graph, and a mapping. Then determine the domain and range.
1. {(-1, -1), (1, 1), (2, 1), (3, 2)}
x
y
O
2. {(0, 4), (-4, -4), (-2, 3), (4, 0)}
3. {(3, -2), (1, 0), (-2, 4), (3, 1)}
x
y
O
Identify the independent and dependent variables for each relation.
4. The more hours Maribel works at her job, the larger her paycheck becomes.
5. Increasing the price of an item decreases the amount of people willing to buy it.
x
y
O
x y
x y
x y
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Chapter 1 40 Glencoe Algebra 1
1-6 Practice Relations
1. Express {(4, 3), (-1, 4), (3, -2), (-2, 1)} as a table, a graph, and a mapping. Then determine the domain and range.
x
y
O
Describe what is happening in each graph.
2. The graph below represents the height of a 3. The graph below represents a tsunami as it travels across an ocean. student taking an exam.
Express the relation shown in each table, mapping, or graph as a set of ordered pairs.
4. X Y
0 9
-8 3
2 -6
1 4
5. X Y
5-5
37
9-6
48
6.
x
y
O
7. BASEBALL The graph shows the number of home runs hit by Andruw Jones of the Atlanta Braves. Express the relation as a set of ordered pairs. Then describe the domain and range.
Time
Number ofQuestionsAnswered
Time
Height
24
32
28
36
40
44
48
52
’02 ’03 ’04 ’05 ’06 ’070
Andruw Jones’ Home Runs
Ho
me
Ru
ns
Year
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Chapter 1 41 Glencoe Algebra 1
1. HEALTH The American Heart Association recommends that your target heart rate during exercise should be between 50% and 75% of your maximum heart rate. Use the data in the table below to graph the approximate maximum heart rates for people of given ages.
Source: American Heart Association
Age
Maximum Heart Rate
200 25 35 40
y
x30
Hea
rt R
ate
180
190
170
160
200
2. NATURE Maple syrup is made by collecting sap from sugar maple trees and boiling it down to remove excess water. The graph shows the number of gallons of tree sap required to make different quantities of maple syrup. Express the relation as a set of ordered pairs.
Gallons of Syrup10 2 4 5
y
x3 7 8 96
Gal
lon
s o
f Sa
p
160
200
120
80
240
280
320
Maple Sap to Syrup
Source: Vermont Maple Sugar Makers’ Association
3. BAKING Identify the graph that best represents the relationship between the number of cookies and the equivalent number of dozens.
Number of dozens
Nu
mb
er o
f co
oki
es
y
x
Graph A
Number of dozens
Nu
mb
er o
f co
oki
es
y
x
Graph B
Number of dozens
Nu
mb
er o
f co
oki
es
y
x
Graph C
4. DATA COLLECTION Margaret collected data to determine the number of books her schoolmates were bringing home each evening. She recorded her data as a set of ordered pairs. She let x be the number of textbooks brought home after school, and y be the number of students with x textbooks. The relation is shown in the mapping.
a. Express the relation as a set of ordered pairs.
b. What is the domain of the relation?
c. What is the range of the relation?
x y
811122328
012345
Age (years) 20 25 30 35 40
Maximum Heart Rate
(beats per minute)200 195 190 185 180
1-6 Word Problem PracticeRelations
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Chapter 1 42 Glencoe Algebra 1
Even and Odd FunctionsWe know that numbers can be either even or odd. It is also true that functions can be defined as even or odd. For a function to be even means that it is symmetric about the y-axis. That is, if you fold the graph along the y-axis, the two halves of the graph match exactly. For a function to be odd means that the function is symmetric about the origin. This means if you rotate the graph using the origin as the center, it will match its original position before completing a full turn.
The function y = x2 is an even function. The function y = x5 is an odd function. If you rotate the graph 180º the graph will lie on itself.
y
xO
1. The table below shows the ordered pairs of an even function. Complete the table. Plot the points and sketch the graph.
2. The table below shows the ordered pairs of an odd function. Complete the table. Plot the points and sketch the graph.
y
xO
y
xO2 4 6 8 10 12-4-6-8-10-12 -2
456
321
-1-2-3-4-5-6
y
xO
2 4 6 8 10-4-6-8-10 -2
810
642
-2-4-6-8
-10
Enrichment
x -12 -5 -1 1 5 12
y 6 3 1
x -10 -4 -2 2 4 10
y 8 4 2
1-6
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Chapter 1 43 Glencoe Algebra 1
Identify Functions Relations in which each element of the domain is paired with exactly one element of the range are called functions.
Determine whether the relation {(6, -3), (4, 1), (7, -2), (-3, 1)} is a function. Explain.
Since each element of the domain is paired with exactly one element of the range, this relation is a function.
Determine whether 3x - y = 6 is a function.
Since the equation is in the form Ax + By = C, the graph of the equation will be a line, as shown at the right.
If you draw a vertical line through each value of x, the vertical line passes through just one point of the graph. Thus, the line represents a function.
ExercisesDetermine whether each relation is a function.
1. 2. 3.
4. 5. 6.
7. {(4, 2), (2, 3), (6, 1)} 8. {(-3, -3), (-3, 4), (-2, 4)} 9. {(-1, 0), (1, 0)}
10. -2x + 4y = 0 11. x2 + y2 = 8 12. x = -4
x
y
Ox
y
Ox
y
O
X Y
4567
-1012
x
y
Ox
y
O
x
y
O
1-7 Study Guide and InterventionFunctions
Example 1 Example 2
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Chapter 1 44 Glencoe Algebra 1
Study Guide and Intervention (continued)
Functions
1-7
Find Function Values Equations that are functions can be written in a form called function notation. For example, y = 2x -1 can be written as f(x) = 2x - 1. In the function, x represents the elements of the domain, and f(x) represents the elements of the range. Suppose you want to find the value in the range that corresponds to the element 2 in the domain. This is written f(2) and is read “f of 2.” The value of f(2) is found by substituting 2 for x in the equation.
If f(x) = 3x - 4, find each value.
a. f(3) f (3) = 3(3) - 4 Replace x with 3.
= 9 - 4 Multiply.
= 5 Simplify.
b. f(-2) f (-2) = 3(-2) - 4 Replace x with -2.
= -6 - 4 Multiply.
= -10 Simplify.
ExercisesIf f(x) = 2x - 4 and g(x) = x2 - 4x, find each value.
1. f (4) 2. g(2) 3. f (-5)
4. g(-3) 5. f (0) 6. g(0)
7. f (3) - 1 8. f ( 1 − 4 ) 9. g ( 1 −
4 )
10. f (a2) 11. f (k + 1) 12. g(2n)
13. f (3x) 14. f (2) + 3 15. g(-4)
Example
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Chapter 1 45 Glencoe Algebra 1
1-7 Skills PracticeFunctions
Determine whether each relation is a function.
1. 2. 3.
4. x y
4 -5
-1 -10
0 -9
1 -7
9 1
5. x y
2 7
5 -3
3 5
-4 -2
5 2
6. x y
3 7
-1 1
1 0
3 5
7 3
7. {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)} 8. {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)}
9. y = 2x - 5 10. y = 11
11. 12. 13.
If f(x) = 3x + 2 and g(x) = x2 - x, find each value.
14. f(4) 15. f(8)
16. f(-2) 17. g(2)
18. g(-3) 19. g(-6)
20. f(2) + 1 21. f(1) - 1
22. g(2) - 2 23. g(-1) + 4
24. f(x + 1) 25. g(3b)
x
y
Ox
y
Ox
y
O
X Y
467
2-1
35
X Y
41
-2
520
-3
X Y
41
-3-5
-6-2
13
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Chapter 1 46 Glencoe Algebra 1
1-7 PracticeFunctions
Determine whether each relation is a function.
1. 2. X Y
1 -5
-4 3
7 6
1 -2
3.
4. {(1, 4), (2, -2), (3, -6), (-6, 3), (-3, 6)} 5. {(6, -4), (2, -4), (-4, 2), (4, 6), (2, 6)}
6. x = -2 7. y = 2
If f(x) = 2x - 6 and g(x) = x - 2x2, find each value.
8. f(2) 9. f (- 1 − 2 ) 10. g(-1)
11. g (- 1 − 3 ) 12. f(7) - 9 13. g(-3) + 13
14. f(h + 9) 15. g(3y) 16. 2[g(b) + 1]
17. WAGES Martin earns $7.50 per hour proofreading ads at a local newspaper. His weekly wage w can be described by the equation w = 7.5h, where h is the number of hours worked.
a. Write the equation in function notation.
b. Find f(15), f(20), and f(25).
18. ELECTRICITY The table shows the relationship between resistance R and current I in a circuit.
Resistance (ohms) 120 80 48 6 4
Current (amperes) 0.1 0.15 0.25 2 3
a. Is the relationship a function? Explain.
b. If the relation can be represented by the equation IR = 12, rewrite the equation in function notation so that the resistance R is a function of the current I.
c. What is the resistance in a circuit when the current is 0.5 ampere?
x
y
O
X Y
03
-2
-3-2
15
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Chapter 1 47 Glencoe Algebra 1
1. TRANSPORTATION The cost of riding in a cab is $3.00 plus $0.75 per mile. The equation that represents this relation is y = 0.75x + 3, where x is the number of miles traveled and y is the cost of the trip. Look at the graph of the equation and determine whether the relation is a function.
Distance (miles)210 43
y
x5 6 7 8 9 10
Co
st (
$)
6
8
4
2
10
16
14
12
2. TEXT MESSAGING Many cell phones have a text messaging option in addition to regular cell phone service. The function for the monthly cost of text messaging service from Noline Wireless Company is f (x) = 0.10x + 2, where x is the number of text messages that are sent. Find f (10) and f (30), the cost of 10 text messages in a month and the cost of 30 text messages in a month.
3. GEOMETRY The area for any square is given by the function y = x2, where x is the length of a side of the square and y is the area of the square. Write the equation in function notation and find the area of a square with a side length of 3.5 inches.
4. TRAVEL The cost for cars entering President George Bush Turnpike at Beltline road is given by the relation x = 0.75, where x is the dollar amount for entrance to the toll road and y is the number of passengers. Determine if this relation is a function. Explain.
5. CONSUMER CHOICES Aisha just received a $40 paycheck from her new job. She spends some of it buying music online and saves the rest in a bank account. Her savings is given by f (x) =
40 – 1.25x, where x is the number of songs she downloads at $1.25 per song.
a. Graph the function.
b. Find f(3), f(18), and f(36). What do these values represent?
c. How many songs can Aisha buy if she wants to save $30?
1-7 Word Problem Practice Functions
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Chapter 1 48 Glencoe Algebra 1
Composite Functions Three things are needed to have a function—a set called the domain, a set called the range, and a rule that matches each element in the domain with only one element in the range. Here is an example.
Rule: f(x) = 2x + 1
3
-5
f(x)
5
x
21
-3
f(x) = 2x + 1
f(1) = 2(1) + 1 = 2 + 1 = 3
f(2) = 2(2) + 1 = 4 + 1 = 5
f(-3) = 2(-3) + 1 = -6 + 1 = -5
Suppose we have three sets A, B, and C and two functions described as shown below.
Rule: f(x) = 2x + 1 Rule: g( y) = 3y - 4 A B C
f(x)
3 5
x
1
g[f(x)]
g( y) = 3y - 4
g(3) = 3(3) - 4 = 5
Let’s find a rule that will match elements of set A with elements of set C without finding any elements in set B. In other words, let’s find a rule for the composite function g[f(x)].
Since f(x) = 2x + 1, g[ f(x)] = g(2x + 1).
Since g( y) = 3y - 4, g(2x + 1) = 3(2x + 1) - 4, or 6x - 1.
Therefore, g[ f(x)] = 6x - 1.
Find a rule for the composite function g[f(x)].
1. f(x) = 3x and g( y) = 2y + 1 2. f(x) = x2 + 1 and g( y) = 4y
3. f(x) = -2x and g( y) = y2 - 3y 4. f(x) = 1 − x - 3
and g( y) = y-1
5. Is it always the case that g[ f(x)] = f[ g(x)]? Justify your answer.
Enrichment 1-7
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Chapter 1 49 Glencoe Algebra 1
1-8 Study Guide and InterventionInterpreting Graphs of Functions
Interpret Intercepts and Symmetry The intercepts of a graph are points where the graph intersects an axis. The y-coordinate of the point at which the graph intersects the y-axis is called a y-intercept. Similarly, the x-coordinate of the point at which a graph intersects the x-axis is called an x-intercept. A graph possesses line symmetry in a line if each half of the graph on either side of the line matches exactly.
ARCHITECTURE The graph shows a function that approximates the shape of the Gateway Arch, where x is the distance from the center point in feet and y is theheight in feet. Identify the function as linear or nonlinear. Then estimate and interpret the intercepts, and describe and interpret any symmetry.
Linear or Nonlinear: Since the graph is a curve and not a line, the graph is nonlinear.y-Intercept: The graph intersects the y-axis at about (0, 630), so the y-intercept of the graph is about 630. This means that the height of the arch is 630 feet at the center point.x-Intercept(s): The graph intersects the x-axis at about (-320, 0) and (320, 0). So the x-intercepts are about -320 and 320. This means that the object touches the ground to the left and right of the center point.Symmetry: The right half of the graph is the mirror image of the left half in the y-axis. In the context of the situation, the symmetry of the graph tells you that the arch is symmetric. The height of the arch at any distance to the right of the center is the same as its height that same distance to the left.
Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph and any symmetry.
1. Right Whale Population
Popu
latio
n
80
0
160
240
Generations Since 20074 8 12
y
x
2. Stock Price
Pric
e Va
riatio
n (p
oint
s)
-2
2
0
Time Since Opening Bell (h)
2 4 6
y
x
3.
y
x
Average GasolinePrice
Pric
e ($
per
gal
lon)
2
3
1
0
4
5
6
Years Since 198715105 2520 30
Example
O
y
x
y -intercept
x -intercept
Gateway Arch
Heig
ht (f
t)
0Distance (ft)
80-80-240 240
160
240
80
320
400
480
560y
x
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Chapter 1 50 Glencoe Algebra 1
Study Guide and Intervention (continued)
Interpreting Graphs of Functions
1-8
Interpret Extrema and End Behavior Interpreting a graph also involves estimating and interpreting where the function is increasing, decreasing, positive, or negative, and where the function has any extreme values, either high or low.
Example
HEALTH The outbreak of the H1N1 virus can be modeled by the function graphed at the right. Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinates of any relative extrema, and the end behavior of the graph.
Positive: for x between 0 and 42 Negative: no parts of domainThis means that the number of reported cases was always positive. This is reasonable because a negative number of cases cannot exist in the context of the situation.Increasing: for x between 0 and 42 Decreasing: no parts of domainThe number of reported cases increased each day from the first day of the outbreak. Relative Maximum: at about x = 42 Relative Minimum: at x = 0The extrema of the graph indicate that the number of reported cases peaked at about day 42.End Behavior: As x increases, y appears to approach 11,000. As x decreases, y decreases. The end behavior of the graph indicates a maximum number of reported cases of 11,000.
Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.
1. Right Whale Population
Popu
latio
n
80
0
160
240
Generations Since 20074 8 12
y
x
2. Stock Price
Pric
e Va
riatio
n (p
oint
s)
-2
2
0
Time Since Opening Bell (h)
2 4 6
y
x
3.
y
x
Average GasolinePrice
Pric
e ($
per
gal
lon)
2
3
1
0
4
5
6
Years Since 198715105 2520 30
y
x
Worldwide H1N1
Repo
rted
Cas
es
4000
0
8000
12,000
Days Since Outbreak21147 3528 42
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Chapter 1 51 Glencoe Algebra 1
Skills PracticeInterpreting Graphs of Functions
1-8
Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.
1. David’s Savings for Car
Savi
ngs
($)
1400
1200
0
1600
1800
2000
2200
Weeks2 4 6 8 10
y
x
3.
y
x
Height of Golf Ball
Heig
ht (f
t)
40
0
80
120
160
Distance from Tee (yd)40 80 120 160
2.
y
x
Baking Supplies
Flou
r (c)
4
0
8
12
16
20
Batches of Cookies4 8 12
4. Solar Reflector
Heig
ht (f
t)
Width (ft)
y
xO
16
8
−8−16
−8
−16
8 16
focus
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Chapter 1 52 Glencoe Algebra 1
PracticeInterpreting Graphs of Functions
1-8
Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.
1.
y
x
Wholesale T-Shirt Order
Tota
l Cos
t ($)
200
0
400
600
800
1000
Shirts (dozens)2 4 6 8 10
3.
y
x
Height of Diver
Heig
ht A
bove
Wat
er (m
)
2
0
4
6
8
10
12
Time (s)0.5 1 1.5 2 2.5
2.
y
x
Water Level
Wat
er L
evel
(cm
)
28
0
32
36
40
44
Time (seconds)40 80 120 160 200 240
4.
y
x
Boys’ Average Height
Heig
ht (i
n.)
24
0
48
72
Age (yr)4 8 12 16 20
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Chapter 1 53 Glencoe Algebra 1
1-8 Word Problem PracticeInterpreting Graphs of Functions
1. HEALTH The graph shows the Calories yburned by a 130-pound person swimming freestyle laps as a function of time x. Identify the function as linear or nonlinear. Then estimate and interpret the intercepts.
y
x
Calories BurnedSwimming
Calo
ries
(kC)
800
1200
400
0
1600
2000
2400
2800
Time (h)321 5 74 6 8
2. TECHNOLOGY The graph below shows the results of a poll that asks Americans whether they used the Internet yesterday. Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinates of any relative extrema, and the end behavior of the graph.
y
x
Did you use theInternet yesterday?
Yes
Resp
onse
s(p
erce
nt o
f pol
led)
60
0
70
Months Since January 200512 24 36 48 60
3. GEOMETRY The graph shows the area yin square centimeters of a rectangle with perimeter 20 centimeters and width xcentimeters. Describe and interpret any symmetry in the graph.
Area (cm2)
Area
(cm
2 )
Width (cm)
10
-10
20
30
0 2 4 6 8 10
y
x
4. EDUCATION Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.
U.S. Education Spending
Spen
ding
(bill
ions
of $
)
200
0
400
600
800
1000
Years Since 1949302010 50 7040 60
y
x
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Chapter 1 54 Glencoe Algebra 1
1-8 Enrichment Symmetry in Graphs of Functions
You have seen that the graphs of some functions have line symmetry. Functions that have line symmetry in the y-axis are called even functions. The graph of a function can also have point symmetry. Recall that a figure has point symmetry if it can be rotated less than 360° about the point so that the image matches the original figure. Functions that are symmetric about the origin are called odd functions.
Even Functions Odd Functions Neither Even nor Odd
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
The graph of a function cannot be symmetric about the x-axis because the graph would fail the Vertical Line Test.
ExercisesIdentify the function graphed as even, odd, or neither.
1. y
xO
2. y
x
3. y
xO
4. y
xO
5. y
xO
6. y
xO
7. y
xO
8. y
xO
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Chapter 1 55 Glencoe Algebra 1
1 Student Recording SheetUse this recording sheet with pages 70–71 of the Student Edition.
Read each question. Then fill in the correct answer.
1. A B C D
2. F G H J
3. A B C D
4. F G H J
5. A B C D
6. F G H J
7. A B C D
Multiple Choice
Record your answers for Question 12 on the back of this paper.
Extended Response
8a.
8b.
8c.
9a.
9b.
10. (grid in)
11a.
11b.
11c.
10.
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
. . . . .
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Record your answer in the blank.
For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.
Short Response/Gridded Response
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1
Chapter 1 56 Glencoe Algebra 1
Rubric for Scoring Extended Response
General Scoring Guidelines
• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete resopnse for full credit.
Exercise 12 Rubric
Score Specific Criteria
4 In part a, the student correctly writes the expression for the volume of a sphere as 4 − 3 πr3. In part b, the student substitutes 6 for the variable r. The student then takes
6 to the third power. The result is multiplied by 4 and then divided by three to give 288π cm3. Pi is irrational so it appears in the answer.
3 A generally correct solution, but may contain minor flaws in reasoning or computation.
2 A partially correct interpretation and/or solution to the problem.
1 A correct solution with no evidence or explanation.
0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.
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Chapter 1 57 Glencoe Algebra 1
SCORE
1.
2.
3.
4.
5.
1. Write a verbal expression for the algebraic expression 2 + 5p.
2. Write an algebraic expression for the verbal expression 8 to the fourth power increased by 6.
Evaluate each expression. 3. 62 - 32
· 8 + 11
4. 43 ÷ 8
5. MULTIPLE CHOICE Evaluate a(4b + c2) if a = 2, b = 5, and c = 1.
A 41 B 42 C 44 D 45
1. Name the property that is used in 5 · n · 2 = 0. Then find the value of n.
2. The equation 2 − 3 [3 ÷ (10 - 8)] = 2 −
3 (3 ÷ 2) is an example of
which property of equality?
3. Evaluate 7 · 2 · 7 · 5 using properties of numbers. Name the property used in each step.
4. Use the Distributive Property to rewrite 7 · 98. Then evaluate.
5. MULTIPLE CHOICE Simplify 16a2 - 7b2
+ 3b - 2a2.
A 14 - 4b B 14a2 - 7b2
+ 3b C 10b D simplified
1.
2.
3.
4.
5.
1 Chapter 1 Quiz 2(Lessons 1-3 and 1-4)
1 Chapter 1 Quiz 1(Lessons 1-1 and 1-2)
SCORE
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Chapter 1 58 Glencoe Algebra 1
SCORE
1.
2.
3.
4.
1. Find the solution of 1 − 2 (x - 3) = 4 if the replacement set is
{8, 9, 10, 11, 12}.
2. MULTIPLE CHOICE Solve r = 7(16 - 5) −
3 + 4(2) .
A 5 1 − 2 B 7 C 11 D 77
3. Candice is typing an average of 40 words per minute. Write and solve an equation to find the time it will take her to type 1000 words.
4. Express the relation {(3, 5), (-4, 6), (3, 8), (2, 4), (1, 3)} as a mapping. Then determine the domain and range.
1. Determine whether the relation is a function.
2. If g(x) = x2 - 3x + 2, find g(-4).
3. MULTIPLE CHOICE Which represents For every hour that Samuel works, he earns $8.50?
A f (h) = 8.5h C f (h) = 8.5 - h
B f (h) = 8.5 + h D f (h) = h ÷ 8.5
4. Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph.
Online Music
Have
Lis
tene
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nlin
e(p
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20
0
40
60
Months SinceAugust 2000
40 80 120
y
x
1 Chapter 1 Quiz 4(Lessons 1-7 and 1-8)
X Y
1 Chapter 1 Quiz 3(Lessons 1-5 and 1-6)
x y
0 1
−2 −1
− 4 1
1.
2.
3.
4.
SCORE
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Chapter 1 59 Glencoe Algebra 1
SCORE
Part I Write the letter for the correct answer in the blank at the right of each question.
1. Write an algebraic expression for 12 less than a number times 7. A 12 < 7n B 12 > 7n C 12 - 7n D 7n - 12
2. Evaluate 20 + 3(8 - 5). F 29 G 39 H 180 J 26
Evaluate each expression if a = 4, b = 6, and c = 2.
3. ab - c A 12 B 16 C 22 D 8
4. 3a + b2c F 36 G 84 H 96 J 240
5. Simplify 4(w - 9). A 4w - 9 B 4w - 13 C w - 5 D 4w - 36
6. Simplify 3r + 2(t + 5r). F 15r + 2t G 8r + 2t H 15r J 13r + 2t
7. Name the property used in (5 + 2) + n = 7 + n. A Additive Identity C Reflexive Property B Multiplicative Identity D Substitution Property
Part II
Evaluate each expression using properties of numbers. Name the property used in each step.
8. 6.4 + 2.7 + 1.6 + 5.3 9. 4 − 3 � 7 � 3 � 10
For Questions 10 and 11, write a verbal expression for each algebraic expression.
10. 18p 11. x2 - 5
12. Name two properties used to evaluate 7 � 1 - 4 � 1 − 4 .
13. Rewrite 6(10 + 2) using the Distributive Property. Then simplify.
14. Simplify 6b + 7b + 2b2.
15. Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?
8.
9.
10.
11.
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15.
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7.
Chapter 1 Mid-Chapter Test(Lessons 1-1 through 1-4)
1
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Chapter 1 60 Glencoe Algebra 1
SCORE
Choose a term from the vocabulary list above to complete the sentence. 1. In the algebraic expression 8q, the letter q is called a(n) .
2. An expression like c3 is an example of a(n) and is read “c cubed.”
3. A function graphed with a line or smooth curve is called a(n) .
4. The process of finding a value for a variable that results in a true sentence is called solving the .
5. are terms that contain the same variables,with corresponding variables having the same power.
6. The of a term is the numerical factor.
7. The set of the first number of the ordered pairs of a function is the .
8. In a(n) , there is exactly one output for each input.
9. The set of second numbers of the ordered pairs in a relation is the of the relation.
Define each term in your own words.
10. end behavior
11. solution set
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
algebraic expression
coefficient
continuous function
coordinate system
dependent variable
discrete function
domain
end behavior
exponent
factors
function
identity
independent variable
intercept
like terms
multiplicative inverses
open sentences
order of operations
power
range
replacement set
reciprocal
solution set
symmetry
variable
Chapter 1 Vocabulary Test1
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Chapter 1 61 Glencoe Algebra 1
SCORE
Write the letter for the correct answer in the blank at the right of each question. 1. Write an algebraic expression for the sum of a number and 8. A 8x B x - 8 C x + 8 D x ÷ 8
2. Write an algebraic expression for 27 decreased by a number.
F 27 + m G 27 - m H m - 27 J 27 − m
3. Write a verbal expression for 19a. A the sum of 19 and a number C the quotient of 19 and a number
B the difference of 19 and a number D the product of 19 and a number
4. Write a verbal expression for x + y. F the sum of x and y H the difference of x and y
G the quotient of x and y J the product of x and y
5. Evaluate 6(8 - 3). A 45 B 30 C 11 D 66
6. Evaluate 2k + m if k = 11 and m = 5. F 32 G 216 H 27 J 18
7. Name the property used in n + 0 = 7. A Multiplicative Inverse Property C Additive Identity Property B Substitution Property D Multiplicative Identity Property
8. Evaluate 13 + 6 + 7 + 4. F 2184 G 29 H 20 J 30
9. Simplify 7b + 2b + 3c. A 12bc B 9b + 3c C 7b + 5c D 5b + 3c
10. Simplify 5(2g + 3). F 10g + 3 G 7g + 3 H 10g + 15 J 7g + 8
11. Evaluate 4 · 1 + 6 · 16 + 0. A 100 B 0 C 8 D 185
12. Which of the following uses the Distributive Property to determine the product 12(185)?
F 12(100) + 12(13) H 12(18) + 12(5) G 12(1) + 12(8) + 12(5) J 12(100) + 12(80) + 12(5)
13. Find the solution of x + 4 = 7 if the replacement set is {1, 2, 3, 4, 5}. A 1 B 3 C 4 D 2
14. A car rental company charges a rental fee of $20 per day in addition to a charge of $0.30 per mile driven. How much does it cost to rent a car for a day and drive it 25 miles?
F $45.30 G $20.30 H $27.50 J $26.00
1.
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Chapter 1 Test, Form 11
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Chapter 1 62 Glencoe Algebra 1
15. Which statement best describes the graph of the price of one share of a company’s stock shown at the right?
A The price increased more in the morning than in the afternoon.
B The price decreased more in the morning than in the afternoon.
C The price increased more in the afternoon than in the morning.
D The price decreased more in the afternoon than in the morning.
16. What is the domain of the relation? F {–1, 0, 1, 3} H {–2, –1, 0, 1, 2, 3} G {–2, 0, 1, 3} J {0, 1, 2, 3}
17. Determine which relation is a function. A X Y
2
4
-2
1
3
5
C x 3 4 4 5
y –1 2 3 6
B y = 1 −
5 x + 2 D {(3, 0), (– 2, – 2), (7, – 2), (– 2, 0)}
18. If h(r) = 2 − 3 r – 6, what is the value of h(–9)?
F 12 G 0 H - 6 2 − 3 J -12
For Questions 19 and 20, use the graph.
19. Interpret the y-intercept of the graph.
A All those polled used a social networking site 8 months after February 2005.
B About 8% of those polled used a social networking site in February 2005.
C No one used a social networking site in February 2005.
D There were 8 social networking sites in February 2005.
20. Interpret the end behavior of the function in terms of social networking. F expected to decrease H expected to level off at 55%
G expected to increase J expected to level off at 8%
Bonus Simplify (4x + 2)3.
Time of DayA.M. Noon P.M.
Pric
e
y
xO
Chapter 1 Test, Form 1 (continued)
15.
16.
17.
18.
19.
20.
1
y
x
Social Networking
Used
Soc
ial N
etw
orki
ng S
ite(p
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nt o
f pol
led)
10
0
20
30
40
Months Since February 200512 24 36 48
B:
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Chapter 1 63 Glencoe Algebra 1
SCORE
Write the letter for the correct answer in the blank at the right of each question.
1. Write an algebraic expression for nine times of the square of a number. A 9 + x2 B 9 - x2 C 9x2 D x2
- 9
2. Write a verbal expression for 2n + 7. F the product of 2, n, and 7 H 7 less than a number times 2 G 7 more than twice a number J 7 more than n and 2
3. Evaluate 6 + 2 · 3 - 1. A 23 B 10 C 16 D 11
4. Evaluate 2(11 - 5) + 9 ÷ 3. F 18 G 15 H 30 J 11
5. Evaluate x2 + xyz if x = 3, y = 5, and z = 4. A 69 B 63 C 85 D 21
6. Which equation illustrates the Multiplicative Inverse Property? F 0 · 16 = 0 H 3 · 1 −
3 =1
G 1(48) = 48 J 9(1 + 0) = 9(1)
7. Evaluate 29 · 1 + 2(20 ÷ 4 - 5). A 0 B 30 C 29 D 28
8. Simplify r2 - 2r3
+ 3r2. F 4r2 - 2r3 G 2r H 3r2 - 2r3 J 4r2
9. Simplify 3(2x + 4y - y). A 5x + 6y B 6x + 9y C 6x + 3y D 5x + 11y
10. Use the Distributive Property to find 6(14 + 7). F 91 G 126 H 42 J 56
11. Simplify 2(a + 3b) + 3(4a + b). A 6a + 6b B 14a + 9b C 14a + 4b D 6a + 7b
12. Evaluate 3 2 − 5 + 7 + 4 1 −
5 .
F 7 3 − 2 + 7 G 14 3 −
10 H 84 3 −
5 J 14 3 −
5
13. Find the solution of n − 2 - 11 = 3 if the replacement set is {26, 28, 29, 30, 31}.
A 26 B 28 C 30 D 31
14. Somerville High School raised $740 to buy winter coats for the homeless at $46.25 each. How many coats can they buy?
F 12 G 16 H 24 J 34,225
Chapter 1 Test, Form 2A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
1
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Chapter 1 64 Glencoe Algebra 1
15. Which statement best describes a daily stock price? A The price increased. B The price decreased. C The price did not change. D The price increased then decreased.
For Questions 16 and 17, use the graph.16. What is the domain of the relation? F {-4, -1, 0, 2, 4} H {-4, -2, -1, 0, 1, 2, 4}
G {-4, -2, -1, 1, 4} J {-1, 1}
17. Which is a true statement about the relation? A The relation is a linear function. B The value of x increases as y decreases. C The value of x increases as y increases. D The relation is not a function.
18. Determine which relation is not a function. F y
xO
G x y
–2 0
0 0
1 2
3 1
H X Y
-4
-3
5
0
2
9
J x y
–4 0
–3 9
5 2
6 9
For Questions 19 and 20, use the graph.
19. Interpret the y-intercept of the graph. A 0 bracelets cost about $30. B 1 dozen bracelets cost about $30. C 28 dozen bracelets cost $0. D Each dozen bracelets costs about $5.
20. Interpret the end behavior of the function. F The total cost decreases. G The cost per dozen decreases. H The total cost increases. J The cost per dozen increases.
Bonus Find the value of f in the equation f = 4 − 5 (200 - m) + a
if m = 100 and a = 132.
y
xO
15.
16.
17.
18.
19.
20.
Time of DayA.M. Noon P.M.
Pric
e
1 Chapter 1 Test, Form 2A (continued)
y
x
Wholesale Bracelets
Tota
l Cos
t ($)
40
60
20
0
80
100120
Bracelets (dozens)42 8 106 12
B:
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Chapter 1 65 Glencoe Algebra 1
SCORE
Write the letter for the correct answer in the blank at the right of each question.
1. Write an algebraic expression for 3 times x squared minus 4 times x. A 3(2x) - 4x B 4 - 3x C 3x2 - 4x D 3(x2 - 4x)
2. Write a verbal expression for 3n - 8. F the product of 3, n, and 8 H 3 times n less than 8 G 8 less than the product of 3 and n J n minus 8 times 3
3. Evaluate 4 + 5 � 7 - 1. A 139 B 15 C 34 D 38
4. Evaluate 3(16 - 9) + 12 ÷ 3. F 33 G 25 H 41 J 28
5. Evaluate m2 + mtp if m = 3, t = 4, and p = 7.
A 93 B 87 C 100 D 23
6. Which equation illustrates the Additive Identity Property? F 8(9 + 0) = 8(9) H 8 � 1 = 8
G 4(0) = 0 J 1 − 4 � 4 = 1
7. Evaluate 16 � 1 + 4(18 ÷ 2 - 9). A 20 B 0 C 16 D 80
8. Simplify 7x2 + 10x2
+ 5y3. F 22 x2y3 G 17x2 + 5y3 H 22 x4 + y3 J 17x4y3 + 5
9. Simplify 2(7n + 5m - 3m). A 14n + 2m B 9n + 7m C 9n + m D 14n + 4m
10. Use the Distributive Property to find 7(11 - 8). F 133 G 21 H 69 J 85
11. Simplify 3(5a + b) + 4(a + 2b). A 9a + 5b B 19a + 3b C 19a + 11b D 9a + 9b
12. Evaluate 4 1 − 5 + 9 + 2 3 −
5 .
F 15 4 − 5 G 15 2 −
5 H 17 4 −
5 J 17 3 −
10
13. Find the solution of 3n - 13 = 38 if the replacement set is {12, 14, 15, 17, 18}. A 12 B 15 C 17 D 18
14. Ari is jogging at an average rate of 2.25 meters per second. Find the time it will take him to jog 270 meters.
F 1 minute G 2 minutes H 3 minutes J 12 minutes
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1 Chapter 1 Test, Form 2B
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Chapter 1 66 Glencoe Algebra 1
15. Which statement best describes a daily stock price? A The price was unchanged then increased sharply. B The price was unchanged then decreased sharply. C The price rose sharply then leveled off. D The price declined sharply then leveled off.
For Questions 16 and 17, use the graph.
16. What is the domain of the relation? F {–4, –2, –1, 0, 1, 2, 3, 4} H {–4, –2, –1, 0, 1, 4} G {–4, –1, 0, 2, 3, 4} J {–4, 4}
17. Which is a true statement about the relation? A The relation is not a function. B The value of x increases as y decreases. C The value of x increases as y increases. D The relation is a linear function.
18. Determine which relation is a function. F G H J
For Questions 19 and 20, use the graph. 19. Interpret the y-intercept of the graph. A Anna owes $10 before any payments. B Each payment Anna makes is $50. C Anna owes $500 before any payments. D Anna pays off the loan in 10 payments.
20. Interpret the end behavior of the function. F The amount owed decreases. G The payment amount decreases. H The amount owed increases. J The payment amount increases.
Bonus Simplify 8(a2 + 3b2) - 24b2.
Time of DayA.M. Noon P.M.
Pric
e
y
xO
X Y
-32
-415
3
-1
2
y
xO
y
xO
x y
–2 7
0 0
1 –2
1 3
Chapter 1 Test, Form 2B (continued)
15.
16.
17.
18.
19.
20.
1
y
x
Anna’s Loan
Loan
Bal
ance
($)
200
300
100
0
400
500600
Weekly Payments2 4 6 8 1210
B:
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Chapter 1 67 Glencoe Algebra 1
SCORE
Write an algebraic expression for each verbal expression.
1. the sum of the square of a number and 34
2. the product of 5 and twice a number
3. Write a verbal expression for 4n3 +
6.
4. Evaluate 23[(15 - 7) (4 ÷ 2)].
5. Evaluate 3w + (8 - v)t if w = 4, v = 5 and t = 2.
For Questions 6 and 7, name the property used in each equation. Then find the value of n.
6. 5 + 0 = n
7. 7 + (4 + 6) = 7 + n
8. Evaluate 4(5 · 1 ÷ 20). Name the property used in each step.
9. Rewrite 3(14 - 5) using the Distributive Property. Then simplify.
Simplify each expression.
10. 15w - 6w + 14w2
11. 7(2y + 1) + 3y
For Questions 12 and 13, evaluate each expression.
12. 32 + 5 + 8 + 15
13. 1 − 3 · 4 · 9 · 1 −
2
14. Find the solution of 5b - 13 = 22 if the replacement set is {5, 6, 7, 8, 9}.
15. Solve 6 + 3 2 (4)
− 7
- 1 = y.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Chapter 1 Test, Form 2C1
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Chapter 1 68 Glencoe Algebra 1
Chapter 1 Test, Form 2C (continued)
For Questions 16 and 17, use the graph that shows temperature as a functionof time.
16. Identify the independent and dependent variables.
17. Name the ordered pair at point C and explain what it represents.
For Questions 18–20, use thetable that shows airmail letter rates to Greenland.
18. Write the data as a set of ordered pairs.
19. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost.
20. Interpret the end behavior of the function.
Bonus Use grouping symbols, exponents, and symbols for addition, subtraction, multiplication, and division with the digits 1, 9, 8, and 7 (in that order) to form expressions that will yield each value.
a. 6 b. 7 c. 9
B: a.
b.
c.
1
Time
Tem
per
atu
re (
°F)
0
81
82
83
84
85
86
87
88
89
90
6 A.M. 7 A.M. 8 A.M. 9 A.M. 10 A.M.
A
E
B
CD
16.
17.
18.
19.
Weight (oz)
Rat
e ($
)
0
1
2
3
4
5
6
7
5.0 6.0 7.0 8.0
20.
Source: World Almanac
Weight (oz) Rate ($)
5.0 4.20
6.0 5.05
7.0 5.90
8.0 6.75
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Chapter 1 69 Glencoe Algebra 1
SCORE
Write an algebraic expression for each verbal expression.
1. the sum of one-third of a number and 27
2. the product of a number squared and 4
3. Write a verbal expression for 5n3 + 9.
4. Evaluate 32[(12 - 4) ÷ 2].
5. Evaluate 4w + (v - 5)t if w = 2, v = 8, and t = 4.
Name the property used in each equation. Then find the value of n.
6. 11 � n = 1
7. 7 + n = 7 + 3
8. Evaluate 6(6 � 1 ÷ 36). Name the property used in each step.
9. Rewrite (10 + 3)5 using the Distributive Property. Then simplify.
Simplify each expression.
10. 4w2 + 7w2
+ 7z2
11. 3x + 4(5x + 2)
Evaluate each expression.
12. 5 � 13 � 4 � 1
13. 17 + 6 + 3 + 14
14. Find the solution of 3x - 8 = 16 if the replacement set is {5, 6, 7, 8, 9}.
15. Solve 6 + 4 2 · 3
− 10 - 1
= y.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
1 Chapter 1 Test, Form 2D
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Chapter 1 70 Glencoe Algebra 1
Chapter 1 Test, Form 2D (continued)
Use the graph that shows Robert’s bowling scores for his last four games.
16. Identify the independent and dependent variables.
17. Describe what may have happened between the first and fourth games.
For Questions 18–20, use the table that shows 2006 airmail letter rates to New Zealand.
18. Write the data as a set of ordered pairs.
19. Draw a graph that shows therelationship between the weight of a letter sent airmail and the total cost.
20. Interpret the end behavior of the function.
Bonus Insert brackets, parentheses, and the symbols for addition, subtraction, and division in the following sequence of numbers to create an expression whose value is 4.
2 5 1 4 1
Game
Sco
re
020406080
100120140
200180160
1 2 3 4
(1, 72)(4, 87)
(2, 103)
(3, 122)
16.
17.
18.
19.
20.
Weight (oz)
Rat
e ($
)
0
1
2
3
4
5
6
1.0 2.0 3.0 4.0 5.0
B:
1
Source: World Almanac
Weight (oz) Rate ($)
2.0 1.80
3.0 2.75
4.0 3.70
5.0 4.65
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Chapter 1 71 Glencoe Algebra 1
SCORE
Write an algebraic expression for each verbal expression.
1. the sum of the cube of a number and 12
2. 42 decreased by twice some number
3. Write a verbal expression for 6g2
− 5 .
4. Evaluate 4[ 3 3 - 5(8 - 6)]
− 3 2 - 7
+ 11.
Evaluate each expression if w = 4, n = 8, v = 5, and t = 2.
5. w2 + n(v2
-t) 6. 3nw - w2 + t3
For Questions 7 and 8, name the property used in each equation. Then find the value of n.
7. 7y + y = 7y + ny 8. (6 + n)x = 15x
9. Evaluate 2 − 3 (3 ÷ 2) + (32
- 9). Name the property used
in each step.
10. Rewrite 2(x + 3y - 2z) using the Distributive Property. Then simplify.
Simplify each expression. If not possible, write simplified.
11. 3 + 6(5a + 4an) + 9na
12. 7a + 7a2 + 14b2
Evaluate each expression.
13. 6 � 8 + 29 + 7 + 3 � 7
14. 32 + 6 � 4 + 7 � 4 + 16
15. Solve 5 · 2 3 - 4 · 3 2 − 1 + 3
= x.
16. Find the solution of 2b + 1 − 2 = 3 if the replacement
set is { 1 − 2 , 3 −
4 , 1, 5 −
4 , 3 −
2 , 7 −
4 } .
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Ass
essm
ent
Chapter 1 Test, Form 31
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Chapter 1 72 Glencoe Algebra 1
17. Some warehouse stores charge members an annual fee to shop there. On his first trip to a warehouse store, Mr. Marshpays a $50 membership fee. Cases of bottled water cost $4 at the warehouse store. Write and solve an equation to find the total amount Mr. Marsh spent on his first trip before tax if he bought 8 cases of water.
18. The graph shown represents a puppy exploring a trail. Describe what is happening in the graph. Is the function discrete or continuous?
For Questions 19 and 20, use the graph that shows the average daily circulation of the Evening Telegraph.
19. Identify the independent and dependent variables.
20. Write a description of what the graph displays.
21. Each day David drives to work in the morning, returns home for lunch, drives back to work, and then goes to a gym to exercise before he returns home for the evening. Draw a reasonable graph to show the distance David is from hishome for a two-day period.
22. Determine whether - 1 − 2 x + 4y = 6 represents a function.
23. If f (x) = -3x2 - 2x + 1, find 2[f (r)].
For Questions 24 and 25, use the graph at the right.
24. Interpret the y-intercept of the graph.
25. Interpret the end behavior of the function
Bonus Simplify 62 + (3 + 4)2 - (21 ÷ 3 + 4 · 2)
−− 14 - 3 · 14
+ 23 - (5 + 1) · 2 .
y
100
20304050607080
2006 2007 2008 2009 2010
New
spap
ers
Sold
(th
ou
san
ds)
Year
Time
Distance fromTrailhead
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
Chapter 1 Test, Form 3 (continued)1
y
x
Ohio Population
Popu
latio
n (m
illio
ns)
105
0
15
3025
20
Years Since 190025 50 75 100 125150
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Chapter 1 73 Glencoe Algebra 1
SCORE
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.
1. a. Write an algebraic expression that includes a sum and a product. Write a verbal expression for your algebraic expression.
b. Write a verbal expression that includes a difference and a quotient. Write an algebraic expression for your verbal expression.
2. Explain how a replacement set and a solution set are used with an open sentence.
3. a. Write an equation that demonstrates one of the identity properties. Name the property used in the equation.
b. Explain how to use the Distributive Property to find 7 · 23. c. Describe how to use the Commutative and Associative Properties
to simplify the evaluation of 18 + 33 + 82 + 67.
4. Think of a situation that could be modeled by this graph. Then label the axes of the graph and write several sentences describing the situation.
5. Use the set {–1, 0, 1, 2} as a domain and the set {–3, –1, 4, 5} as a range.
a. Create a relation. Express the relation as a set of ordered pairs.
b. Create a relation that is not a function. Express the relation as a table, a graph, and a mapping.
c. Explain why the relation created for part b is not a function.
6. Identify the function graphed as linear or nonlinear. Then estimate and interpret key features of the graph.
1 Chapter 1 Extended-Response Test
y
xO
y
x
How often do you use theInternet away from home?
Seve
ral T
imes
a D
ay (p
erce
nt o
f pol
led)
2
3
1
0
4
5
6
7
8
9
10
11
12
Months Since March 200412 186 24 30 36 42 48 54 60 66 72
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Chapter 1 74 Glencoe Algebra 1
SCORE
1. Write an algebraic expression to represent the number of pens that can be bought with 30 cents if each pen costs c cents. (Lesson 1-1)
A 30 - c B 30 − c C 30 + c D 30c
2. Evaluate 7a + b − b + c
if a = 2, b = 6, and c = 4. (Lesson 1-2)
F 3 1 − 3 G 1 1 −
2 H 3 J 2
3. Find the solution of 3(y + 7) ≤ 39 if the replacement set is {2, 4, 6, 8, 10, 12}. (Lesson 1-5)
A {2, 4} B {6, 8, 10, 12} C {8, 10, 12} D {2, 4, 6}
4. The equation 4 + 9 = 4 + 9 is an example of which property of equality? (Lesson 1-3)
F Substitution G Reflexive H Symmetric J Transitive
5. Simplify 7x2 + 5x + 4x. (Lesson 1-4)
A 7x2 + 9x B 16x4 C 12x3
+ 4x D 7x2 + x
6. Simplify 7(2x + y) + 6(x + 5y). (Lesson 1-4)
F 20x + 37y G 20x + 6y H 13x + 42y J 15x + 6y
For Questions 7 and 8, use the following statement.If x is a multiple of 2, then x is divisible by 4.
7. Identify the hypothesis of the statement. (Lesson 1-8)
A x is a multiple of 2 C x is divisible by 4 B x = 2 D x = 4
8. Which number is a counterexample for the statement? (Lesson 1-8)
F 20 G 4 H 32 J 10
9. The distance an airplane travels increases as the duration of the flight increases. Identify the dependent variable. (Lesson 1-6)
A time B direction C airplane D distance
10. Omari drives a car that gets 18 miles per gallon of gasoline. The car’s gasoline tank holds 15 gallons. The distance Omari drives before refueling is a function of the number of gallons of gasoline in the tank. Identify a reasonable domain for this situation. (Lesson 1-6)
F 0 to 18 miles H 0 to 270 miles G 0 to 15 gallons J 0 to 60 mph
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. F G H J
A B C D
F G H J
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
1 Standardized Test Practice(Chapter 1)
A B C D
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
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Chapter 1 75 Glencoe Algebra 1
11. Evaluate x2 + y2 + z, if x = 7, y = 6, and z = 4. (Lesson 1-2)
A 17 B 101 C 89 D 59
12. Find the solution of 20 = 5(7 - x) if the replacement set is {0, 1, 2, 3, 4, 5, 6}. (Lesson 1-5)
F 0 G 1 H 2 J 3
13. Using the Distributive Property to find 9 (5 2 − 3 ) would give
which expression? (Lesson 1-4)
A 9(5) + 2 − 3 B 9 ( 17 −
3 ) C 9(5) + 9 ( 2 −
3 ) D 9(5) ( 2 −
3 )
14. Which sentence best describes the end behavior of the function shown? (Lesson 1-8)
F As x increases, y decreases, and as x decreases, y decreases.
G As x increases, y increases, and as x decreases, y decreases.
H As x increases, y decreases, and as x decreases, y increases.
J As x increases, y increases, and as x decreases, y increases.
15. If g(x) = x 2 + 5, find g(3). (Lesson 1-7)
A 8 B 9 C 11 D 14
16. Evaluate 4(16 ÷ 2 + 6). 17. Evaluate 2 + x(2y + z) if (Lesson 1-2) x = 5, y = 3, and z = 4.
(Lesson 1-2)
11.
12.
13.
14.
15.
F G H J
1 Standardized Test Practice (continued)
A B C D
A B C D
F G H J
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
Part 2: Gridded Response
Instructions: Enter your answer by writing each digit of the answer in a column box and
then shading in the appropriate circle that corresponds to that entry.
A B C D
y
xO
−20
−10
−2−3−4
20
10
1 2 3 4
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Chapter 1 76 Glencoe Algebra 1
Find each product or quotient.(Prerequisite Skill)
18. 17 · 8 19. 84 ÷ 7
20. 0.9 · 5.6 21. 8 − 9 ÷ 16 −
3
22. Write an algebraic expression for six less than twice a number. (Lesson 1-1)
23. Write a verbal expression for 4m2 + 2. (Lesson 1-1)
24. Evaluate 13 - 1 − 3 (11 - 5). (Lesson 1-2)
25. Evaluate 2b + c2
− a , if a = 2, b = 4, and c = 6. (Lesson 1-2)
26. Evaluate 3(5 · 2 - 9) + 2 · 1 − 2 . (Lesson 1-2)
27. Evaluate 1 − 3 . 20 . 6 . 1 −
5 using the properties of numbers.
(Lesson 1-3)
Simplify each expression.
28. 7n + 4n 29. 5y + 3(2y + 1) (Lesson 1-4) (Lesson 1-4)
30. Solve 2(7) + 4 = x. (Lesson 1-5)
31. Find the solution of 3x - 4 = 2 if the replacement set is{0, 1, 2, 3, 4, 5}. (Lesson 1-5)
32. Alvin is mowing his front lawn. His mailbox is on the edge of the lawn. Draw a reasonable graph that shows the distance Alvin is from the mailbox as he mows. Let the horizontal axis show the time and the vertical axis show the distance from the mailbox. (Lesson 1-6)
33. Identify and interpret
y
x
Computer Virus
Affe
cted
Com
pute
rs
40006000
2000
0
800010,000
Time (minutes)40 6020 80 100
each feature of the graph shown. (Lesson 1-8)
a. intercept(s)
b. end behavior
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33a.
33b.
Part 3: Short Response
Instructions: Write your answers in the space.
1 Standardized Test Practice (continued)
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swer
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Chapter 1 A1 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-1
Cha
pte
r 1
5 G
lenc
oe A
lgeb
ra 1
Wri
te V
erb
al E
xpre
ssio
ns
An
alg
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ic e
xpre
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n c
onsi
sts
of o
ne
or m
ore
nu
mbe
rs a
nd
vari
able
s al
ong
wit
h o
ne
or m
ore
arit
hm
etic
ope
rati
ons.
In
alg
ebra
, var
iab
les
are
sym
bols
use
d to
rep
rese
nt
un
spec
ifie
d n
um
bers
or
valu
es. A
ny
lett
er m
ay b
e u
sed
as a
va
riab
le.
W
rite
a v
erb
al e
xpre
ssio
n f
or e
ach
alg
ebra
ic e
xpre
ssio
n.
a. 6
n2
the
prod
uct
of
6 an
d n
squ
ared
b.
n3
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2mth
e di
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ence
of
n c
ube
d an
d tw
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tim
es m
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cise
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n f
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ssio
n.
1. w
- 1
2.
1 −
3 a3
3. 8
1 +
2x
4. 1
2d
5. 8
4 6.
62
7. 2
n2
+ 4
8.
a3
․
b3
9. 2
x3 -
3
10.
6k3
−
5
11.
1 −
4 b2
12. 7
n5
13. 3
x +
4
14.
2 −
3 k5
15. 3
b2 +
2a3
16
. 4(n
2 +
1)
1-1
Stud
y G
uide
and
Inte
rven
tion
Vari
ab
les a
nd
Exp
ressio
ns
Exam
ple
1–16
. Sam
ple
an
swer
s ar
e g
iven
.
on
e th
ird
th
e cu
be
of
a
12 t
imes
d
the
squ
are
of
6
the
sum
of
4 an
d t
wic
e th
e sq
uar
e o
f n
th
e d
iffer
ence
of
twic
e a
nu
mb
er c
ub
ed a
nd
3
th
e su
m o
f th
ree
tim
es a
nu
mb
er a
nd
4
3
tim
es b
sq
uar
ed
plu
s 2
tim
es a
cu
bed
4
tim
es t
he
sum
o
f th
e sq
uar
e o
f n
an
d 1
on
e le
ss t
han
w
eig
hty
-on
e in
crea
sed
by
twic
e x
eig
ht
to t
he
fou
rth
po
wer
a c
ub
ed t
imes
b c
ub
ed
6 ti
mes
th
e cu
be
of
k d
ivid
ed b
y 5
two
-th
ird
s th
e fi
fth
po
wer
of
k
on
e-fo
urt
h t
he
squ
are
of
bse
ven
tim
es t
he
fi ft
h p
ow
er o
f n
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
3 G
lenc
oe A
lgeb
ra 1
B
efor
e yo
u b
egin
Ch
ap
ter
1
•
Rea
d ea
ch s
tate
men
t.
•
Dec
ide
wh
eth
er y
ou A
gree
(A
) or
Dis
agre
e (D
) w
ith
th
e st
atem
ent.
•
Wri
te A
or
D i
n t
he
firs
t co
lum
n O
R i
f yo
u a
re n
ot s
ure
wh
eth
er y
ou a
gree
or
disa
gree
, wri
te N
S (
Not
Su
re).
Aft
er y
ou c
omp
lete
Ch
ap
ter
1
•
Rer
ead
each
sta
tem
ent
and
com
plet
e th
e la
st c
olu
mn
by
ente
rin
g an
A o
r a
D.
•
Did
an
y of
you
r op
inio
ns
abou
t th
e st
atem
ents
ch
ange
fro
m t
he
firs
t co
lum
n?
•
For
th
ose
stat
emen
ts t
hat
you
mar
k w
ith
a D
, use
a p
iece
of
pape
r to
wri
te a
n
exam
ple
of w
hy
you
dis
agre
e.
1A
ntic
ipat
ion
Gui
deE
xp
ressio
ns, E
qu
ati
on
s, an
d F
un
cti
on
s
Step
1
Step
2
ST
EP
1A
, D, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
An
alg
ebra
ic e
xpre
ssio
n c
onta
ins
one
or m
ore
nu
mbe
rs,
vari
able
s, a
nd
arit
hm
etic
ope
rati
ons.
2.
Th
e ex
pres
sion
x4
mea
ns
x +
x +
x +
x.
3.
Acc
ordi
ng
to t
he
orde
r of
ope
rati
ons,
all
mu
ltip
lica
tion
an
d di
visi
on s
hou
ld b
e do
ne
befo
re a
nyt
hin
g el
se.
4.
Sin
ce 2
mak
es t
he
equ
atio
n 3
t -
1 =
5 t
rue,
{2}
is
the
solu
tion
se
t fo
r th
e eq
uat
ion
.
5.
Bec
ause
of
the
Ref
lexi
ve P
rope
rty
of E
qual
ity,
if
a +
b =
c t
hen
c
= a
+ b
.
6.
Th
e m
ult
ipli
cati
ve i
nve
rse
of 2
3 is
1 −
23 .
7.
Th
e D
istr
ibu
tive
Pro
pert
y st
ates
th
at a
(b +
c)
wil
l eq
ual
ab
+ c
.
8.
Th
e or
der
in w
hic
h y
ou a
dd o
r m
ult
iply
nu
mbe
rs d
oes
not
ch
ange
th
eir
sum
or
prod
uct
.
9.
A g
raph
has
sym
met
ry i
n a
lin
e if
eac
h h
alf
of t
he
grap
h o
n
eith
er s
ide
of t
he
lin
e m
atch
es e
xact
ly.
10.
In t
he
coor
din
ate
plan
e, t
he
x-ax
is i
s h
oriz
onta
l an
d th
e y-
axis
is
ver
tica
l.
A D D A D A A AD A
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
6 G
lenc
oe A
lgeb
ra 1
Wri
te A
lgre
bra
ic E
xpre
ssio
ns
Tra
nsl
atin
g ve
rbal
exp
ress
ion
s in
to a
lgeb
raic
ex
pres
sion
s is
an
im
port
ant
alge
brai
c sk
ill.
W
rite
an
alg
ebra
ic e
xpre
ssio
n f
or e
ach
ver
bal
exp
ress
ion
.
a. f
our
mor
e th
an a
nu
mb
er n
Th
e w
ords
mor
e th
an i
mpl
y ad
diti
on.
fou
r m
ore
than
a n
um
ber
n4
+ n
Th
e al
gebr
aic
expr
essi
on i
s 4
+ n
.
b.
the
dif
fere
nce
of
a n
um
ber
sq
uar
ed a
nd
8T
he e
xpre
ssio
n di
ffer
ence
of
impl
ies
subt
ract
ion.
the
diff
eren
ce o
f a
nu
mbe
r sq
uar
ed a
nd
8n
2 -
8T
he
alge
brai
c ex
pres
sion
is
n2
- 8
.
Exer
cise
sW
rite
an
alg
ebra
ic e
xpre
ssio
n f
or e
ach
ver
bal
exp
ress
ion
.
1. a
nu
mbe
r de
crea
sed
by 8
2. a
nu
mbe
r di
vide
d by
8
3. a
nu
mbe
r sq
uar
ed
4. f
our
tim
es a
nu
mbe
r
5. a
nu
mbe
r di
vide
d by
6
6. a
nu
mbe
r m
ult
ipli
ed b
y 37
7. t
he
sum
of
9 an
d a
nu
mbe
r
8. 3
les
s th
an 5
tim
es a
nu
mbe
r
9. t
wic
e th
e su
m o
f 15
an
d a
nu
mbe
r
10. o
ne-
hal
f th
e sq
uar
e of
b
11. 7
mor
e th
an t
he
prod
uct
of
6 an
d a
nu
mbe
r
12. 3
0 in
crea
sed
by 3
tim
es t
he
squ
are
of a
nu
mbe
r
1-1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Vari
ab
les a
nd
Exp
ressio
ns
Exam
ple
b -
8
h
−
8
n2 4n
n
−
6
37n
9 +
n
5n -
3
2(15
+ n
)
1 −
2 b2
6n +
7
30 +
3n
2
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NA
ME
DAT
E
P
ER
IOD
Lesson 1-1
Cha
pte
r 1
7 G
lenc
oe A
lgeb
ra 1
Wri
te a
ver
bal
exp
ress
ion
for
eac
h a
lgeb
raic
exp
ress
ion
.
1. 9
a2 2.
52
3. c
+ 2
d
4. 4
- 5
h
5. 2
b2 6.
7x3
- 1
7. p
4 +
6r
8. 3
n2
- x
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n.
9. t
he
sum
of
a n
um
ber
and
10
10. 1
5 le
ss t
han
k
11. t
he
prod
uct
of
18 a
nd
q
12. 6
mor
e th
an t
wic
e m
13. 8
in
crea
sed
by t
hre
e ti
mes
a n
um
ber
14. t
he
diff
eren
ce o
f 17
an
d 5
tim
es a
nu
mbe
r
15. t
he
prod
uct
of
2 an
d th
e se
con
d po
wer
of
y
16. 9
les
s th
an g
to
the
fou
rth
pow
er
1-1
Skill
s Pr
acti
ceVari
ab
les a
nd
Exp
ressio
ns
x
+ 1
0
1
8q
8
+ 3
x
2
y2
t
he
pro
du
ct o
f 9
and
a
5 sq
uar
ed
sq
uar
ed
t
he
sum
of
c a
nd
tw
ice
d
the
dif
fere
nce
of
4 an
d 5
tim
es h
2
tim
es b
sq
uar
ed
1 le
ss t
han
7 t
imes
x
cub
ed
p
to
th
e fo
urt
h p
ow
er p
lus
6 ti
mes
r
3 t
imes
n s
qu
ared
m
inu
s x
k
- 1
5
2
m +
6
1
7 -
5x
g
4 -
9
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Answers (Lesson 1-1)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A2A01_A14_ALG1_A_CRM_C01_AN_660498.indd A2 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
8 G
lenc
oe A
lgeb
ra 1
Wri
te a
ver
bal
exp
ress
ion
for
eac
h a
lgeb
raic
exp
ress
ion
.
1. 2
3f
2. 7
3
3. 5
m2
+ 2
4.
4d
3 -
10
5. x
3 ․
y4
6.
b2
- 3
c3
7.
k5 −
6 8.
4n2
−
7
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n.
9. t
he
diff
eren
ce o
f 10
an
d u
10. t
he
sum
of
18 a
nd
a n
um
ber
11. t
he
prod
uct
of
33 a
nd
j
12. 7
4 in
crea
sed
by 3
tim
es y
13. 1
5 de
crea
sed
by t
wic
e a
nu
mbe
r
14. 9
1 m
ore
than
th
e sq
uar
e of
a n
um
ber
15. t
hre
e fo
urt
hs
the
squ
are
of b
16. t
wo
fift
hs
the
cube
of
a n
um
ber
17. B
OO
KS
A u
sed
book
stor
e se
lls
pape
rbac
k fi
ctio
n b
ooks
in
exc
elle
nt
con
diti
on f
or
$2.5
0 an
d in
fai
r co
ndi
tion
for
$0.
50. W
rite
an
exp
ress
ion
for
th
e co
st o
f bu
yin
g x
exce
llen
t-co
ndi
tion
pap
erba
cks
and
f fa
ir-c
ondi
tion
pap
erba
cks.
18. G
EOM
ETRY
Th
e su
rfac
e ar
ea o
f th
e si
de o
f a
righ
t cy
lin
der
can
be
fou
nd
by m
ult
iply
ing
twic
e th
e n
um
ber
π b
y th
e ra
diu
s ti
mes
th
e h
eigh
t. I
f a
circ
ula
r cy
lin
der
has
rad
ius
r an
d h
eigh
t h
, wri
te a
n e
xpre
ssio
n t
hat
rep
rese
nts
th
e su
rfac
e ar
ea o
f it
s si
de.
1-1
Prac
tice
Vari
ab
les a
nd
Exp
ressio
ns
the
pro
du
ct o
f 23
an
d f
seve
n c
ub
ed
2 m
ore
th
an 5
tim
es m
sq
uar
ed
4 ti
mes
d c
ub
ed m
inu
s 10
x c
ub
ed t
imes
y t
o t
he
b
sq
uar
ed m
inu
s 3
tim
es c
cu
bed
fou
rth
po
wer
1– 8
. Sam
ple
an
swer
s ar
e g
iven
.
o
ne
sixt
h o
f th
e fi
fth
po
wer
of
k
on
e se
ven
th o
f 4
tim
es n
sq
uar
ed
2.50
x +
0.5
0f 2πrh
10
- u
33j
15
- 2
x
3 −
4 b2
18 +
x
74 +
3y
x2
+ 9
1
2 −
5 x3
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NA
ME
DAT
E
P
ER
IOD
Lesson 1-1
Cha
pte
r 1
9 G
lenc
oe A
lgeb
ra 1
1. S
OLA
R S
YST
EM I
t ta
kes
Ear
th a
bou
t 36
5 da
ys t
o or
bit
the
Su
n. I
t ta
kes
Ura
nu
s ab
out
85 t
imes
as
lon
g. W
rite
a
nu
mer
ical
exp
ress
ion
to
desc
ribe
th
e n
um
ber
of d
ays
it t
akes
Ura
nu
s to
orb
it
the
Su
n.
2. T
ECH
NO
LOG
Y T
her
e ar
e 10
24 b
ytes
in
a
kilo
byte
. Wri
te a
n e
xpre
ssio
n t
hat
de
scri
bes
the
nu
mbe
r of
byt
es i
n a
co
mpu
ter
chip
wit
h n
kil
obyt
es.
3. T
HEA
TER
H. H
owar
d H
ugh
es, P
rofe
ssor
E
mer
itu
s of
Tex
as W
esle
yan
Col
lege
an
d h
is w
ife
Eri
n C
onn
or H
ugh
es a
tten
ded
a re
cord
613
6 th
eatr
ical
sh
ows.
Wri
te a
n
expr
essi
on f
or t
he
aver
age
nu
mbe
r of
sh
ows
they
att
ende
d pe
r ye
ar i
f th
ey
accu
mu
late
d th
e re
cord
ove
r y
year
s.
4. T
IDES
Th
e di
ffer
ence
bet
wee
n h
igh
an
d lo
w t
ides
alo
ng
the
Mai
ne
coas
t in
N
ovem
ber
is 1
9 fe
et o
n M
onda
y an
d x
feet
on
Tu
esda
y. W
rite
an
exp
ress
ion
to
show
th
e av
erag
e ri
se a
nd
fall
of
the
tide
fo
r M
onda
y an
d T
ues
day.
5. B
LOC
KS
A t
oy m
anu
fact
ure
r pr
odu
ces
a se
t of
blo
cks
that
can
be
use
d by
ch
ildr
en
to b
uil
d pl
ay s
tru
ctu
res.
Th
e pr
odu
ct
pack
agin
g te
am i
s an
alyz
ing
diff
eren
t ar
ran
gem
ents
for
pac
kagi
ng
thei
r bl
ocks
. O
ne
idea
th
ey h
ave
is t
o ar
ran
ge t
he
bloc
ks i
n t
he
shap
e of
a c
ube
, wit
h
b bl
ocks
alo
ng
one
edge
.
a. W
rite
an
exp
ress
ion
rep
rese
nti
ng
the
tota
l n
um
ber
of b
lock
s pa
ckag
ed i
n a
cu
be m
easu
rin
g b
bloc
ks o
n o
ne
edge
.
b.
Th
e pa
ckag
ing
team
dec
ides
to
take
on
e la
yer
of b
lock
s of
f th
e to
p of
th
is
pack
age.
Wri
te a
n e
xpre
ssio
n
repr
esen
tin
g th
e n
um
ber
of b
lock
s in
th
e to
p la
yer
of t
he
pack
age.
c. T
he
team
fin
ally
dec
ides
th
at t
hei
r fa
vori
te p
acka
ge a
rran
gem
ent
is t
o ta
ke 2
lay
ers
of b
lock
s of
f th
e to
p of
a
cube
mea
suri
ng
b bl
ocks
alo
ng
one
edge
. Wri
te a
n ex
pres
sion
rep
rese
ntin
g th
e n
um
ber
of b
lock
s le
ft b
ehin
d af
ter
the
top
two
laye
rs a
re r
emov
ed.
b
b
b
1-1
Wor
d Pr
oble
m P
ract
ice
Vari
ab
les a
nd
Exp
ressio
ns
365
× 8
5
1024
× n
or
1024
n
6136
−
y
b3
b2
19 +
x
−
2
b3
- 2
b2
or
(b -
2)
× b
2
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5:20
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Answers (Lesson 1-1)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A3A01_A14_ALG1_A_CRM_C01_AN_660498.indd A3 12/21/10 6:44 PM12/21/10 6:44 PM
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
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cGraw
-Hill C
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Chapter 1 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
10
Gle
ncoe
Alg
ebra
1
Too
thp
ick T
rian
gle
sV
aria
ble
expr
essi
ons
can
be
use
d to
rep
rese
nt
patt
ern
s an
d h
elp
solv
e pr
oble
ms.
Con
side
r th
e pr
oble
m o
f cr
eati
ng
tria
ngl
es o
ut
of t
ooth
pick
s sh
own
bel
ow. F
igu
re 3
Fig
ure
2F
igu
re 1
1. H
ow m
any
toot
hpi
cks
does
it
take
to
crea
te e
ach
fig
ure
?
2. H
ow m
any
toot
hpi
cks
does
it
take
to
mak
e u
p th
e pe
rim
eter
of
each
im
age?
3. S
ketc
h t
he
nex
t th
ree
figu
res
in t
he
patt
ern
.
Fig
ure
4F
igu
re 5
Fig
ure
6
4. C
onti
nu
e th
e pa
tter
n t
o co
mpl
ete
the
tabl
e.
5. L
et t
he
vari
able
n r
epre
sen
t th
e fi
gure
nu
mbe
r. W
rite
an
exp
ress
ion
th
at c
an b
e u
sed
to
fin
d th
e n
um
ber
of t
ooth
pick
s n
eede
d to
cre
ate
figu
re n
.
6. L
et t
he
vari
able
n r
epre
sen
t th
e fi
gure
nu
mbe
r. W
rite
an
exp
ress
ion
th
at c
an b
e u
sed
to
fin
d th
e n
um
ber
of t
ooth
pick
s in
th
e pe
rim
eter
of
figu
re n
.
1-1
Enri
chm
ent
Imag
e N
um
ber
12
34
56
78
910
Nu
mb
er o
f to
oth
pic
ks3
57
Nu
mb
er o
f to
oth
pic
ks in
P
erim
eter
34
5
3; 5
; 7
3; 4
; 5
9
11
13
15
17
19
21
6
7
8
9
1
0
11
12
2n +
1
n +
2
001_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-2
Cha
pte
r 1
11
Gle
ncoe
Alg
ebra
1
Eval
uat
e N
um
eric
al E
xpre
ssio
ns
Nu
mer
ical
exp
ress
ion
s of
ten
con
tain
mor
e th
an
one
oper
atio
n. T
o ev
alu
ate
them
, use
th
e ru
les
for
orde
r of
ope
rati
ons
show
n b
elow
.
Ord
er o
fO
per
atio
ns
Ste
p 1
Eva
lua
te e
xp
ressio
ns in
sid
e g
rou
pin
g s
ym
bo
ls.
Ste
p 2
Eva
lua
te a
ll p
ow
ers
.
Ste
p 3
Do
all
mu
ltip
lica
tio
n a
nd
/or
div
isio
n f
rom
le
ft t
o r
igh
t.
Ste
p 4
Do
all
ad
ditio
n a
nd
/or
su
btr
actio
n f
rom
le
ft t
o r
igh
t.
E
valu
ate
each
exp
ress
ion
.
a. 3
4 34 =
3 ․
3 ․
3 ․
3
Use 3
as a
facto
r 4 t
imes.
=
81
Multip
ly.
b.
63 63 =
6 ․
6 ․
6
Use 6
as a
facto
r 3 t
imes.
=
216
M
ultip
ly.
E
valu
ate
each
exp
ress
ion
.
a. 3
[2 +
(12
÷ 3
)2 ]3[
2 +
(12
÷ 3
)2 ] =
3(2
+ 4
2 ) D
ivid
e 1
2 b
y 3
.
=
3(2
+ 1
6) Fi
nd 4
square
d.
=
3(1
8)
Add 2
and 1
6.
=
54
Multip
ly 3
and 1
8.
b.
3 +
23
−
42 · 3
3 +
23
−
42 · 3 =
3 +
8
−
42 · 3
E
valu
ate
pow
er
in n
um
era
tor.
=
11
−
42 · 3
A
dd 3
and 8
in t
he n
um
era
tor.
=
11
−
16 · 3
E
valu
ate
pow
er
in d
enom
inato
r.
=
11
−
48
Multip
ly.
Exer
cise
sE
valu
ate
each
exp
ress
ion
.
1. 5
2 2.
33
3. 1
04
4. 1
22 5.
83
6. 2
8
7. (
8 -
4)
․
2
8. (
12 +
4)
․
6
9. 1
0 +
8 ․
1
10. 1
5 -
12
÷ 4
11
. 12(
20 -
17)
- 3
․ 6
12
. 24
÷ 3
․ 2
- 3
2
13. 3
2 ÷
3 +
22
․
7 -
20
÷ 5
14
. 4
+ 32
−
12 +
1
15. 2
50 ÷
[5(
3 ․
7 +
4)]
16.
2 · 4
2 -
8 ÷
2
−
(5
+ 2)
· 2
17
. 4(
52 ) -
4
· 3
−
4(4
· 5 +
2)
18.
52
- 3
−
20(3)
+
2(
3)
1-2
Stud
y G
uide
and
Inte
rven
tion
Ord
er
of
Op
era
tio
ns
Exam
ple
1Ex
amp
le 2
896
1218
27
2
1 −
3
25
27
10,0
00
144
512
256
18
7
1
21
001_
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Answers (Lesson 1-1 and Lesson 1-2)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A4A01_A14_ALG1_A_CRM_C01_AN_660498.indd A4 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
12
Gle
ncoe
Alg
ebra
1
Eval
uat
e A
lgeb
raic
Exp
ress
ion
s A
lgeb
raic
exp
ress
ion
s m
ay c
onta
in m
ore
than
on
e op
erat
ion
. Alg
ebra
ic e
xpre
ssio
ns
can
be
eval
uat
ed i
f th
e va
lues
of
the
vari
able
s ar
e kn
own
. F
irst
, rep
lace
th
e va
riab
les
wit
h t
hei
r va
lues
. Th
en u
se t
he
orde
r of
ope
rati
ons
to c
alcu
late
th
e va
lue
of t
he
resu
ltin
g n
um
eric
al e
xpre
ssio
n.
E
valu
ate
x3 +
5(y
- 3
) if
x =
2 a
nd
y =
12.
x3 +
5(y
- 3
) =
23
+ 5
(12
- 3
)
R
epla
ce x
with 2
and y
with 1
2.
= 8
+ 5
(12
- 3
) E
valu
ate
23.
= 8
+ 5
(9)
Subtr
act
3 f
rom
12.
= 8
+ 4
5 M
ultip
ly 5
and 9
.
= 5
3 A
dd 8
and 4
5.
Th
e so
luti
on i
s 53
.
Exer
cise
sE
valu
ate
each
exp
ress
ion
if
x =
2, y
= 3
, z =
4, a
= 4 −
5 , an
d b
= 3 −
5 .
1. x
+ 7
2.
3x
- 5
3.
x +
y2
4. x
3 +
y +
z2
5.
6a
+ 8
b
6. 2
3 -
(a
+ b
)
7.
y2 −
x2
8. 2
xyz
+ 5
9.
x(2
y +
3z)
10. (
10x)
2 +
100
a
11.
3xy
- 4
−
7x
12
. a2
+ 2
b
13.
z2 -
y2
−
x2
14. 6
xz +
5xy
15
. (z
- y )
2 −
x
16.
25ab
+ y
−
xz
17.
5 a 2 b
−
y
18.
(z ÷
x)2
+ a
x
19. (
x −
z ) 2 +
(
y −
z ) 2
20.
x +
z
−
y +
2z
21
. ( z
÷ x
−
y )
+ (
y ÷
x −
z )
1-2
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Ord
er
of
Op
era
tio
ns
Exam
ple 9
111
2721
3 −
5
9 −
4 53
36
480
1 21
−
25
7 −
4 78
1 −
2
1 7 −
8 16
−
25
5 3 −
5
13
−
16
6 −
11
1 1
−
24
19 3 −
5
001_
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8.in
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10
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-2
Cha
pte
r 1
13
Gle
ncoe
Alg
ebra
1
Eva
luat
e ea
ch e
xpre
ssio
n.
1. 8
2 2.
34
3. 5
3 4.
33
5. (
5 +
4)
� 7
6.
(9
- 2
) � 3
7. 4
+ 6
� 3
8.
12
+ 2
� 2
9. (
3 +
5)
� 5
+ 1
10
. 9 +
4(3
+ 1
)
11. 3
0 -
5 �
4 +
2
12. 1
0 +
2 �
6 +
4
13. 1
4 ÷
7 �
5 -
32
14
. 4[3
0 -
(10
- 2
) � 3
]
15. 5
+ [
30 -
(6
- 1
)2 ]
16. 2
[12
+ (
5 -
2)2 ]
Eva
luat
e ea
ch e
xpre
ssio
n i
f x
= 6
, y =
8, a
nd
z =
3.
17. x
y+
z
18. y
z -
x
19. 2
x +
3y
- z
20
. 2(x
+ z
) -
y
21. 5
z +
(y
- x
)
22. 5
x -
(y
+ 2
z)
23. x
2 +
y2
- 1
0z
24. z
3 +
(y2
- 4
x)
25.
y +
xz
−
2
26.
3y +
x2
−
z
1-2
Skill
s Pr
acti
ceO
rder
of
Op
era
tio
ns
6321
2216
4125
1226
124
1042
5118
3310
1716
7067
1320
6481
125
27
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Answers (Lesson 1-2)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A5A01_A14_ALG1_A_CRM_C01_AN_660498.indd A5 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
14
Gle
ncoe
Alg
ebra
1
Eva
luat
e ea
ch e
xpre
ssio
n.
1. 1
12 2.
83
3. 5
4
4. (
15 -
5)
․
2
5. 9
․ (
3 +
4)
6.
5 +
7 ․
4
7. 4
(3 +
5)
- 5
․ 4
8.
22
÷ 1
1 ․
9 -
32
9.
62
+ 3
․ 7
- 9
10. 3
[10
- (
27 ÷
9)]
11
. 2[5
2 +
(36
÷ 6
)]
12. 1
62 ÷
[6(
7 -
4)2 ]
13.
52 ․ 4
- 5
․ 4
2
−
5(4)
14.
(2 ․
5)2
+ 4
−
32 -
5
15
. 7
+ 32
−
42 · 2
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
= 1
2, b
= 9
, an
d c
= 4
.
16. a
2 +
b -
c2
17
. b2
+ 2
a -
c2
18. 2
c(a
+ b
)
19. 4
a +
2b
- c
2
20. (
a2 ÷
4b)
+ c
21
. c2
· (2b
- a
)
22.
bc2 +
a
−
c
23.
2c3 -
ab
−
4
24. 2
(a
- b)
2
-
5c
25
. b2
- 2c
2 −
a +
c
- b
26. C
AR
REN
TAL
An
n C
arly
le i
s pl
ann
ing
a bu
sin
ess
trip
for
wh
ich
sh
e n
eeds
to
ren
t a
car.
Th
e ca
r re
nta
l co
mpa
ny
char
ges
$36
per
day
plu
s $0
.50
per
mil
e ov
er 1
00 m
iles
. Su
ppos
e M
s. C
arly
le r
ents
th
e ca
r fo
r 5
days
an
d dr
ives
180
mil
es.
a. W
rite
an
exp
ress
ion
for
how
mu
ch i
t w
ill
cost
Ms.
Car
lyle
to
ren
t th
e ca
r.
b.
Eva
luat
e th
e ex
pres
sion
to
dete
rmin
e h
ow m
uch
Ms.
Car
lyle
mu
st p
ay t
he
car
ren
tal
com
pan
y.
27. G
EOM
ETRY
Th
e le
ngt
h o
f a
rect
angl
e is
3n
+ 2
an
d it
s w
idth
is
n -
1. T
he
peri
met
er
of t
he
rect
angl
e is
tw
ice
the
sum
of
its
len
gth
an
d it
s w
idth
.
a. W
rite
an
exp
ress
ion
th
at r
epre
sen
ts t
he
peri
met
er o
f th
e re
ctan
gle.
b.
Fin
d th
e pe
rim
eter
of
the
rect
angl
e w
hen
n =
4 i
nch
es.
1-2
Prac
tice
O
rder
of
Op
era
tio
ns
2063
33
129
48
2162
3
126
137
89
168
50
896
395
7
5(36
) +
0.5
(180
- 1
00)
$220
.00
2[(3
n +
2)
+ (
n -
1)]
34 in
.
1 −
2
-2
121
512
625
013_
023_
ALG
1_A
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M_C
01_C
R_6
6049
8.in
dd
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/21/
10
5:20
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-2
Cha
pte
r 1
15
Gle
ncoe
Alg
ebra
1
1. S
CH
OO
LS J
effe
rson
Hig
h S
choo
l h
as
100
less
th
an 5
tim
es a
s m
any
stu
den
ts
as T
aft
Hig
h S
choo
l. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n t
o fi
nd
the
nu
mbe
r of
st
ude
nts
at
Jeff
erso
n H
igh
Sch
ool
if T
aft
Hig
h S
choo
l h
as 3
00 s
tude
nts
.
2. G
EOG
RA
PHY
Gu
adal
upe
Pea
k in
Tex
as
has
an
alt
itu
de t
hat
is
671
feet
mor
e th
an d
oubl
e th
e al
titu
de o
f M
oun
t S
un
flow
er i
n K
ansa
s. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n f
or t
he
alti
tude
of
Gu
adal
upe
Pea
k if
Mou
nt
Su
nfl
ower
has
an
alt
itu
de o
f 40
39 f
eet.
3. T
RA
NSP
OR
TATI
ON
Th
e P
laid
Tax
i C
ab
Com
pan
y ch
arge
s $1
.75
per
pass
enge
r pl
us
$3.4
5 pe
r m
ile
for
trip
s le
ss t
han
10
mil
es. W
rite
an
d ev
alu
ate
an
expr
essi
on t
o fi
nd
the
cost
for
Max
to
take
a P
laid
tax
i 8
mil
es t
o th
e ai
rpor
t.
4. G
EOM
ETRY
Th
e ar
ea o
f a
circ
le i
s re
late
d to
th
e ra
diu
s of
th
e ci
rcle
su
ch
that
th
e pr
odu
ct o
f th
e sq
uar
e of
th
e ra
diu
s an
d a
nu
mbe
r π
giv
es t
he
area
. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n f
or t
he
area
of
a ci
rcu
lar
pizz
a be
low
. A
ppro
xim
ate
π a
s 3.
14.
7 in
.
5.B
IOLO
GY
Lav
ania
is
stu
dyin
g th
e gr
owth
of
a po
pula
tion
of
fru
it f
lies
in
her
la
bora
tory
. Sh
e n
otic
es t
hat
th
e n
um
ber
of f
ruit
fli
es i
n h
er e
xper
imen
t is
fiv
e ti
mes
as
larg
e af
ter
any
six-
day
peri
od.
Sh
e ob
serv
es 2
0 fr
uit
fli
es o
n O
ctob
er 1
. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n t
o pr
edic
t th
e po
pula
tion
of
fru
it f
lies
L
avan
ia w
ill
obse
rve
on O
ctob
er 3
1.
6. C
ON
SUM
ER S
PEN
DIN
G D
uri
ng
a lo
ng
wee
ken
d, D
evon
pai
d a
tota
l of
x d
olla
rs
for
a re
nta
l ca
r so
he
cou
ld v
isit
his
fa
mil
y. H
e re
nte
d th
e ca
r fo
r 4
days
at
a ra
te o
f $3
6 pe
r da
y. T
her
e w
as a
n
addi
tion
al c
har
ge o
f $0
.20
per
mil
e af
ter
the
firs
t 20
0 m
iles
dri
ven
.
a. W
rite
an
alg
ebra
ic e
xpre
ssio
n t
o re
pres
ent
the
amou
nt
Dev
on p
aid
for
addi
tion
al m
ilea
ge o
nly
.
b.
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
repr
esen
t th
e n
um
ber
of m
iles
ove
r 20
0 m
iles
th
at D
evon
dro
ve t
he
ren
ted
car.
c. H
ow m
any
mil
es d
id D
evon
dri
ve
over
all
if h
e pa
id a
tot
al o
f $1
74 f
or
the
car
ren
tal?
1-2
Wor
d Pr
oble
m P
ract
ice
Ord
er
of
Op
era
tio
ns
5t -
10
0; 1
400
stu
den
ts
2n +
671
; 87
49 f
t
$1.7
5 +
$3.
45m
; $2
9.35
πr2 ;
153
.86
in 2
20 ×
55 ;
62,
500
fl ies
x -
(36
× 4
)
350
mi
x -
(36
× 4
)
−
0.20
013_
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Answers (Lesson 1-2)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A6A01_A14_ALG1_A_CRM_C01_AN_660498.indd A6 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
16
Gle
ncoe
Alg
ebra
1
Th
e F
ou
r D
igit
s P
rob
lem
On
e w
ell-
know
n m
ath
emat
ics
prob
lem
is
to w
rite
exp
ress
ion
s fo
r co
nse
cuti
ve n
um
bers
be
gin
nin
g w
ith
1. O
n t
his
pag
e, y
ou w
ill
use
th
e di
gits
1, 2
, 3, a
nd 4
. Eac
h di
git
is u
sed
only
on
ce. Y
ou m
ay u
se a
ddit
ion,
su
btra
ctio
n, m
ult
ipli
cati
on (
not
div
isio
n),
expo
nen
ts, a
nd
pare
nth
eses
in
an
y w
ay y
ou w
ish.
Als
o, y
ou c
an u
se t
wo
digi
ts t
o m
ake
one
num
ber,
such
as
12 o
r 34
.
Exp
ress
eac
h n
um
ber
as
a co
mb
inat
ion
of
the
dig
its
1, 2
, 3, a
nd
4.
1 =
(3
× 1
) -
(4
- 2
) 18
=
35
= 2
(4+
1) +
3
2 =
19 =
3(2
+ 4
) +
1
36 =
3 =
20 =
37 =
4 =
21 =
38 =
5 =
22 =
39 =
6 =
23 =
31
- (
4 ×
2)
40 =
7 =
24 =
41 =
8 =
25 =
42 =
9 =
26 =
43 =
42
+ 1
3
10 =
27 =
44 =
11 =
28 =
45 =
12 =
29 =
46 =
13 =
30
=
47
=
14 =
31 =
48 =
15 =
32 =
49 =
16 =
33 =
50 =
17 =
34 =
Doe
s a
calc
ula
tor
hel
p in
sol
vin
g th
ese
type
s of
pu
zzle
s? G
ive
reas
ons
for
you
r op
inio
n.
1-2
Enri
chm
ent
An
swer
s w
ill v
ary.
Sam
ple
an
swer
s ar
e g
iven
.
(4 -
3)
+ (
2 -
1)
34 +
(2
× 1
)
21 -
(4
- 3
)
4 +
3 +
1 -
2
3(4
- 1)
- 2
(2 +
4)
× (
3 +
1)
(2 +
3)
× (
4 +
1)
An
swer
s w
ill v
ary.
Usi
ng
a c
alcu
lato
r is
a g
oo
d w
ay t
o c
hec
k yo
ur
solu
tio
ns.
4 +
3 +
2 +
1
(4 -
3)
+ (
2 ×
1)
(4 -
2)
+ (
3 -
1)
(4 -
2)
+ (
3 ×
1)
4 +
3 +
2 -
1
4 +
2 +
(3
× 1
)24
+
(3
- 1
)
21 +
3 +
4
2(4 +
1)
- 3
(2 ×
3)
× (
4 +
1)
34 -
(2
+
1)
42 ×
(3
- 1
)
21 +
(3
× 4
)
2 ×
(14
+
3)
43 +
(2
- 1
)
43 +
(2
× 1
)
43 +
(2
+
1)
31 +
42
42 ×
(3
× 1
)
41 +
23
41 +
32
(2 ×
3)
× (
4 -
1)
(4 +
3)
× (
2 +
1)
(4 ×
3) +
(2
- 1
)
(4 ×
3)
× (
2 -
1)
(4 ×
3) +
(2
× 1
)
(4 ×
3) -
(2
- 1
)
2(3
+ 4)
+
1
(4 ×
2)
× (
3 -
1)
3(2
+ 4)
- 1
21 +
(4
- 3
)
32 ×
(4
- 1
)
31 +
2
+ 4
42 -
(3
+
1)
42 -
(3
× 1
)
41 -
(3
- 2
)
43 -
(2
× 1
)
43 -
(2
- 1
)
013_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-2
Cha
pte
r 1
17
Gle
ncoe
Alg
ebra
1
Wh
en e
valu
atin
g al
gebr
aic
expr
essi
ons,
it
is s
omet
imes
hel
pfu
l to
use
th
e st
ore
key
on t
he
calc
ula
tor,
espe
cial
ly t
o ch
eck
solu
tion
s, e
valu
ate
seve
ral
expr
essi
ons
for
the
sam
e va
lues
of
vari
able
s, o
r ev
alu
ate
the
sam
e ex
pres
sion
for
mu
ltip
le v
alu
es o
f th
e va
riab
les.
E
valu
ate
a2 -
4a
+
6
if a
=
8.
Fir
st, o
pen
a n
ew C
alcu
lato
r pa
ge o
n t
he
TI-
Nsp
ire.
Th
en, d
elet
e an
y in
stan
ces
of s
tore
d va
riab
les
by
ente
rin
g C
LE
AR
AZ
.
Sto
re 8
as
the
valu
e fo
r a.
Fin
ally
en
ter
the
expr
essi
on, i
ncl
udi
ng
the
vari
able
s, t
o ev
alu
ate.
Th
e an
swer
is
38.
Exer
cise
s
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
= 4
, b =
6, x
= 8
, an
d y
= 1
2. E
xpre
ss a
nsw
ers
as
inte
gers
or
frac
tion
s.
1. b
x -
ay
÷
b
2. a
[ x
+ (y
÷
a)
2 ]
3. a
3 -
(y
- b
)2 +
x2
4.
b +
a2
−
x2 -
b2
5. 2a
(x -
b)
−
xy
- 9b
6.
b3 -
[3(
a +
b2 )
+
5b
]
−−
y ÷
a(
x -
1)
E
valu
ate
xy -
4y
−
5x i
f x
= 4
an
d y
= 1
2.
En
ter
4 as
th
e va
lue
for
x an
d 12
as
the
valu
e fo
r y.
Eva
luat
e th
e ex
pres
sion
. Th
e T
I-N
spir
e w
ill
disp
lay
the
answ
er
as a
fra
ctio
n.
Th
e an
swer
is
228
−
5 .
1-2
TI-N
spir
e® A
ctiv
ity
Usin
g t
he S
tore
Key
Exam
ple
1
Exam
ple
2
4
0 68
92
8 −
21
22
−
7 11
−
14
013_
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Answers (Lesson 1-2)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A7A01_A14_ALG1_A_CRM_C01_AN_660498.indd A7 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
18
Gle
ncoe
Alg
ebra
1
E
valu
ate
24 �
1 -
8 +
5(9
÷ 3
- 3
). N
ame
the
pro
per
ty u
sed
in
eac
h s
tep
.24
․ 1
- 8
+ 5
(9 ÷
3 -
3)
= 2
4 ․
1 -
8 +
5(3
- 3
) Su
bstitu
tion; 9 ÷
3 =
3
=
24
․
1 -
8 +
5(0
)
Substitu
tion; 3 -
3 =
0
=
24
- 8
+ 5
(0)
M
ultip
licative
Identity
; 24 ․
1 =
24
=
24
- 8
+ 0
Multip
licative
Pro
pert
y o
f Z
ero
; 5(0
) =
0
=
16
+ 0
Substitu
tion; 24 -
8 =
16
=
16
A
dditiv
e I
dentity
; 16 +
0 =
16
Exer
cise
sE
valu
ate
each
exp
ress
ion
. Nam
e th
e p
rop
erty
use
d i
n e
ach
ste
p.
1. 2
[ 1 −
4 + ( 1
−
2 ) 2 ]
2.
15
․
1 -
9 +
2(1
5 ÷
3 -
5)
3. 2
(3 ․
5 ․
1 -
14)
- 4
․ 1 −
4 4.
18
․
1 -
3 ․
2 +
2(6
÷ 3
- 2
)
1-3
Stud
y G
uide
and
Inte
rven
tion
Pro
pert
ies o
f N
um
bers
Iden
tity
an
d E
qu
alit
y Pr
op
erti
es T
he
iden
tity
an
d eq
ual
ity
prop
erti
es i
n t
he
char
t be
low
can
hel
p yo
u s
olve
alg
ebra
ic e
quat
ion
s an
d ev
alu
ate
mat
hem
atic
al e
xpre
ssio
ns.
Ad
dit
ive
Iden
tity
Fo
r a
ny n
um
be
r a,
a +
0 =
a.
Ad
dit
ive
Inve
rse
Fo
r a
ny n
um
be
r a,
a +
(-
a) =
0.
Mu
ltip
licat
ive
Iden
tity
Fo
r a
ny n
um
be
r a,
a .
1 =
a.
Mu
ltip
licat
ive
Pro
per
ty o
f 0
Fo
r a
ny n
um
be
r a,
a .
0 =
0.
Mu
ltip
licat
ive
Inve
rse
Pro
per
tyF
or
eve
ry n
um
be
r a −
b ,
wh
ere
a,
b ≠
0,
the
re is e
xactly
on
e n
um
be
r b
−
a su
ch
th
at
a −
b .
b
−
a = 1.
Refl
exi
ve P
rop
erty
Fo
r a
ny n
um
be
r a,
a =
a.
Sym
met
ric
Pro
per
tyF
or
any n
um
be
rs a
an
d b
, if a
= b
, th
en
b =
a.
Tran
siti
ve P
rop
erty
Fo
r a
ny n
um
be
rs a
, b
, a
nd
c,
if a
= b
an
d b
= c
, th
en
a =
c.
Su
bst
ituti
on
Pro
per
tyIf
a =
b,
the
n a
may b
e r
ep
lace
d b
y b
in
any e
xp
ressio
n.
Exam
ple
= 2
(15
�
1 -
14)
- 4
� 1 −
4 S
ub
st.
= 1
8 �
1 -
3 �
2 +
2(2
- 2
) S
ub
st.
= 2
(15
- 1
4) -
4 �
1 −
4 M
ult
. Id
enti
ty
= 1
8 �
1 -
3 �
2 +
2(0
) S
ub
stitu
tio
n
= 2
(1)
- 4
� 1 −
4 S
ub
stitu
tio
n
= 1
8 -
3 �
2 +
2(0
) M
ult
. Id
enti
ty
= 2
- 4
� 1 −
4 M
ult
. Id
enti
ty
= 1
8 -
6 +
2(0
) S
ub
stitu
tio
n
= 2
- 1
M
ult
. Inv
erse
=
18
- 6
+ 0
M
ult
. Pro
p. Z
ero
= 1
S
ub
stitu
tio
n
= 1
2 +
0
Su
bst
ituti
on
= 1
2 A
dd
. Id
enti
ty
=
2 (
1 −
4 + 1 −
4 )
Su
bst
ituti
on
=
15
�
1 -
9 +
2(5
- 5
) S
ub
stitu
tio
n
=
2 (
1 −
2 )
Su
bst
ituti
on
=
15
�
1 -
9 +
2(0)
S
ub
stitu
tio
n
=
1
Mu
lt. I
nver
se
= 1
5 �
1 -
9 +
0
Mu
lt. P
rop
. Zer
o
=
15
- 9
+ 0
Mu
lt. I
den
tity
=
6 -
0
S
ub
stitu
tio
n
= 6
Su
bst
ituti
on
013_
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-3
Cha
pte
r 1
19
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Pro
pert
ies o
f N
um
bers
1-3
Co
mm
uta
tive
an
d A
sso
ciat
ive
Pro
per
ties
Th
e C
omm
uta
tive
an
d A
ssoc
iati
ve
Pro
pert
ies
can
be
use
d to
sim
plif
y ex
pres
sion
s. T
he
Com
mu
tati
ve P
rope
rtie
s st
ate
that
th
e or
der
in w
hic
h y
ou a
dd o
r m
ult
iply
nu
mbe
rs d
oes
not
ch
ange
th
eir
sum
or
prod
uct
. Th
e A
ssoc
iati
ve P
rope
rtie
s st
ate
that
th
e w
ay y
ou g
rou
p th
ree
or m
ore
nu
mbe
rs w
hen
add
ing
or
mu
ltip
lyin
g do
es n
ot c
han
ge t
hei
r su
m o
r pr
odu
ct.
E
valu
ate
6 �
2 �
3 �
5
usi
ng
pro
per
ties
of
nu
mb
ers.
Nam
e th
e p
rop
erty
use
d i
n e
ach
ste
p.
6 ․
2 ․
3 ․
5 =
6 ․
3 ․
2 ․
5
Com
muta
tive
Pro
pert
y
=
(6
․
3)(
2 ․
5)
Associa
tive
Pro
pert
y
=
18
․ 1
0 M
ultip
ly.
=
18
0 M
ultip
ly.
Th
e pr
odu
ct i
s 18
0.
E
valu
ate
8.2
+ 2
.5 +
2.5
+ 1
.8 u
sin
g p
rop
erti
es o
f n
um
ber
s. N
ame
the
pro
per
ty u
sed
in
ea
ch s
tep
.8.
2 +
2.5
+ 2
.5 +
1.8
=
8.2
+ 1
.8 +
2.5
+ 2
.5
Com
muta
tive
Pro
p.
=
(8.
2 +
1.8
) +
(2.
5 +
2.5
) As
socia
tive
Pro
p.
=
10
+ 5
A
dd.
=
15
Add.
Th
e su
m i
s 15
.
Exer
cise
sE
valu
ate
each
exp
ress
ion
usi
ng
pro
per
ties
of
nu
mb
ers.
Nam
e th
e p
rop
erty
use
d i
n
each
ste
p.
1. 1
2 +
10
+ 8
+ 5
2.
16
+ 8
+ 2
2 +
12
3.
10
․
7 ․
2.5
4. 4
․ 8
․ 5
․ 3
5.
12
+ 2
0 +
10
+ 5
6.
26
+ 8
+ 4
+ 2
2
7. 3
1 −
2 + 4
+ 2
1 −
2 + 3
8.
3 −
4 ․ 1
2 ․
4 ․
2
9. 3
.5 +
2.4
+ 3
.6 +
4.2
10. 4
1 −
2 + 5
+ 1 −
2 + 3
11
. 0.5
․ 2
.8 ․
4
12. 2
.5 +
2.4
+ 2
.5 +
3.6
13.
4 −
5 ․ 1
8 ․
25
․
2 −
9
14. 3
2 ․
1 −
5 ․ 1 −
2 ․ 1
0
15.
1 −
4 ․ 7
․ 1
6 ․
1 −
7
16. 3
.5 +
8 +
2.5
+ 2
17
. 18
․
8 ․
1 −
2 ․ 1 −
9 18
. 3 −
4 ․ 1
0 ․
16
․
1 −
2
Exam
ple
1Ex
amp
le 2
3558
175
480
4760
1372
13.7
135.
611
8032
4
168
60
Pro
per
ties
will
var
y. S
ee s
tud
ents
’ wo
rk.
Co
mm
uta
tive
Pro
per
ties
Fo
r a
ny n
um
be
rs a
an
d b
, a
+ b
= b
+ a
an
d a
� b
= b
� a
.
Ass
oci
ativ
e P
rop
erti
esF
or
any n
um
be
rs a
, b
, a
nd
c,
(a +
b)
+ c
= a
+ (
b +
c )
an
d (
ab)c
= a
(bc)
.
013_
023_
ALG
1_A
_CR
M_C
01_C
R_6
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8.in
dd
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/21/
10
5:20
PM
Answers (Lesson 1-3)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A8A01_A14_ALG1_A_CRM_C01_AN_660498.indd A8 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
20
Gle
ncoe
Alg
ebra
1
Eva
luat
e ea
ch e
xpre
ssio
n. N
ame
the
pro
per
ty u
sed
in
eac
h s
tep
.
1. 7
(16
÷ 4
2 )
2. 2
[5 -
(15
÷ 3
)]
3. 4
- 3
[7 -
(2
․
3)]
4.
4[8
- (
4 ․
2)]
+ 1
5. 6
+ 9
[10
- 2
(2 +
3)]
6.
2(6
÷ 3
- 1
) ․
1 −
2
7. 1
6 +
8 +
14
+ 1
2
8. 3
6 +
23
+ 1
4 +
7
9. 5
․ 3
․ 4
․ 3
10
. 2 ․
4 ․
5 ․
3
1-3
Skill
s Pr
acti
ceP
rop
ert
ies o
f N
um
bers
=
7(1
6 ÷
16
) S
ub
stit
uti
on
=
2(5
- 5
) S
ub
stit
uti
on
=
7(1
) S
ub
stit
uti
on
=
2(0
) S
ub
stit
uti
on
=
7
Mu
ltip
licat
ive
Iden
tity
=
0
Mu
lt. P
rop
. of
Zer
o
=
4 -
3(7
- 6
) S
ub
stit
uti
on
= 4
(8 -
8)
+ 1
Su
bst
itu
tio
n
= 4
- 3
(1)
Su
bst
itu
tio
n
=
4(0
) +
1
Su
bst
itu
tio
n
= 4
- 3
M
ult
iplic
ativ
e Id
enti
ty
= 0
+ 1
M
ult
. Pro
p. o
f Z
ero
=
1
Su
bst
itu
tio
n
=
1
Ad
dit
ive
Iden
tity
=
6 +
9[1
0 -
2(5
)] S
ub
stit
uti
on
=
2(2
- 1
) �
1 −
2 Su
bst
itu
tio
n
= 6
+ 9
(10
- 1
0)
Su
bst
itu
tio
n
= 2
(1)
�
1 −
2
Su
bst
itu
tio
n
=
6 +
9(0
) S
ub
stit
uti
on
= 6
+ 0
Mu
lt. P
rop
. of
Zer
o
= 2
� 1 −
2
Mu
ltip
licat
ive
Iden
tity
=
6
Ad
dit
ive
Iden
tity
=
1
M
ult
iplic
ativ
e In
vers
e
=
16
+ 1
4 +
8 +
12
C
om
mu
tativ
e (+
) =
36
+ 1
4 +
23
+ 7
C
om
mu
tativ
e (+
)
= (
16 +
14)
+ (
8 +
12)
Ass
oci
ativ
e (+
) =
(36
+ 1
4) +
(23
+ 7
)
A
sso
ciat
ive
(+)
=
30
+ 2
0 o
r 50
S
ub
stit
uti
on
=
50
+ 3
0 o
r 80
Su
bst
ituti
on
=
5 ·
4 · 3
· 3
C
om
mu
tativ
e (×
)
= 2
· 5
· 4 ·
3
Co
mm
uta
tive
(×)
=
(5
· 4)
· (3
· 3) A
sso
ciat
ive
(×)
=
(2
· 5)
· (4
· 3)
Ass
oci
ativ
e (×
)
= 2
0 · 9
or
180
Su
bst
ituti
on
=
10
· 12
or
120
Su
bst
ituti
on
013_
023_
ALG
1_A
_CR
M_C
01_C
R_6
6049
8.in
dd
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/21/
10
5:20
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-3
Cha
pte
r 1
21
Gle
ncoe
Alg
ebra
1
Eva
luat
e ea
ch e
xpre
ssio
n. N
ame
the
pro
per
ty u
sed
in
eac
h s
tep
.
1. 2
+ 6
(9 -
32 )
- 2
2.
5(1
4 -
39
÷ 3
) +
4 ․
1 −
4
Eva
luat
e ea
ch e
xpre
ssio
n u
sin
g p
rop
erti
es o
f n
um
ber
s. N
ame
the
pro
per
ty u
sed
in
ea
ch s
tep
.
3. 1
3 +
23
+ 1
2 +
7
4. 6
․ 0
.7 ․
5
5. S
ALE
S A
lth
ea p
aid
$5.0
0 ea
ch f
or t
wo
brac
elet
s an
d la
ter
sold
eac
h f
or $
15.0
0. S
he
paid
$8
.00
each
for
th
ree
brac
elet
s an
d so
ld e
ach
of
them
for
$9.
00.
a.
Wri
te a
n e
xpre
ssio
n t
hat
rep
rese
nts
th
e pr
ofit
Alt
hea
mad
e.
b
. Eva
luat
e th
e ex
pres
sion
. Nam
e th
e pr
oper
ty u
sed
in e
ach
ste
p.
6. S
CH
OO
L SU
PPLI
ES K
rist
en p
urc
has
ed t
wo
bin
ders
th
at c
ost
$1.2
5 ea
ch, t
wo
bin
ders
th
at c
ost
$4.7
5 ea
ch, t
wo
pack
ages
of
pape
r th
at c
ost
$1.5
0 pe
r pa
ckag
e, f
our
blu
e pe
ns
that
cos
t $1
.15
each
, an
d fo
ur
pen
cils
th
at c
ost
$0.3
5 ea
ch.
a.
Wri
te a
n e
xpre
ssio
n t
o re
pres
ent
the
tota
l co
st o
f su
ppli
es b
efor
e ta
x.
b
. Wh
at w
as t
he
tota
l co
st o
f su
ppli
es b
efor
e ta
x?
1-3
Prac
tice
Pro
pert
ies o
f N
um
bers
2(15
-
5)
+
3(
9 -
8)
2(15
− 5
) + 3(
9 -
8)
= 2
(10)
+
3(
1)
=
20
+ 3(
1)
=
20
+ 3
= 2
3
= (
13 +
12
) + (2
3 +
7)
C
om
mu
. Pro
p.
= 2
5 +
30
S
ub
stitu
tio
n=
55
Su
bst
ituti
on
2(1.
25 +
4.7
5 +
1.5
0) +
4(1
.15
+ 0
.35)
= 2
+ 6
(9 -
9)
- 2
S
ub
stitu
tio
n=
2 +
6(0
) -
2
S
ub
stitu
tio
n=
2 +
0 -
2
Mu
lt. P
rop
. of
Zer
o=
2 -
2
Ad
dit
ive
Iden
tity
= 0
S
ub
stitu
tio
n
= 5
(14
- 1
3) +
4 �
1 −
4 S
ub
stitu
tio
n
= 5
(1)
+ 4
� 1 −
4
Su
bst
ituti
on
= 5
+ 4
� 1 −
4 M
ult
iplic
ativ
e Id
enti
ty
= 5
+ 1
M
ult
iplic
ativ
e In
vers
e=
6
Su
bst
ituti
on
$21.
00
= (
6 .
5) .
(0
.7)
Ass
oc.
Pro
p.
= 3
0 .
0.
7 S
ub
stitu
tio
n=
21
Su
bst
ituti
on
Su
bst
ituti
on
S
ub
stitu
tio
n
Mu
ltip
licat
ive
Iden
tity
S
ub
stitu
tio
n
013_
023_
ALG
1_A
_CR
M_C
01_C
R_6
6049
8.in
dd
2112
/21/
10
5:20
PM
Answers (Lesson 1-3)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A9A01_A14_ALG1_A_CRM_C01_AN_660498.indd A9 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
1.EX
ERC
ISE
An
nik
a go
es o
n a
wal
k ev
ery
day
in o
rder
to
get
the
exer
cise
her
do
ctor
rec
omm
ends
. If
she
wal
ks a
t a
r
ate
of 3
mil
es p
er h
our
for
1−
3 o
f an
hou
r,
th
en s
he
wil
l h
ave
wal
ked
3 ×
1−
3 m
iles
.
Eva
luat
e th
e ex
pres
sion
an
d n
ame
the
prop
erty
use
d.
2. S
CH
OO
L SU
PPLI
ES A
t a
loca
l sc
hoo
l su
pply
sto
re, a
hig
hli
ghte
r co
sts
$1.2
5, a
ba
llpo
int
pen
cos
ts $
0.80
, an
d a
spir
al
not
eboo
k co
sts
$2.7
5. U
se m
enta
l m
ath
an
d th
e A
ssoc
iati
ve P
rope
rty
of A
ddit
ion
to
fin
d th
e to
tal
cost
if
one
of e
ach
ite
m i
s pu
rch
ased
.
3. M
ENTA
L M
ATH
Th
e tr
ian
gula
r ba
nn
er
has
a b
ase
of 9
cen
tim
eter
s an
d a
hei
ght
of 6
cen
tim
eter
s. U
sin
g th
e fo
rmu
la f
or
area
of
a tr
ian
gle,
th
e ba
nn
er’s
are
a ca
n
b
e ex
pres
sed
as 1 −
2 × 9
×
6. G
abri
elle
f
inds
it
easi
er t
o w
rite
an
d ev
alu
ate
(
1 −
2 × 6
)
× 9
to f
ind
the
area
. Is
G
abri
elle
’s e
xpre
ssio
n e
quiv
alen
t to
th
e ar
ea f
orm
ula
? E
xpla
in.
b
h
4.A
NA
TOM
Y T
he
hu
man
bod
y h
as 6
0 bo
nes
in
th
e ar
ms
and
han
ds, 8
4 bo
nes
in
th
e u
pper
bod
y an
d h
ead,
an
d 62
bon
es
in t
he
legs
an
d fe
et. U
se t
he
Ass
ocia
tive
P
rope
rty
to w
rite
an
d ev
alu
ate
an
expr
essi
on t
hat
rep
rese
nts
th
e to
tal
nu
mbe
r of
bon
es i
n t
he
hu
man
bod
y.
5. T
OLL
RO
AD
S S
ome
toll
hig
hw
ays
asse
ss t
olls
bas
ed o
n w
her
e a
car
ente
red
and
exit
ed. T
he
tabl
e be
low
sh
ows
the
hig
hw
ay t
olls
for
a c
ar e
nte
rin
g an
d ex
itin
g at
a v
arie
ty o
f ex
its.
Ass
um
e th
at
the
toll
for
th
e re
vers
e di
rect
ion
is
the
sam
e.
En
tere
dE
xite
dTo
ll
Exit 5
Exit 8
$0
.50
Exit 8
Exit 1
0$
0.2
5
Exit 1
0E
xit 1
5$
1.0
0
Exit 1
5E
xit 1
8$
0.5
0
Exit 1
8E
xit 2
2$
0.7
5
a.
Ru
nn
ing
an e
rran
d, J
uli
o tr
avel
s fr
om
Exi
t 8
to E
xit
5. W
hat
pro
pert
y w
ould
yo
u u
se t
o de
term
ine
the
toll
?
b
. Gor
don
tra
vels
fro
m h
ome
to w
ork
and
back
eac
h d
ay. H
e li
ves
at E
xit
15 o
n
the
toll
roa
d an
d w
orks
at
Exi
t 22
. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n t
o fi
nd
his
dai
ly t
oll
cost
. Wh
at p
rope
rty
or p
rope
rtie
s di
d yo
u u
se?
Wor
d Pr
oble
m P
ract
ice
Pro
pert
ies o
f N
um
bers
1-3
Cha
pte
r 1
22
Gle
ncoe
Alg
ebra
1
1
mi;
Mu
ltip
licat
ive
Inve
rse
Sym
met
ric
Pro
per
ty o
f E
qu
alit
y
t =
2 ×
($0
.50
+ $0
.75)
;
t =
$2.
50;
Su
bst
ituti
on
Sam
ple
an
swer
: (6
0 +
84
) + 62
=84
+
(6
0 +
62
) =
206
$4.8
0
Y
es;
the
Co
mm
uta
tive
an
d
Ass
oci
ativ
e P
rop
erti
es o
f M
ult
iplic
atio
n a
llow
it t
o b
e re
wri
tten
.
013_
023_
ALG
1_A
_CR
M_C
01_C
R_6
6049
8.in
dd
2212
/21/
10
5:20
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-3
Cha
pte
r 1
23
Gle
ncoe
Alg
ebra
1
Pro
pert
ies o
f O
pera
tio
ns
Let
’s m
ake
up
a n
ew o
per
atio
n a
nd
den
ote
it b
y �
, so
that
a �
b
mea
ns
ba.
2 �
3 =
32
= 9
(1 �
2)
�
3 =
21
�
3 =
32
= 9
1. W
hat
nu
mbe
r is
rep
rese
nte
d by
2 �
3?
2. W
hat
nu
mbe
r is
rep
rese
nte
d by
3 �
2?
3. D
oes
the
oper
atio
n �
app
ear
to b
e co
mm
uta
tive
?
4. W
hat
nu
mbe
r is
rep
rese
nte
d by
(2
�
1)
�
3?
5. W
hat
nu
mbe
r is
rep
rese
nte
d by
2 �
(1
�
3)?
6. D
oes
the
oper
atio
n �
app
ear
to b
e as
soci
ativ
e?
Let
’s m
ake
up
an
oth
er o
per
atio
n a
nd
den
ote
it b
y ⊕
, so
that
a ⊕
b =
(a
+ 1
)(b
+ 1
).
3 ⊕
2 =
(3
+ 1
)(2
+ 1
) =
4 ․
3 =
12
(1 ⊕
2)
⊕ 3
= (
2 ․
3)
⊕ 3
= 6
⊕ 3
= 7
․ 4
= 2
8
7. W
hat
nu
mbe
r is
rep
rese
nte
d by
2 ⊕
3?
8. W
hat
nu
mbe
r is
rep
rese
nte
d by
3 ⊕
2?
9. D
oes
the
oper
atio
n ⊕
app
ear
to b
e co
mm
uta
tive
?
10. W
hat
nu
mbe
r is
rep
rese
nte
d by
(2
⊕ 3
) ⊕
4?
11. W
hat
nu
mbe
r is
rep
rese
nte
d by
2 ⊕
(3
⊕ 4
)?
12. D
oes
the
oper
atio
n ⊕
app
ear
to b
e as
soci
ativ
e?
13. W
hat
nu
mbe
r is
rep
rese
nte
d by
1 �
(3
⊕ 2
)?
14. W
hat
nu
mbe
r is
rep
rese
nte
d by
(1
� 3)
⊕ (
1 �
2)
?
15. D
oes
the
oper
atio
n �
ap
pear
to
be d
istr
ibu
tive
ove
r th
e op
erat
ion
⊕?
16. L
et’s
exp
lore
th
ese
oper
atio
ns
a li
ttle
fu
rth
er. W
hat
nu
mbe
r is
rep
rese
nte
d by
3
� (4
⊕ 2
)?
17. W
hat
nu
mbe
r is
rep
rese
nte
d by
(3
� 4)
⊕ (
3 �
2)
?
18. I
s th
e op
erat
ion
� ac
tual
ly d
istr
ibu
tive
ove
r th
e op
erat
ion
⊕?
1-3
Enri
chm
ent
32 =
9
23 =
8
no
3 9
no
12 12
yes
65 63
no
12
12
yes
3375
585
no
013_
023_
ALG
1_A
_CR
M_C
01_C
R_6
6049
8.in
dd
2312
/21/
10
5:20
PM
Answers (Lesson 1-3)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A10A01_A14_ALG1_A_CRM_C01_AN_660498.indd A10 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
24
Gle
ncoe
Alg
ebra
1
Eval
uat
e Ex
pre
ssio
ns
Th
e D
istr
ibu
tive
Pro
pert
y ca
n b
e u
sed
to h
elp
eval
uat
e ex
pres
sion
s.
Dis
trib
uti
ve P
rop
erty
Fo
r a
ny n
um
be
rs a
, b
, a
nd
c,
a(b
+ c
) =
ab
+ a
c a
nd
(b
+ c
)a =
ba
+ c
a a
nd
a(b
- c
) =
ab
- a
c a
nd
(b
- c
)a =
ba
- c
a.
U
se t
he
Dis
trib
uti
ve P
rop
erty
to
rew
rite
6(8
+ 10
). T
hen
eva
luat
e.
6(8
+ 1
0) =
6 ․
8 +
6 ․
10
Dis
trib
utive
Pro
pert
y
=
48
+ 6
0 M
ultip
ly.
=
108
A
dd.
U
se t
he
Dis
trib
uti
ve P
rop
erty
to
rew
rite
-2(
3x2
+ 5
x +
1).
T
hen
sim
pli
fy.
-2(
3x2
+ 5
x +
1)
= -
2(3x
2 ) +
(-
2)(5
x) +
(-
2)(1
) D
istr
ibutive
Pro
pert
y
= -
6x2
+ (
-10
x) +
(-
2)
Multip
ly.
= -
6x2
- 1
0x -
2
Sim
plif
y.
Exer
cise
sU
se t
he
Dis
trib
uti
ve P
rop
erty
to
rew
rite
eac
h e
xpre
ssio
n. T
hen
eva
luat
e.
1. 2
0(31
) 2.
12
� 4
1 −
2 3.
5(3
11)
4. 5
(4x
- 9
)
5. 3
(8 -
2x)
6.
12
(6 -
1 −
2 x )
7. 1
2 (2
+ 1 −
2 x )
8. 1 −
4 (12
- 4
t)
9. 3
(2x
- y
)
10. 2
(3x
+ 2
y -
z)
11. (
x -
2)y
12
. 2(3
a -
2b
+ c
)
13.
1 −
4 (16x
- 1
2y +
4z)
14
. (2
- 3
x +
x2 )
3 15
. -2(
2x2
+ 3
x +
1)
1-4
Stud
y G
uide
and
Inte
rven
tion
Th
e D
istr
ibu
tive P
rop
ert
y
Exam
ple
1
Exam
ple
2
20x -
45
24 -
6x
72 -
6x
24 +
6x
3 -
t6x
- 3
y
6
x +
4y -
2z
xy -
2y
6a -
4b
+ 2
c
4
x -
3y +
z
6 -
9x +
3x
2 -
4x2
- 6
x -
2
620
5415
55
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-4
Cha
pte
r 1
25
Gle
ncoe
Alg
ebra
1
Sim
plif
y Ex
pre
ssio
ns
A t
erm
is
a n
um
ber,
a va
riab
le, o
r a
prod
uct
or
quot
ien
t of
n
um
bers
an
d va
riab
les.
Lik
e te
rms
are
term
s th
at c
onta
in t
he
sam
e va
riab
les,
wit
h
corr
espo
ndi
ng
vari
able
s h
avin
g th
e sa
me
pow
ers.
Th
e D
istr
ibu
tive
Pro
pert
y an
d pr
oper
ties
of
equ
alit
ies
can
be
use
d to
sim
plif
y ex
pres
sion
s. A
n e
xpre
ssio
n i
s in
sim
ple
st f
orm
if
it i
s re
plac
ed b
y an
eq
uiv
alen
t ex
pres
sion
wit
h n
o li
ke t
erm
s or
par
enth
eses
.
Sim
pli
fy 4
(a2
+ 3
ab)
- a
b.
4(a2
+ 3
ab)
- a
b =
4(a
2 +
3ab
) -
1ab
M
ultip
licative
Identity
=
4a2
+ 1
2ab
- 1
ab
Dis
trib
utive
Pro
pert
y
=
4a2
+ (
12 -
1)a
b D
istr
ibutive
Pro
pert
y
=
4a2
+ 1
1ab
Substitu
tion
Exer
cise
sS
imp
lify
eac
h e
xpre
ssio
n. I
f n
ot p
ossi
ble
, wri
te s
imp
lifi
ed.
1. 1
2a -
a
2. 3
x +
6x
3.
3x
- 1
4. 2
0a +
12a
- 8
5.
3x2
+ 2
x2 6.
-6x
+ 3
x2 +
10x
2
7. 2
p +
1 −
2 q
8. 1
0xy
- 4
(xy
+ x
y)
9. 2
1a +
18a
+ 3
1b -
3b
10. 4
x +
1 −
4 (16x
- 2
0y)
11. 2
- 1
- 6
x +
x2
12. 4
x2 +
3x2
+ 2
x
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n. T
hen
sim
pli
fy,
ind
icat
ing
the
pro
per
ties
use
d.
13. s
ix t
imes
th
e di
ffer
ence
of
2a a
nd
b, i
ncr
ease
d by
4b
14. t
wo
tim
es t
he
sum
of
x sq
uar
ed a
nd
y sq
uar
ed, i
ncr
ease
d by
th
ree
tim
es t
he
sum
of
x sq
uar
ed a
nd
y sq
uar
ed
1-4
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Th
e D
istr
ibu
tive P
rop
ert
y
Exam
ple
1
1a
9x
sim
plifi
ed
3
2a -
85x
2 -
6x +
13x
2
8
x -
5y
1 -
6x +
x
2 7
x2
+ 2
x
s
imp
lifi e
d
2xy
39a
+ 2
8b
2(x
2 +
y
2 ) +
3(
x2
+ y
2 )
2x2
+ 2y
2 +
3x
2 +
3y
2 D
istr
ibu
tive
Pro
per
ty5x
2 +
5y
2 S
ub
stitu
tio
n
= 6
(2a -
b) +
4b
=
12a
- 6
b +
4b
D
istr
ibu
tive
Pro
per
ty=
12a
- 2
b
Su
bst
ituti
on
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Answers (Lesson 1-4)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A11A01_A14_ALG1_A_CRM_C01_AN_660498.indd A11 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
26
Gle
ncoe
Alg
ebra
1
Use
th
e D
istr
ibu
tive
Pro
per
ty t
o re
wri
te e
ach
exp
ress
ion
. Th
en e
valu
ate.
1. 4
(3 +
5)
2.
2(6
+ 1
0)
3. 5
(7 -
4)
4.
(6
- 2
)8
5. 5
․ 8
9
6. 9
․ 9
9
7. 1
5 ․
104
8.
15 (
2 1 −
3 )
Use
th
e D
istr
ibu
tive
Pro
per
ty t
o re
wri
te e
ach
exp
ress
ion
. Th
en e
valu
ate.
9. (
a +
7)2
10
. 7(h
- 1
0)
11. 3
(m +
n)
12
. 2(x
- y
+ 1
)
Sim
pli
fy e
ach
exp
ress
ion
. If
not
pos
sib
le, w
rite
sim
pli
fied
.
13. 2
x +
8x
14
. 17g
+ g
15. 2
x2 +
6x2
16
. 7a2
- 2
a2
17. 3
y2 -
2y
18
. 2(n
+ 2
n)
19. 4
(2b
- b
)
20. 3
q2 +
q -
q2
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n. T
hen
sim
pli
fy,
ind
icat
ing
the
pro
per
ties
use
d.
21. T
he
prod
uct
of
9 an
d t
squ
ared
, in
crea
sed
by t
he
sum
of
the
squ
are
of t
an
d 2
22. 3
tim
es t
he
sum
of
r an
d d
squ
ared
min
us
2 ti
mes
th
e su
m o
f r
and
d s
quar
ed
Skill
s Pr
acti
ceTh
e D
istr
ibu
tive P
rop
ert
y
1-4
4 .
3 +
4 .
5; 3
22
.
6 +
2 .
10;
32
5 .
7 -
5 .
4; 1
56
.
8 -
2 .
8; 3
2
9t
2 +
(t2
+ 2
) =
(9t
2 +
t2 )
+ 2
A
sso
ciat
ive
(+)
=
10
t2 +
2
S
ub
stitu
tio
n
7 .
h -
7 .
10;
7h -
70
5(90
- 1
); 4
459(
100-
1)
; 89
1
15(1
00
+ 4
); 1
560
15 (2
+ 1 −
3 ) ; 3
5
10x
18g
8x2
5a2
sim
plifi
ed
6n
4b2q
2 +
q
3 .
m +
3 .
n;
3m +
3n
2
. x -
2 .
y +
2 .
1; 2
x -
2y +
2
a .
2 +
7 .
2; 2
a +
14
3(r
+ d
2 ) -
2(r
+ d
2 ) =
3r
+ 3
d2
- 2
r -
2d
2 D
istr
ibu
tive
= (3
d2
- 2
d2 )
+ (
3r -
2r)
A
sso
ciat
ive
= d
2 +
r
S
ub
stitu
tio
n
024_
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-4
Cha
pte
r 1
27
Gle
ncoe
Alg
ebra
1
Use
th
e D
istr
ibu
tive
Pro
per
ty t
o re
wri
te e
ach
exp
ress
ion
. Th
en e
valu
ate.
1. 9
(7 +
8)
2. 7
(6 -
4)
3. (
4 +
6)1
1
4. 9
․ 4
99
5. 7
․ 1
10
6. 1
6 (4
1 −
4 )
Use
th
e D
istr
ibu
tive
pro
per
ty t
o re
wri
te e
ach
exp
ress
ion
. Th
en s
imp
lify
.
7. (
9 -
p)3
8.
(5y
- 3
)7
9. 1
5 ( f
+ 1 −
3 )
10. 1
6(3b
- 0
.25)
11
. m(n
+ 4
) 12
. (c
- 4
)d
Sim
pli
fy e
ach
exp
ress
ion
. If
not
pos
sib
le, w
rite
sim
pli
fied
.
13. w
+ 1
4w -
6w
14
. 3(5
+ 6
h)
15
. 12b
2 +
9b2
16. 2
5t3
- 1
7t3
17
. 3a2
+ 6
a +
2b2
18. 4
(6p
+ 2
q -
2p)
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n. T
hen
sim
pli
fy,
ind
icat
ing
the
pro
per
ties
use
d.
19. 4
tim
es t
he
diff
eren
ce o
f f
squ
ared
an
d g,
in
crea
sed
by t
he
sum
of
f sq
uar
ed a
nd
2g
20. 3
tim
es t
he
sum
of
x an
d y
squ
ared
plu
s 5
tim
es t
he
diff
eren
ce o
f 2x
an
d y
21. D
ININ
G O
UT
Th
e R
oss
fam
ily
rece
ntl
y di
ned
at
an I
tali
an r
esta
ura
nt.
Eac
h o
f th
e fo
ur
fam
ily
mem
bers
ord
ered
a p
asta
dis
h t
hat
cos
t $1
1.50
, a d
rin
k th
at c
ost
$1.5
0, a
nd
dess
ert
that
cos
t $2
.75.
a.
Wri
te a
n e
xpre
ssio
n t
hat
cou
ld b
e u
sed
to c
alcu
late
th
e co
st o
f th
e R
oss’
din
ner
bef
ore
addi
ng
tax
and
a ti
p.
b
. Wh
at w
as t
he
cost
of
din
ing
out
for
the
Ros
s fa
mil
y?
1-4
Prac
tice
Th
e D
istr
ibu
tive P
rop
ert
y
9
(50
0 -
1)
; 44
91
7(1
00
+ 10
);
770
16 (
4 +
1 −
4 ) ;
68
9
� 3
- p
� 3
; 27
- 3
p
5y �
7 -
3 �
7;
35y -
21
15
�
f +
15
�
1 −
3 ;
15f
+ 5
1
6 �
3b
- 1
6 �
0.2
5;
m �
n +
m �
4;
c �
d -
4 �
d;
48
b -
4
mn
+ 4
m
cd
- 4
d
9w15
+ 1
8h21
b2
8t3
s
imp
lifi e
d
16p
+ 8
q
4(11
.5 +
1.5
+ 2
.75)
$63.
00
= 4
(f 2
- g
) + (f
2 +
2g
) =
4f 2
- 4g
+
f 2
+ 2g
D
istr
ibu
tive
Pro
per
ty=
5f 2
- 2g
S
ub
stitu
tio
n
= 3
(x +
y2 )
+
5(
2x -
y)
= 3
x +
3y
2 +
10
x -
5y
D
istr
ibu
tive
Pro
per
ty=
3y
2 -
5y +
13
x
Su
bst
ituti
on
9
� 7
+ 9
� 8
; 13
5 7
�
6
- 7
� 4
; 14
4
� 1
1 +
6 �
11;
110
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Answers (Lesson 1-4)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A12A01_A14_ALG1_A_CRM_C01_AN_660498.indd A12 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
28
Gle
ncoe
Alg
ebra
1
1.O
PER
A M
r. D
elon
g’s
dram
a cl
ass
is
plan
nin
g a
fiel
d tr
ip t
o se
e M
ozar
t’s
fam
ous
oper
a D
on G
iova
nn
i. T
icke
ts c
ost
$39
each
, an
d th
ere
are
23 s
tude
nts
an
d 2
teac
her
s go
ing
on t
he
fiel
d tr
ip. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n t
o fi
nd
the
grou
p’s
tota
l ti
cket
cos
t.
2. S
ALA
RY I
n a
rec
ent
year
, th
e m
edia
n
sala
ry f
or a
n e
ngi
nee
r in
th
e U
nit
ed
Sta
tes
was
$55
,000
an
d th
e m
edia
n
sala
ry f
or a
com
pute
r pr
ogra
mm
er w
as
$52,
000.
Wri
te a
nd
eval
uat
e an
ex
pres
sion
to
esti
mat
e th
e to
tal
cost
for
a
busi
nes
s to
em
ploy
an
en
gin
eer
and
a pr
ogra
mm
er f
or 5
yea
rs.
3. C
OST
UM
ES I
sabe
lla’
s ba
llet
cla
ss i
s pe
rfor
min
g a
spri
ng
reci
tal
for
wh
ich
th
ey n
eed
butt
erfl
y co
stu
mes
. Eac
h
b
utt
erfl
y co
stu
me
is m
ade
from
3 3 −
5 yar
ds
o
f fa
bric
. Use
th
e D
istr
ibu
tive
Pro
pert
y to
fin
d th
e n
um
ber
of y
ards
of
fabr
ic
nee
ded
for
5 co
stu
mes
. (H
int:
A m
ixed
n
um
ber
can
be
wri
tten
as
the
sum
of
an
inte
ger
and
a fr
acti
on.)
4. F
ENC
ES D
emon
stra
te t
he
Dis
trib
uti
ve
Pro
pert
y by
wri
tin
g tw
o eq
uiv
alen
t ex
pres
sion
s to
rep
rese
nt
the
peri
met
er o
f th
e fe
nce
d do
g pe
n b
elow
.
5. M
ENTA
L M
ATH
Du
rin
g a
mat
h f
acts
sp
eed
con
test
, Jam
al c
alcu
late
d th
e fo
llow
ing
expr
essi
on f
aste
r th
an a
nyo
ne
else
in
his
cla
ss.
19
7 ×
4
Wh
en c
lass
mat
es a
sked
him
how
he
was
ab
le t
o an
swer
so
quic
kly,
he
told
th
em
he
use
d th
e D
istr
ibu
tive
Pro
pert
y to
th
ink
of t
he
prob
lem
dif
fere
ntl
y. W
rite
an
d ev
alu
ate
an e
xpre
ssio
n u
sin
g th
e D
istr
ibu
tive
Pro
pert
y th
at w
ould
hel
p Ja
mal
per
form
th
e ca
lcu
lati
on q
uic
kly.
6. IN
VES
TMEN
TS L
etis
ha
and
Noe
l ea
ch
open
ed a
ch
ecki
ng
acco
un
t, a
sav
ings
ac
cou
nt,
an
d a
coll
ege
fun
d. T
he
char
t be
low
sh
ows
the
amou
nts
th
at t
hey
de
posi
ted
into
eac
h a
ccou
nt.
Ch
ecki
ng
Sav
ing
sC
olle
ge
Let
ish
a$
12
5$
75
$5
0
No
el$
25
0$
50
$5
0
a. I
f N
oel
use
d on
ly $
50 b
ills
wh
en h
e de
posi
ted
the
mon
ey t
o op
en h
is
acco
un
ts, h
ow m
any
$50
bill
s di
d h
e de
posi
t?
b.
If a
ll a
ccou
nts
ear
n 1
.5%
in
tere
st p
er
year
an
d n
o fu
rth
er d
epos
its
are
mad
e, h
ow m
uch
in
tere
st w
ill
Let
ish
a h
ave
earn
ed o
ne
year
aft
er h
er
acco
un
ts w
ere
open
ed?
m
nDo
g Pe
n
Wor
d Pr
oble
m P
ract
ice
Th
e D
istr
ibu
tive P
rop
ert
y
1-4 $3
9(23
+ 2
) =
$97
5
5 (3
3 −
5 ) =
5 (3
+ 3 −
5 ) =
5(3
) +
5 ( 3
−
5 )
= 1
5 +
3 =
18
2n +
2m
an
d 2
(n +
m)
4(20
0 -
3)
= 8
00
- 1
2 =
788
7 $5
0 b
ills
$3.7
5
5(55
,00
0 +
52,
00
0)=
$53
5,0
00
024_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-4
Cha
pte
r 1
29
Gle
ncoe
Alg
ebra
1
Th
e M
aya
Th
e M
aya
wer
e a
Nat
ive
Am
eric
an p
eopl
e w
ho
live
d fr
om a
bou
t 15
00 B
.C. t
o ab
out
1500
A.D
. in
th
e re
gion
th
at t
oday
en
com
pass
es
mu
ch o
f C
entr
al A
mer
ica
and
sou
ther
n M
exic
o. T
hei
r m
any
acco
mpl
ish
men
ts i
ncl
ude
exc
epti
onal
arc
hit
ectu
re, p
otte
ry,
pain
tin
g, a
nd
scu
lptu
re, a
s w
ell
as s
ign
ific
ant
adva
nce
s in
th
e fi
elds
of
astr
onom
y an
d m
ath
emat
ics.
T
he
May
a de
velo
ped
a sy
stem
of
nu
mer
atio
n t
hat
was
bas
ed o
n
the
nu
mbe
r tw
enty
. Th
e ba
sic
sym
bols
of
this
sys
tem
are
sh
own
in
th
e ta
ble
at t
he
righ
t. T
he
plac
es i
n a
May
an n
um
eral
are
wri
tten
ve
rtic
ally
—th
e bo
ttom
pla
ce r
epre
sen
ts o
nes
, th
e pl
ace
abov
e re
pres
ents
tw
enti
es, t
he
plac
e ab
ove
that
rep
rese
nts
20
× 2
0, o
r fo
ur
hu
nd
red
s, a
nd
so o
n. F
or i
nst
ance
, th
is i
s h
ow t
o w
rite
th
e n
um
ber
997
in M
ayan
nu
mer
als.
←
2
×
40
0
=
800
←
9
×
20
=
18
0
←
17
×
1
=
17
99
7
Eva
luat
e ea
ch e
xpre
ssio
n w
hen
v =
•
__
__
_, w
=
• •
• _
__
__
__
__
__
__
__, x
= •
• •
•, y
= �
, an
d
z =
•
•_
__
__
__
__
_. T
hen
wri
te t
he
answ
er i
n M
ayan
nu
mer
als.
Exe
rcis
e 5
is d
one
for
you
.
1. z −
w
2. v
+ w
+ z
−
x
3. x
v
4. v
xy
5. w
x -
z
6. v
z +
xy
7. w
(v +
x +
z)
8.
vw
z
9. z
(wx
- x
)
Tel
l w
het
her
eac
h s
tate
men
t is
tru
e or
fa
lse.
10.
• •
•_
__
__
__
__
_ +
•
__
__
_ =
•
__
__
_ +
•
• •
__
__
__
__
__
11.
• •
•_
__
__
__
__
_
•_
__
__ =
•
__
__
_
• •
•_
__
__
__
__
_
12.
• •
•_
__
__
__
__
__
__
__ =
•
• •
__
__
__
__
__
__
__
__
__
__
13. (
• •
• +
__
__
_)
+ _
__
__
__
__
_ =
• •
• +
(_
__
__ +
__
__
__
__
__)
14. H
ow a
re E
xerc
ises
10
and
11 a
like
? H
ow a
re t
hey
dif
fere
nt?
• •
__
__
__
__
__
__
__
_
• •
• •
__
__
_
• •
0
10
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
�
• • •
• •
•
• •
• •
__
__
_
•_
__
__
• •
__
__
_
• •
•_
__
__
• •
• •
__
__
_
__
__
__
__
__
•_
__
__
__
__
_
• •
__
__
__
__
__
• •
•_
__
__
__
__
_
• •
• •
__
__
__
__
__
__
__
_
• •
• •
__
__
__
__
__
__
__
__
__
__
__
__
_
•_
__
__
__
__
__
__
__
• •
__
__
__
__
__
__
__
_
• •
• _
__
__
__
__
__
__
__
Enri
chm
ent
1-4 •
• •
t
rue
fals
e
fals
e
tru
e
B
oth
invo
lve
chan
gin
g t
he
ord
er o
f th
e sy
mb
ols
. Exe
rcis
e 10
invo
lves
ch
ang
ing
th
e o
rder
of
the
add
end
s in
an
ad
dit
ion
pro
ble
m. E
xerc
ise
11
invo
lves
ch
ang
ing
th
e o
rder
of
the
dig
its
in a
nu
mer
al.
• •
• •
__
__
_•
• •
• •
�
• •
•
• •
__
__
__
__
__
• •
• •
__
__
__
__
__
__
__
_
•_
__
__
__
__
__
__
__
• •
•
• •
• •
•_
__
__
__
__
__
__
__
• •
�
•_
__
__
__
__
__
__
__
• •
•
�
024_
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ALG
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Answers (Lesson 1-4)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A13A01_A14_ALG1_A_CRM_C01_AN_660498.indd A13 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
30
Gle
ncoe
Alg
ebra
1
Solv
e Eq
uat
ion
s A
mat
hem
atic
al s
ente
nce
wit
h o
ne
or m
ore
vari
able
s is
cal
led
an
open
sen
ten
ce. O
pen
sen
ten
ces
are
solv
ed b
y fi
ndi
ng
repl
acem
ents
for
th
e va
riab
les
that
re
sult
in
tru
e se
nte
nce
s. T
he
set
of n
um
bers
fro
m w
hic
h r
epla
cem
ents
for
a v
aria
ble
may
be
chos
en i
s ca
lled
th
e re
pla
cem
ent
set.
Th
e se
t of
all
rep
lace
men
ts f
or t
he
vari
able
th
at
resu
lt i
n t
rue
stat
emen
ts i
s ca
lled
th
e so
luti
on s
et f
or t
he
vari
able
. A s
ente
nce
th
at
con
tain
s an
equ
al s
ign
, =, i
s ca
lled
an
eq
uat
ion
.
F
ind
th
e so
luti
on
set
of 3
a +
12
= 3
9 if
th
e re
pla
cem
ent
set
is {
6, 7
, 8, 9
, 10}
.
Rep
lace
a i
n 3
a +
12
= 3
9 w
ith
eac
h
valu
e in
th
e re
plac
emen
t se
t.3(
6) +
12
� 3
9 →
30
≠ 3
9 fa
lse
3(7)
+ 1
2 �
39
→ 3
3 ≠
39
fals
e
3(8)
+ 1
2 �
39
→ 3
6 ≠
39
fals
e
3(9)
+ 1
2 �
39
→ 3
9 =
39
true
3(10
) +
12
� 3
9 →
42
≠ 3
9 fa
lse
Sin
ce a
= 9
mak
es t
he
equ
atio
n
3a +
12
= 3
9 tr
ue,
th
e so
luti
on i
s 9.
Th
e so
luti
on s
et i
s {9
}.
S
olve
2(3
+ 1
) −
3(7
- 4
) =
b.
2(3
+ 1)
−
3(7
- 4)
=
b
Ori
gin
al equation
2(
4)
−
3(3)
= b
Add in t
he n
um
era
tor;
subtr
act
in t
he d
enom
inato
r.
8 −
9 = b
S
implif
y.
Th
e so
luti
on i
s 8 −
9 .
Exer
cise
sF
ind
th
e so
luti
on o
f ea
ch e
qu
atio
n i
f th
e re
pla
cem
ent
sets
are
x =
{
1 −
4 , 1 −
2 , 1,
2, 3
}
an
d y
= {
2, 4
, 6, 8
}.
1. x
+ 1 −
2 = 5 −
2 2.
x +
8 =
11
3.
y -
2 =
6
4. x
2 -
1 =
8
5. y
2 -
2 =
34
6.
x2
+ 5
= 5
1 −
16
7. 2
(x +
3)
= 7
8.
(y
+ 1
)2 =
9
9. y
2 +
y =
20
Sol
ve e
ach
eq
uat
ion
.
10. a
= 2
3 -
1
11. n
= 6
2 -
42
12
. w =
62
․
32
13.
1 −
4 + 5 −
8 = k
14
. 18
- 3
−
2 +
3
= p
15
. t =
15
- 6
−
27 -
24
16. 1
8.4
- 3
.2 =
m
17. k
= 9
.8 +
5.7
18
. c =
3 1 −
2 + 2
1 −
4
Stud
y G
uide
and
Inte
rven
tion
Eq
uati
on
s
1-5
Exam
ple
1Ex
amp
le 2
{2}
{3}
{8}
{3}
{6} {2}
{4}
720
324
33
15.2
15.5
5 3 −
4
7 −
8 { 1 −
2 }
{ 1 −
4 }
024_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-5
Cha
pte
r 1
31
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Eq
uati
on
s
1-5
Solv
e Eq
uat
ion
s w
ith
Tw
o V
aria
ble
s S
ome
equ
atio
ns
con
tain
tw
o va
riab
les.
It
is
ofte
n u
sefu
l to
mak
e a
tabl
e of
val
ues
in
wh
ich
you
can
use
su
bsti
tuti
on t
o fi
nd
the
corr
espo
ndi
ng
valu
es o
f th
e se
con
d va
riab
le.
MU
SIC
DO
WN
LOA
DS
Em
ily
bel
ongs
to
an I
nte
rnet
mu
sic
serv
ice
that
ch
arge
s $5
.99
per
mon
th a
nd
$0.
89 p
er s
ong.
Wri
te a
nd
sol
ve a
n e
qu
atio
n t
o fi
nd
th
e to
tal
amou
nt
Em
ily
spen
ds
if s
he
dow
nlo
ads
10 s
ongs
th
is m
onth
.
Th
e co
st o
f th
e m
usi
c se
rvic
e is
a f
lat
rate
. Th
e va
riab
le i
s th
e n
um
ber
of s
ongs
sh
e do
wn
load
s. T
he
tota
l co
st i
s th
e pr
ice
of t
he
serv
ice
plu
s $0
.89
tim
es t
he
nu
mbe
r of
son
gs.
C =
0.8
9n +
5.9
9
To
fin
d th
e to
tal
cost
for
th
e m
onth
, su
bsti
tute
10
for
n i
n t
he
equ
atio
n.
C =
0.8
9n +
5.9
9
Ori
gin
al equation
=
0.8
9(10
) +
5.9
9
Substitu
te 1
0 for
n.
=
8.9
0 +
5.9
9 M
ultip
ly.
=
14.
89
Add.
Em
ily
spen
t $1
4.89
on
mu
sic
dow
nlo
ads
in o
ne
mon
th.
Exer
cise
s 1
. AU
TO R
EPA
IR A
mec
han
ic r
epai
rs M
r. E
stes
’ car
. Th
e am
oun
t fo
r pa
rts
is $
48.0
0 an
d th
e ra
te f
or t
he
mec
han
ic i
s $4
0.00
per
hou
r. W
rite
an
d so
lve
an e
quat
ion
to
fin
d th
e to
tal
cost
of
repa
irs
to M
r. E
stes
’ car
if
the
mec
han
ic w
orks
for
1.5
hou
rs.
2. S
HIP
PIN
G F
EES
Mr.
Moo
re p
urc
has
es a
n i
nfl
atab
le k
ayak
wei
ghin
g 30
pou
nds
fro
m a
n
onli
ne
com
pan
y. T
he
stan
dard
rat
e to
sh
ip h
is p
urc
has
e is
$2.
99 p
lus
$0.8
5 pe
r po
un
d.
Wri
te a
nd
solv
e an
equ
atio
n t
o fi
nd
the
tota
l am
oun
t M
r. M
oore
wil
l pa
y to
hav
e th
e ka
yak
ship
ped
to h
is h
ome.
3. S
OU
ND
Th
e sp
eed
of s
oun
d is
108
8 fe
et p
er s
econ
d at
sea
lev
el a
t 32
° F
. Wri
te a
nd
solv
e an
equ
atio
n t
o fi
nd
the
dist
ance
sou
nd
trav
els
in 8
sec
onds
un
der
thes
e co
ndi
tion
s.
4. V
OLL
EYB
ALL
You
r to
wn
dec
ides
to
buil
d a
voll
eyba
ll c
ourt
. If
the
cou
rt i
s ap
prox
imat
ely
40 b
y 70
fee
t an
d it
s su
rfac
e is
of
san
d, o
ne
foot
dee
p, t
he
cou
rt w
ill
requ
ire
abou
t 16
6 to
ns
of s
and.
A l
ocal
san
d pi
t se
lls
san
d fo
r $1
1.00
per
ton
wit
h a
de
live
ry c
har
ge o
f $3
.00
per
ton
. Wri
te a
nd
solv
e an
equ
atio
n t
o fi
nd
the
tota
l co
st o
f th
e sa
nd
for
this
cou
rt.
Exam
ple
C =
48
+ 4
0x; $
108.
00
C =
2.9
9 +
0.8
5x; $2
8.49
d =
108
8x; 8
704
ft
C =
14x
; $23
24.0
0
024_
041_
ALG
1_A
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M_C
01_C
R_6
6049
8.in
dd
3112
/21/
10
5:20
PM
Answers (Lesson 1-5)
A01_A14_ALG1_A_CRM_C01_AN_660498.indd A14A01_A14_ALG1_A_CRM_C01_AN_660498.indd A14 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
32
Gle
ncoe
Alg
ebra
1
Fin
d t
he
solu
tion
of
each
eq
uat
ion
if
the
rep
lace
men
t se
ts a
re A
= {
4, 5
, 6, 7
, 8}
and
B =
{9,
10,
11,
12,
13}
.
1. 5
a -
9 =
26
2.
4a
- 8
= 1
6
3. 7
a +
21
= 5
6
4. 3
b +
15
= 4
8
5. 4
b -
12
= 2
8
6. 36
−
b -
3 =
0
Fin
d t
he
solu
tion
of
each
eq
uat
ion
usi
ng
the
give
n r
epla
cem
ent
set.
7.
1 −
2 + x
= 5 −
4 ; {
1 −
2 , 3 −
4 , 1,
5 −
4 }
8. x
+ 2 −
3 = 13
−
9 ; { 5
−
9 , 2 −
3 , 7 −
9 }
9.
1 −
4 (x +
2)
= 5 −
6 ; {
2 −
3 , 3 −
4 , 5 −
4 , 4 −
3 }
10. 0
.8(x
+ 5
) =
5.2
; {1.
2, 1
.3, 1
.4, 1
.5}
Sol
ve e
ach
eq
uat
ion
.
11. 1
0.4
- 6
.8 =
x
12. y
= 2
0.1
- 1
1.9
13.
46 -
15
−
3 +
28
=
a
14. c
=
6 +
18
−
31 -
25
15.
2(4)
+ 4
−
3(3
- 1)
=
b
16.
6(7
- 2
) −
3(8)
+ 6 =
n
17. S
HO
PPIN
G O
NLI
NE
Jen
nif
er i
s pu
rch
asin
g C
Ds
and
a n
ew C
D p
laye
r fr
om a
n o
nli
ne
stor
e. S
he
pays
$10
for
eac
h C
D, a
s w
ell
as $
50 f
or t
he
CD
pla
yer.
Wri
te a
nd
solv
e an
eq
uat
ion
to
fin
d th
e to
tal
amou
nt
Jen
nif
er s
pen
t if
sh
e bu
ys 4
CD
s an
d a
CD
pla
yer
from
th
e st
ore.
18. T
RA
VEL
An
air
plan
e ca
n t
rave
l at
a s
peed
of
550
mil
es p
er h
our.
Wri
te a
nd
solv
e an
eq
uat
ion
to
fin
d th
e ti
me
it w
ill
take
to
fly
from
Lon
don
to
Mon
trea
l, a
dist
ance
of
appr
oxim
atel
y 33
00 m
iles
.
Skill
s Pr
acti
ceE
qu
ati
on
s
1-5
76
511
1012
1.5
3.6
8.2
14
21
7 −
9
4 −
3
3 −
4
50 +
10
(4)
= t;
t =
$
90
330
0 −
550
= t;
t =
6
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NA
ME
DAT
E
P
ER
IOD
Lesson 1-5
Cha
pte
r 1
33
Gle
ncoe
Alg
ebra
1
Fin
d t
he
solu
tion
of
each
eq
uat
ion
if
the
rep
lace
men
t se
ts a
re a
= {0
, 1 −
2 , 1,
3 −
2 , 2 }
and
b =
{3,
3.5
, 4, 4
.5, 5
}.
1. a
+ 1 −
2 = 1
2.
4b
- 8
= 6
3.
6a
+ 1
8 =
27
4. 7
b -
8 =
16.
5
5. 1
20 -
28a
= 7
8
6. 28
−
b +
9 =
16
Sol
ve e
ach
eq
uat
ion
.
7. x
= 1
8.3
- 4
.8
8. w
= 2
0.2
- 8
.95
9.
37
- 9
−
18 -
11
= d
10.
97 -
25
−
41 -
23
= k
11
. y =
4(22
- 4)
−
3(6)
+
6
12
. 5(
2 2 ) +
4(
3)
−
4( 2 3
-
4)
=
p
13. T
EAC
HIN
G A
tea
cher
has
15
wee
ks i
n w
hic
h t
o te
ach
six
ch
apte
rs. W
rite
an
d th
en s
olve
an
equ
atio
n t
hat
rep
rese
nts
th
e n
um
ber
of l
esso
ns
the
teac
her
mu
st t
each
per
wee
k if
th
ere
is a
n a
vera
ge o
f 8.
5 le
sson
s pe
r ch
apte
r.
14. C
ELL
PHO
NES
Gab
riel
pay
s $4
0 a
mon
th f
or b
asic
cel
l ph
one
serv
ice.
In
add
itio
n,
Gab
riel
can
sen
d te
xt m
essa
ges
for
$0.2
0 ea
ch. W
rite
an
d so
lve
an e
quat
ion
to
fin
d th
e to
tal
amou
nt
Gab
riel
spe
nt
this
mon
th i
f h
e se
nds
40
text
mes
sage
s.
1-5
Prac
tice
Eq
uati
on
s
3.5
3.5
4
3 −
2 1 −
2
3 −
2
n =
6(8.
5)
−
15
; 3.
4 13.5
11.2
54
23
4
c =
40
+ 0
.20(
40);
$48
.00
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Answers (Lesson 1-5)
A15_A26_ALG1_A_CRM_C01_AN_660498.indd A15A15_A26_ALG1_A_CRM_C01_AN_660498.indd A15 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
34
Gle
ncoe
Alg
ebra
1
1.TI
ME
Th
ere
are
6 ti
me
zon
es i
n t
he
Un
ited
Sta
tes.
Th
e ea
ster
n p
art
of t
he
U.S
., in
clu
din
g N
ew Y
ork
Cit
y, i
s in
th
e E
aste
rn T
ime
Zon
e. T
he
cen
tral
par
t of
th
e U
.S.,
incl
udi
ng
Dal
las,
is
in t
he
Cen
tral
Tim
e Z
one,
wh
ich
is
one
hou
r be
hin
d E
aste
rn T
ime.
San
Die
go i
s in
th
e P
acif
ic T
ime
Zon
e, w
hic
h i
s 3
hou
rs
beh
ind
Eas
tern
Tim
e. W
rite
an
d so
lve
an
equ
atio
n t
o de
term
ine
wh
at t
ime
it i
s in
C
alif
orn
ia i
f it
is
noo
n i
n N
ew Y
ork.
2. F
OO
D P
art
of t
he
Nu
trit
ion
Fac
ts l
abel
fr
om a
box
of
mac
aron
i an
d ch
eese
is
show
n b
elow
.
Nu
trit
ion
Fac
tsS
erv
ing
Siz
e 1
cu
p (
22
8g
)
Se
rvin
gs P
er
Co
nta
ine
r 2
Am
ount P
er
Serv
ing
Cal
ori
es 2
50
Ca
lorie
s f
rom
Fa
t 1
10
To
tal F
at 1
2g
Sa
tura
ted
Fa
t 3
g
Tran
s F
at
3g
Ch
ole
ster
ol 3
0m
g
% D
aily
Val
ue
*
18 %
15 %
10 %
W
rite
an
d so
lve
an e
quat
ion
to
dete
rmin
e h
ow m
any
serv
ings
of
this
ite
m A
lisa
can
ea
t ea
ch d
ay i
f sh
e w
ants
to
con
sum
e ex
actl
y 45
gra
ms
of c
hol
este
rol.
3. C
RA
FTS
You
nee
d 30
yar
ds o
f ya
rn t
o cr
och
et a
sm
all
scar
f. C
her
yl b
ough
t a
100-
yard
bal
l of
yar
n a
nd
has
alr
eady
u
sed
10 y
ards
. Wri
te a
nd
solv
e an
eq
uat
ion
to
fin
d h
ow m
any
scar
ves
she
can
cro
chet
if
she
plan
s on
usi
ng
up
the
enti
re b
all.
4.PO
OLS
Th
ere
are
appr
oxim
atel
y 20
2 ga
llon
s pe
r cu
bic
yard
of
wat
er. W
rite
an
d so
lve
an e
quat
ion
for
th
e n
um
ber
of
gall
ons
of w
ater
th
at f
ill
a po
ol w
ith
a
volu
me
of 1
161
cubi
c fe
et. (
Hin
t: T
her
e ar
e 27
cu
bic
feet
per
cu
bic
yard
.)
5. V
EHIC
LES
Rec
entl
y de
velo
ped
hyb
rid
cars
con
tain
bot
h a
n e
lect
ric
and
a ga
soli
ne
engi
ne.
Hyb
rid
car
batt
erie
s st
ore
extr
a en
ergy
, su
ch a
s th
e en
ergy
pr
odu
ced
by b
raki
ng.
Sin
ce t
he
car
can
u
se t
his
sto
red
ener
gy t
o po
wer
th
e ca
r, th
e h
ybri
d u
ses
less
gas
olin
e pe
r m
ile
than
car
s po
wer
ed o
nly
by
gaso
lin
e.
Su
ppos
e a
new
hyb
rid
car
is r
ated
to
driv
e 45
mil
es p
er g
allo
n o
f ga
soli
ne.
a. I
t co
sts
$40
to f
ill
the
gaso
lin
e ta
nk
wit
h g
as t
hat
cos
ts $
3.00
per
gal
lon
. W
rite
an
d so
lve
an e
quat
ion
to
fin
d th
e di
stan
ce t
he
hyb
rid
car
can
go
usi
ng
one
tan
k of
gas
.
b. W
rite
an
d so
lve
an e
quat
ion
to
fin
d th
e co
st o
f ga
soli
ne
per
mil
e fo
r th
is h
ybri
d ca
r. R
oun
d to
th
e n
eare
st c
ent.
1-5
Wor
d Pr
oble
m P
ract
ice
Eq
uati
on
s
12 -
c =
3;
9:0
0 A
M
c =
45
−
30 ;
1.5
serv
ing
s
100
- 1
0 =
30s
;
g
= g
al in
po
ol
g
= 11
61
−
27
× 2
02;
8686
gal
40
−
3.0
0 (45
) =
m;
600
mi
3.0
0 −
45
= c
; ≈
7¢ p
er m
i
3 sc
arve
s
024_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-5
Cha
pte
r 1
35
Gle
ncoe
Alg
ebra
1
So
luti
on
Sets
Con
side
r th
e fo
llow
ing
open
sen
ten
ce.
It i
s th
e n
ame
of a
mon
th b
etw
een
Mar
ch a
nd
July
.
You
kn
ow t
hat
a r
epla
cem
ent
for
the
vari
able
It
mu
st b
e fo
un
d in
ord
er t
o de
term
ine
if t
he
sen
ten
ce i
s tr
ue
or f
alse
. If
It i
s re
plac
ed b
y ei
ther
Apr
il, M
ay, o
r Ju
ne,
th
e se
nte
nce
is
tru
e.T
he
set
{Apr
il, M
ay, J
un
e} i
s ca
lled
th
e so
luti
on s
et o
f th
e op
en s
ente
nce
giv
en a
bove
. Th
is
set
incl
ude
s al
l re
plac
emen
ts f
or t
he
vari
able
th
at m
ake
the
sen
ten
ce t
rue.
Wri
te t
he
solu
tion
set
for
eac
h o
pen
sen
ten
ce.
1. I
t is
th
e n
ame
of a
sta
te b
egin
nin
g w
ith
th
e le
tter
A.
2. I
t is
a p
rim
ary
colo
r.
3. I
ts c
apit
al i
s H
arri
sbu
rg.
4. I
t is
a N
ew E
ngl
and
stat
e.
5. x
+ 4
= 1
0
6. I
t is
th
e n
ame
of a
mon
th t
hat
con
tain
s th
e le
tter
r.
7. S
he
was
th
e w
ife
of a
U.S
. Pre
side
nt
wh
o se
rved
in
th
e ye
ars
2000
-20
10.
8. I
t is
an
eve
n n
um
ber
betw
een
1 a
nd
13.
9. 3
1 =
72
- k
10. I
t is
th
e sq
uar
e of
2, 3
, or
4.
Wri
te a
n o
pen
sen
ten
ce f
or e
ach
sol
uti
on s
et.
11. {
A, E
, I, O
, U}
12. {
1, 3
, 5, 7
, 9}
13. {
Jun
e, J
uly
, Au
gust
}
14. {
Atl
anti
c, P
acif
ic, I
ndi
an, A
rcti
c}
Enri
chm
ent
1-5
{
Ala
bam
a, A
lask
a, A
rizo
na,
Ark
ansa
s}
{
red
, yel
low
, blu
e}
{Pen
nsy
lvan
ia}
{Mai
ne,
New
Ham
psh
ire,
{6}
{
Jan
, Feb
, Mar
, Ap
r, S
ept,
Oct
, No
v, D
ec}
{
Hill
ary
Clin
ton
, Lau
ra B
ush
, Mic
hel
le O
bam
a}
{2, 4
, 6, 8
, 10,
12}
{41}
{4, 9
, 16}
It is
a v
ow
el.
It is
an
od
d n
um
ber
bet
wee
n 0
an
d 1
0.
It is
a s
um
mer
mo
nth
.
It is
an
oce
an.
V
erm
on
t, M
assa
chu
sett
s, R
ho
de
Isla
nd
, Co
nn
ecti
cut}
024_
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Answers (Lesson 1-5)
A15_A26_ALG1_A_CRM_C01_AN_660498.indd A16A15_A26_ALG1_A_CRM_C01_AN_660498.indd A16 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
A s
prea
dshe
et is
a t
ool f
or w
orki
ng w
ith
and
anal
yzin
g nu
mer
ical
dat
a. T
he d
ata
is e
nte
red
into
a
tabl
e in
wh
ich
eac
h r
ow i
s n
um
bere
d an
d ea
ch c
olu
mn
is
labe
led
by a
lett
er. Y
ou c
an u
se a
sp
read
shee
t to
find
sol
utio
ns o
f ope
n se
nten
ces.
Exer
cise
s
Use
a s
pre
adsh
eet
to f
ind
th
e so
luti
on o
f ea
ch e
qu
atio
n u
sin
g th
e gi
ven
re
pla
cem
ent
set.
1. x
+
7.
5 =
18
.3; {
8.8,
9.8
, 10.
8, 1
1.8}
2.
6(x
+ 2
) =
18;
{0,
1, 2
, 3, 4
, 5}
3. 4
x +
1
= 17
; {0,
1, 2
, 3, 4
, 5}
4. 4
.9 -
x =
2.
2; {
2.6,
2.7
, 2.8
, 2.9
, 3.0
}
5. 2
.6x
= 16
.9; {
6.1,
6.3
, 6.5
, 6.7
, 6.9
} 6.
12x
- 8
=
22
; {2.
1, 2
.2, 2
.3, 2
.4, 2
.5, 2
.6}
U
se a
sp
read
shee
t to
fin
d t
he
solu
tion
for
4(
x -
3)
=
32
if
the
rep
lace
men
t se
t is
{7,
8, 9
, 10,
11,
12}
.
You
can
sol
ve t
he
open
sen
ten
ce b
y re
plac
ing
x w
ith
eac
h v
alu
e in
th
e re
plac
emen
t se
t.
Ste
p 1
U
se t
he
firs
t co
lum
n o
f th
e sp
read
shee
t fo
r th
e re
plac
emen
t se
t. E
nte
r th
e n
um
bers
usi
ng
the
form
ula
bar
. Cli
ck o
n a
cel
l of
th
e sp
read
shee
t,
type
th
e n
um
ber
and
pres
s E
NT
ER
.
Ste
p 2
T
he
seco
nd
colu
mn
con
tain
s th
e fo
rmu
la f
or
the
left
sid
e of
th
e op
en s
ente
nce
. To
ente
r a
form
ula
, en
ter
an e
qual
s si
gn f
ollo
wed
by
the
form
ula
. Use
th
e n
ame
of t
he
cell
con
tain
ing
each
rep
lace
men
t va
lue
to e
valu
ate
the
form
ula
for
th
at v
alu
e. F
or e
xam
ple,
in
cel
l B
2, t
he
form
ula
con
tain
s A
2 in
pla
ce o
f x.
Th
e so
luti
on i
s th
e va
lue
of x
for
wh
ich
th
e fo
rmu
la i
n
colu
mn
B r
etu
rns
32. T
he
solu
tion
is
11.
A
1 4 5 6 7 8 2 3
B
C
4(x
- 3)
=
4*(A
2-3)
=
4*(A
3-3)
=
4*(A
4-3)
=
4*(A
5-3)
=
4*(A
6-3)
=
4*(A
7-3)
x 7 8 9 10
11
12
Sh
eet
1 S
hee
t 2
Sh
eet
3
A
1 4 5 6 7 8 2 3
B
C
4(x
- 3)
x
7 8 9 10
11
12
16
20
24
28
32
36
Sh
eet
1 S
hee
t 2
Sh
eet
3
1-5
Spre
adsh
eet
Act
ivit
yS
olv
ing
Op
en
Sen
ten
ces
Exam
ple
Cha
pte
r 1
36
Gle
ncoe
Alg
ebra
1
{1
0.8}
{1
}
{4
}
{2.7
}
{6
.5}
{2
.5}
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NA
ME
DAT
E
P
ER
IOD
Lesson 1-6
Cha
pte
r 1
37
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
Rela
tio
ns
1-6
Rep
rese
nt
a R
elat
ion
A r
elat
ion
is
a se
t of
ord
ered
pai
rs. A
rel
atio
n c
an b
e re
pres
ente
d by
a s
et o
f or
dere
d pa
irs,
a t
able
, a g
raph
, or
a m
app
ing.
A m
appi
ng
illu
stra
tes
how
eac
h e
lem
ent
of t
he
dom
ain
is
pair
ed w
ith
an
ele
men
t in
th
e ra
nge
. Th
e se
t of
fir
st
nu
mbe
rs o
f th
e or
dere
d pa
irs
is t
he
dom
ain
. Th
e se
t of
sec
ond
nu
mbe
rs o
f th
e or
dere
d pa
irs
is t
he
ran
ge o
f th
e re
lati
on.
a.
Exp
ress
th
e re
lati
on {
(1, 1
), (
0, 2
), (
3, -
2)}
as a
tab
le, a
gra
ph
, an
d
a m
app
ing.
x
y
11
02
3-
2
x
y O
X
Y
1 0 3
1 2-
2
b. D
eter
min
e th
e d
omai
n a
nd
th
e ra
nge
of
the
rela
tion
.
Th
e do
mai
n f
or t
his
rel
atio
n i
s {0
, 1, 3
}. T
he
ran
ge f
or t
his
rel
atio
n i
s {-
2, 1
, 2}.
Exer
cise
s 1A
. Exp
ress
th
e re
lati
on {
(-2,
-
1), (3,
3)
, (4,
3)
} as
a ta
ble,
a
grap
h, an
d a
map
pin
g.
1B. D
eter
min
e th
e do
mai
n a
nd
the
ran
ge o
f th
e re
lati
on.
Exam
ple
x
y
O
XY
-2 3 4
-1 3
xy
-2
-1
33
43
do
mai
n {-
2, 3
, 4};
ra
ng
e {-
1, 3
}
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Answers (Lesson 1-5 and Lesson 1-6)
A15_A26_ALG1_A_CRM_C01_AN_660498.indd A17A15_A26_ALG1_A_CRM_C01_AN_660498.indd A17 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
38
Gle
ncoe
Alg
ebra
1
Gra
ph
s o
f a
Rel
atio
n T
he
valu
e of
th
e va
riab
le i
n a
rel
atio
n t
hat
is
subj
ect
to c
hoi
ce i
s ca
lled
th
e in
dep
end
ent
vari
able
. Th
e va
riab
le w
ith
a v
alu
e th
at i
s de
pen
den
t on
th
e va
lue
of t
he
inde
pen
den
t va
riab
le i
s ca
lled
th
e d
epen
den
t va
riab
le. T
hes
e re
lati
ons
can
be
grap
hed
wit
hou
t a
scal
e on
eit
her
axi
s, a
nd
inte
rpre
ted
by a
nal
yzin
g th
e sh
ape.
T
he
grap
h b
elow
re
pre
sen
ts t
he
hei
ght
of a
foo
tbal
l af
ter
it i
s k
ick
ed d
own
fiel
d. I
den
tify
th
e in
dep
end
ent
and
th
e d
epen
den
t va
riab
le f
or t
he
rela
tion
. Th
en d
escr
ibe
wh
at h
app
ens
in t
he
grap
h.
Th
e in
depe
nde
nt
vari
able
is
tim
e, a
nd
the
depe
nde
nt
vari
able
is
hei
ght.
Th
e fo
otba
ll
star
ts o
n t
he
grou
nd
wh
en i
t is
kic
ked.
It
gain
s al
titu
de u
nti
l it
rea
ches
a m
axim
um
h
eigh
t, t
hen
it
lose
s al
titu
de u
nti
l it
fal
ls t
o th
e gr
oun
d.
Tim
e
Hei
gh
t
T
he
grap
h b
elow
re
pre
sen
ts t
he
pri
ce o
f st
ock
ove
r ti
me.
Id
enti
fy t
he
ind
epen
den
t an
d
dep
end
ent
vari
able
for
th
e re
lati
on.
Th
en d
escr
ibe
wh
at h
app
ens
in t
he
grap
h.
Th
e in
depe
nde
nt
vari
able
is
tim
e an
d th
e de
pen
den
t va
riab
le i
s pr
ice.
Th
e pr
ice
incr
ease
s st
eadi
ly, t
hen
it
fall
s, t
hen
in
crea
ses,
th
en f
alls
aga
in.
Tim
e
Pric
e
Exer
cise
sId
enti
fy t
he
ind
epen
den
t an
d d
epen
den
t va
riab
les
for
each
rel
atio
n. T
hen
des
crib
e w
hat
is
hap
pen
ing
in e
ach
gra
ph
.
1. T
he
grap
h r
epre
sen
ts t
he
spee
d of
a c
ar a
s it
tra
vels
to
the
groc
ery
st
ore.
2. T
he
grap
h r
epre
sen
ts t
he
bala
nce
of
a sa
vin
gs a
ccou
nt
over
tim
e.
3. T
he
grap
h r
epre
sen
ts t
he
hei
ght
of a
bas
ebal
l af
ter
it i
s h
it.
Tim
e
Hei
gh
t
Tim
e
Acc
ou
nt
Bal
ance
(do
llars
)
Tim
e
Spee
d
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Rela
tio
ns
1-6
Exam
ple
1Ex
amp
le 2
I
nd
: ti
me;
dep
: sp
eed
. Th
e ca
r st
arts
fro
m a
sta
nd
still
, ac
cele
rate
s, t
hen
tra
vels
at
a co
nst
ant
spee
d f
or
a w
hile
.Th
en it
slo
ws
do
wn
an
d s
top
s.
I
nd
: ti
me;
dep
: b
alan
ce. T
he
acco
un
t b
alan
ce h
as a
n
init
ial v
alu
e th
en it
incr
ease
s as
dep
osi
ts a
re m
ade.
It
then
sta
ys t
he
sam
e fo
r a
wh
ile, a
gai
n in
crea
ses,
an
d
last
ly g
oes
to
0 a
s w
ith
dra
wal
s ar
e m
ade.
I
nd
: ti
me;
dep
: h
eig
ht.
Th
e b
all i
s h
it a
cer
tain
hei
gh
t ab
ove
th
e g
rou
nd
. Th
e h
eig
ht
of
the
bal
l in
crea
ses
un
til
it r
each
es it
s m
axim
um
val
ue,
th
en t
he
hei
gh
t d
ecre
ases
u
nti
l th
e b
all h
its
the
gro
un
d.
024_
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-6
Cha
pte
r 1
39
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceR
ela
tio
ns
1-6
Exp
ress
eac
h r
elat
ion
as
a ta
ble
, a g
rap
h, a
nd
a m
app
ing.
Th
en d
eter
min
e th
e d
omai
n a
nd
ran
ge.
1. {
(-1,
-1)
, (1,
1),
(2, 1
), (3
, 2)}
x
y
O
X
Y
-1 1 2
-1 1 2 3
2. {
(0, 4
), (-
4, -
4), (
-2,
3),
(4, 0
)}
3. {
(3, -
2), (
1, 0
), (-
2, 4
), (3
, 1)}
x
y
O
XY
-2 0 4 1
3 1-
2
Iden
tify
th
e in
dep
end
ent
and
dep
end
ent
vari
able
s fo
r ea
ch r
elat
ion
.
4. T
he
mor
e h
ours
Mar
ibel
wor
ks a
t h
er jo
b, t
he
larg
er h
er p
aych
eck
beco
mes
.
5. I
ncr
easi
ng
the
pric
e of
an
ite
m d
ecre
ases
th
e am
oun
t of
peo
ple
wil
lin
g to
bu
y it
.
x
y
O
xy
0
4
-4
-4
-2
3
4
0
xy
3
-2
1
0
-2
4
3
1
xy
-1
-1
1
1
2
1
3
2 D
= {
-1,
1, 2
, 3};
R =
{-
1, 1
, 2}
D =
{-
4, -
2, 0
, 4};
R =
{-
4, 0
, 3, 4
}
XY
0-
4-
2 4
4-
4 3 0
D =
{-
2, 1
, 3};
R =
{-
2, 0
, 1, 4
}
ind
epen
den
t: h
ou
rs w
ork
ed, d
epen
den
t: s
ize
of
pay
chec
k
ind
epen
den
t: p
rice
of
an it
em,
dep
end
ent:
nu
mb
er o
f p
eop
le w
illin
g t
o b
uy it
024_
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Answers (Lesson 1-6)
A15_A26_ALG1_A_CRM_C01_AN_660498.indd A18A15_A26_ALG1_A_CRM_C01_AN_660498.indd A18 12/21/10 6:44 PM12/21/10 6:44 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
40
Gle
ncoe
Alg
ebra
1
1-6
Prac
tice
R
ela
tio
ns
1. E
xpre
ss {
(4, 3
), (-
1, 4
), (3
, -2)
, (-
2, 1
)} a
s a
tabl
e, a
gra
ph, a
nd
a m
appi
ng.
Th
en
dete
rmin
e th
e do
mai
n a
nd
ran
ge.
X
Y
43
-1
43
-2
-2
1
x
y
O
Des
crib
e w
hat
is
hap
pen
ing
in e
ach
gra
ph
.
2. T
he
grap
h b
elow
rep
rese
nts
th
e h
eigh
t of
a
3.
T
he
grap
h b
elow
rep
rese
nts
a
tsu
nam
i as
it
trav
els
acro
ss a
n o
cean
.
st
ude
nt
taki
ng
an e
xam
.
Exp
ress
th
e re
lati
on s
how
n i
n e
ach
tab
le, m
app
ing,
or
grap
h a
s a
set
of o
rder
ed
pai
rs.
4.
XY
09
-8
3
2-
6
14
5.
X
Y 5-
5 3 7
9-
6 4 8
6.
x
y
O
7. B
ASE
BA
LL T
he
grap
h s
how
s th
e n
um
ber
of h
ome
run
s h
it b
y A
ndr
uw
Jon
es o
f th
e A
tlan
ta B
rave
s.
Exp
ress
th
e re
lati
on a
s a
set
of o
rder
ed p
airs
. T
hen
des
crib
e th
e do
mai
n a
nd
ran
ge.
Tim
e
Nu
mb
er o
fQ
ues
tio
ns
An
swer
ed
Tim
e
Hei
gh
t
2432 283640444852
’02
’03
’04
’05
’06
’07
0
An
dru
w J
on
es’
Ho
me R
un
s
Home Runs
Yea
r
XY 3 4
-2 1
4-
1 3-
2
D =
{-
2, -
1, 3
, 4};
R =
{-
2, 1
, 3, 4
}
{
(0, 9
), (-
8, 3
),
{(9,
5),
(9, 3
), (-
6, -
5),
{(-
3, -
1), (
-2,
-2)
,(2
, -6)
, (1,
4)}
(4, 3
), (8
, -5)
, (8,
7)}
(-
1, -
3), (
1, 1
), (2
, 1)}
T
he
lon
ger
it t
rave
ls, t
he
hig
her
T
he
stu
den
t re
pea
ted
ly a
nsw
ers
the
tsu
nam
i bec
om
es.
q
ues
tio
ns
and
th
en p
ause
s.
{
('02,
35)
, ('03
, 36)
, ('04
, 29)
, ('05
, 51)
, ('0
6, 4
1), (
'07
, 26)
};
D =
{'
02, '
03, '
04, '
05, '
06, '
07};
R
=
{2
6, 2
9, 3
5, 3
6, 4
1, 5
1}
024_
041_
ALG
1_A
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10
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-6
Cha
pte
r 1
41
Gle
ncoe
Alg
ebra
1
1.H
EALT
H T
he
Am
eric
an H
eart
A
ssoc
iati
on r
ecom
men
ds t
hat
you
r ta
rget
hea
rt r
ate
duri
ng
exer
cise
sh
ould
be
betw
een
50%
an
d 75
% o
f yo
ur
max
imu
m h
eart
rat
e. U
se t
he
data
in
th
e ta
ble
belo
w t
o gr
aph
th
e ap
prox
imat
e m
axim
um
hea
rt r
ates
for
pe
ople
of
give
n a
ges.
So
urce
: Am
eric
an H
eart
Ass
ocia
tion
Ag
e
Maxim
um
Heart
Rate
200
2535
40
y
x30
Heart Rate
180
190
170
160
200
2. N
ATU
RE
Map
le s
yru
p is
mad
e by
co
llec
tin
g sa
p fr
om s
uga
r m
aple
tre
es
and
boil
ing
it d
own
to
rem
ove
exce
ss
wat
er. T
he
grap
h s
how
s th
e n
um
ber
of
gall
ons
of t
ree
sap
requ
ired
to
mak
e di
ffer
ent
quan
titi
es o
f m
aple
syr
up.
E
xpre
ss t
he
rela
tion
as
a se
t of
ord
ered
pa
irs.
Gal
lon
s o
f Sy
rup
10
24
5
y
x3
78
96
Gallons of Sap16
0
200
120 80240
280
320
Map
le S
ap
to
Syru
p
So
urce
: Ve
rmon
t M
aple
Sug
ar M
aker
s’ A
ssoc
iatio
n
3.B
AK
ING
Ide
nti
fy t
he
grap
h t
hat
bes
t re
pres
ents
th
e re
lati
onsh
ip b
etw
een
th
e n
um
ber
of c
ooki
es a
nd
the
equ
ival
ent
nu
mbe
r of
doz
ens.
Nu
mb
er o
f d
oze
ns
Number of cookies
y
x
Gra
ph
A
Nu
mb
er o
f d
oze
ns
Number of cookies
y
x
Gra
ph
B
Nu
mb
er o
f d
oze
ns
Number of cookies
y
x
Gra
ph
C
4. D
ATA
CO
LLEC
TIO
N M
arga
ret
coll
ecte
d da
ta t
o de
term
ine
the
nu
mbe
r of
boo
ks
her
sch
oolm
ates
wer
e br
ingi
ng
hom
e ea
ch e
ven
ing.
Sh
e re
cord
ed h
er d
ata
as a
se
t of
ord
ered
pai
rs. S
he
let
x be
th
e n
um
ber
of t
extb
ooks
bro
ugh
t h
ome
afte
r sc
hoo
l, an
d y
be t
he
nu
mbe
r of
stu
den
ts
wit
h x
tex
tboo
ks. T
he
rela
tion
is
show
n
in t
he
map
pin
g.
a. E
xpre
ss t
he
rela
tion
as
a se
t of
or
dere
d pa
irs.
b.
Wh
at i
s th
e do
mai
n o
f th
e re
lati
on?
c. W
hat
is
the
ran
ge o
f th
e re
lati
on?
xy 8 11 12 23 28
0 1 2 3 4 5
Ag
e (y
ears
)2
02
53
03
54
0
Max
imu
m H
eart
Rat
e(b
eats
per
min
ute
)2
00
19
519
018
518
0
1-6
Wor
d Pr
oble
m P
ract
ice
Rela
tio
ns
{(0,
12)
, (1,
8),
(2, 2
3), (
3, 2
8),
(4, 1
1), (
5, 1
1)}
{0, 1
, 2, 3
, 4, 5
}
{8, 1
1, 1
2, 2
3, 2
8}
{(2,
80)
, (3,
120
), (6
, 240
), (8
, 320
)}
Gra
ph
B
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pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
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cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A20 Glencoe Algebra 1
Answers (Lesson 1-6 and Lesson 1-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
42
Gle
ncoe
Alg
ebra
1
Even
an
d O
dd
Fu
ncti
on
sW
e kn
ow t
hat
nu
mbe
rs c
an b
e ei
ther
eve
n o
r od
d. I
t is
als
o tr
ue
that
fu
nct
ion
s ca
n b
e de
fin
ed a
s ev
en o
r od
d. F
or a
fu
nct
ion
to
be e
ven
mea
ns
that
it
is s
ymm
etri
c ab
out
the
y-ax
is. T
hat
is,
if
you
fol
d th
e gr
aph
alo
ng
the
y-ax
is, t
he
two
hal
ves
of t
he
grap
h m
atch
ex
actl
y. F
or a
fu
nct
ion
to
be o
dd m
ean
s th
at t
he
fun
ctio
n i
s sy
mm
etri
c ab
out
the
orig
in.
Th
is m
ean
s if
you
rot
ate
the
grap
h u
sin
g th
e or
igin
as
the
cen
ter,
it w
ill
mat
ch i
ts o
rigi
nal
po
siti
on b
efor
e co
mpl
etin
g a
full
tu
rn.
Th
e fu
nct
ion
y =
x2
is a
n e
ven
fu
nct
ion
. T
he
fun
ctio
n y
=
x5
is a
n o
dd f
un
ctio
n. I
f yo
u
rota
te t
he
grap
h 1
80º t
he
grap
h w
ill
lie
on i
tsel
f.
y
xO
1. T
he
tabl
e be
low
sh
ows
the
orde
red
pair
s of
an
eve
n f
un
ctio
n. C
ompl
ete
the
tabl
e. P
lot
the
poin
ts a
nd
sket
ch t
he
grap
h.
2. T
he
tabl
e be
low
sh
ows
the
orde
red
pair
s of
an
odd
fu
nct
ion
. Com
plet
e th
e ta
ble.
Plo
t th
e po
ints
an
d sk
etch
th
e gr
aph
.
y
xO
y
xO
24
68
1012
-4
-6
-8
-10
-12
-2
456 3 2 1
-1
-2
-3
-4
-5
-6 y
xO
24
68
10-
4-
6-
8-
10-
2
810 6 4 2
-2
-4
-6
-8
-10
Enri
chm
ent
x-
12
-5
-1
15
12
y
6
3
11
36
x-
10
-4
-2
24
10
y
8
4
2-
2-
4-
8
1-6
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Lesson X-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-7
Cha
pte
r 1
43
Gle
ncoe
Alg
ebra
1
Iden
tify
Fu
nct
ion
s R
elat
ion
s in
wh
ich
eac
h e
lem
ent
of t
he
dom
ain
is
pair
ed w
ith
ex
actl
y on
e el
emen
t of
th
e ra
nge
are
cal
led
fun
ctio
ns.
D
eter
min
e w
het
her
th
e re
lati
on {
(6, -
3),
(4, 1
), (
7, -
2), (
-3,
1)}
is
a fu
nct
ion
. Exp
lain
.
Sin
ce e
ach
ele
men
t of
th
e do
mai
n i
s pa
ired
wit
h e
xact
ly o
ne
elem
ent
of
the
ran
ge, t
his
rel
atio
n i
s a
fun
ctio
n.
D
eter
min
e w
het
her
3x
- y
= 6
is
a f
un
ctio
n.
Sin
ce t
he
equ
atio
n i
s in
th
e fo
rm
Ax
+ B
y =
C, t
he
grap
h o
f th
e eq
uat
ion
wil
l be
a l
ine,
as
show
n
at t
he
righ
t.
If y
ou d
raw
a v
erti
cal
lin
e th
rou
gh e
ach
val
ue
of x
, th
e ve
rtic
al l
ine
pass
es t
hro
ugh
just
on
e po
int
of t
he
grap
h. T
hu
s, t
he
lin
e re
pres
ents
a f
un
ctio
n.
Exer
cise
sD
eter
min
e w
het
her
eac
h r
elat
ion
is
a fu
nct
ion
.
1.
2.
3.
4.
5.
6.
7. {
(4, 2
), (2
, 3),
(6, 1
)}
8. {
(-3,
-3)
, (-
3, 4
), (-
2, 4
)}
9. {
(-1,
0),
(1, 0
)}
10. -
2x +
4y
= 0
11
. x2
+ y
2 =
8
12. x
= -
4
x
y
Ox
y
Ox
y O
XY 4 5 6 7
-1 0 1 2
x
y
Ox
y
O
x
y
O
1-7
Stud
y G
uide
and
Inte
rven
tion
Fu
ncti
on
s
Exam
ple
1Ex
amp
le 2
y
es
yes
n
o
n
o
no
y
es
y
es
no
y
es
y
es
no
n
o
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An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A21 Glencoe Algebra 1
Answers (Lesson 1-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
44
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Fu
ncti
on
s
1-7
Fin
d F
un
ctio
n V
alu
es E
quat
ions
tha
t ar
e fu
ncti
ons
can
be w
ritt
en i
n a
form
cal
led
fun
ctio
n n
otat
ion
. For
exa
mpl
e, y
= 2
x -
1 ca
n be
wri
tten
as
f(x)
= 2
x -
1. I
n th
e fu
ncti
on,
x re
pres
ents
the
ele
men
ts o
f th
e do
mai
n, a
nd f
(x)
repr
esen
ts t
he e
lem
ents
of
the
rang
e.
Sup
pose
you
wan
t to
fin
d th
e va
lue
in t
he r
ange
tha
t co
rres
pond
s to
the
ele
men
t 2
in t
he
dom
ain.
Thi
s is
wri
tten
f(2
) an
d is
rea
d “f
of
2.”
The
val
ue o
f f(
2) i
s fo
und
by s
ubst
itut
ing
2 fo
r x
in t
he e
quat
ion.
If
f(x
) =
3x
- 4
, fin
d e
ach
val
ue.
a. f
(3)
f(3)
= 3
(3)
- 4
R
epla
ce x
with 3
.
=
9 -
4
Multip
ly.
=
5
Sim
plif
y.
b.
f(-
2) f(
-2)
= 3
(-2)
- 4
R
epla
ce x
with -
2.
=
-6
- 4
M
ultip
ly.
=
-10
S
implif
y.
Exer
cise
sIf
f(x
) =
2x
- 4
an
d g
(x)
= x
2 -
4x,
fin
d e
ach
val
ue.
1. f
(4)
2. g
(2)
3. f
(-5)
4. g
(-3)
5.
f(0
) 6.
g(0
)
7. f
(3)
- 1
8.
f ( 1 −
4 ) 9.
g ( 1 −
4 )
10. f
(a2 )
11
. f(k
+ 1
) 12
. g(2
n)
13. f
(3x)
14
. f(2
) +
3
15. g
(-4)
Exam
ple
4
-
4 -
14
2
1 -
4 0
1
-
3 1 −
2 -
15
−
16
2
a2
- 4
2
k -
2
4n
2 -
8n
6
x -
4
3
32
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-7
Cha
pte
r 1
45
Gle
ncoe
Alg
ebra
1
1-7
Skill
s Pr
acti
ceFu
ncti
on
s
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.
1.
2.
3.
4.
xy
4
-
5
-1
-10
0
-
9
1
-
7
9
1
5.
x
y
2
7
5
-3
3
5
-4
-2
5
2
6.
x
y
3
7
-1
1
1
0
3
5
7
3
7. {
(2, 5
), (4
, -2)
, (3,
3),
(5, 4
), (-
2, 5
)}
8. {
(6, -
1), (
-4,
2),
(5, 2
), (4
, 6),
(6, 5
)}
9.
y =
2x
- 5
10
. y
= 1
1
11.
12
.
13.
If f
(x)
= 3
x +
2 a
nd
g(x
) =
x2
- x
, fin
d e
ach
val
ue.
14. f
(4)
15
. f(
8)
16. f
(-2)
17
. g(2
)
18. g
(-3)
19
. g(-
6)
20. f
(2)
+ 1
21
. f(1
) -
1
22. g
(2)
- 2
23
. g(-
1) +
4
24. f
(x +
1)
25
. g(3
b)
x
y
Ox
y
Ox
y
O
XY
4 6 7
2-
1 3 5
XY 4 1
-2
5 2 0-
3
XY 4 1
-3
-5
-6
-2 1 3
yes
yes
no
yes
no
no
yes
no
yes
yes
yes
no
no
1426
-4
2
1242
94
06
3x +
59b
2 -
3b
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Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A22 Glencoe Algebra 1
Answers (Lesson 1-7)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
46
Gle
ncoe
Alg
ebra
1
1-7
Prac
tice
Fu
ncti
on
s
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.
1.
2.
X
Y
1
-5
-4
3
7
6
1
-2
3.
4. {
(1, 4
), (2
, -2)
, (3,
-6)
, (-
6, 3
), (-
3, 6
)}
5. {
(6, -
4), (
2, -
4), (
-4,
2),
(4, 6
), (2
, 6)}
6. x
= -
2 7.
y =
2
If f
(x)
= 2
x -
6 a
nd
g(x
) =
x -
2x2 ,
fin
d e
ach
val
ue.
8. f
(2)
9.
f (-
1 −
2 )
10
. g(
-1)
11. g
(-
1 −
3 ) 12
. f(7
) -
9
13. g
(-3)
+ 1
3
14. f
(h +
9)
15
. g(3
y)
16. 2
[g(b
) +
1]
17. W
AG
ES M
arti
n e
arn
s $7
.50
per
hou
r pr
oofr
eadi
ng
ads
at a
loc
al n
ewsp
aper
. His
wee
kly
wag
e w
can
be
desc
ribe
d by
th
e eq
uat
ion
w =
7.5
h, w
her
e h
is
the
nu
mbe
r of
hou
rs
wor
ked.
a. W
rite
th
e eq
uat
ion
in
fu
nct
ion
not
atio
n.
b.
Fin
d f(
15),
f(20
), an
d f(
25).
18. E
LEC
TRIC
ITY
Th
e ta
ble
show
s th
e re
lati
onsh
ip b
etw
een
res
ista
nce
R a
nd
curr
ent
I in
a c
ircu
it.
Res
ista
nce
(o
hm
s)12
08
04
86
4
Cu
rren
t (a
mp
eres
)0
.10
.15
0.2
52
3
a. I
s th
e re
lati
onsh
ip a
fu
nct
ion
? E
xpla
in.
b.
If t
he
rela
tion
can
be
repr
esen
ted
by t
he
equ
atio
n I
R =
12,
rew
rite
th
e eq
uat
ion
in
fu
nct
ion
not
atio
n s
o th
at t
he
resi
stan
ce R
is
a fu
nct
ion
of
the
curr
ent
I.
c. W
hat
is
the
resi
stan
ce i
n a
cir
cuit
wh
en t
he
curr
ent
is 0
.5 a
mpe
re?
x
y
O
XY 0 3
-2
-3
-2 1 5
yes
no
yes
y
es
n
on
oye
s
2h +
12
3y -
18y
22b
- 4
b2
+ 2
f(h
) =
7.5
h
112.
50, 1
50, 1
87.5
0
Yes;
fo
r ea
ch v
alu
e in
th
e d
om
ain
, th
ere
is o
nly
on
e va
lue
in t
he
ran
ge.
24 o
hm
s
-2
-7
-3
f(I)
= 12
−
I
-
5 −
9 -
1 -
8
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PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-7
Cha
pte
r 1
47
Gle
ncoe
Alg
ebra
1
1.TR
AN
SPO
RTA
TIO
N T
he
cost
of
ridi
ng
in a
cab
is
$3.0
0 pl
us
$0.7
5 pe
r m
ile.
Th
e eq
uat
ion
th
at r
epre
sen
ts t
his
rel
atio
n i
s y
= 0.
75x
+ 3,
wh
ere
x is
th
e n
um
ber
of
mil
es t
rave
led
and
y is
th
e co
st o
f th
e tr
ip. L
ook
at t
he
grap
h o
f th
e eq
uat
ion
an
d de
term
ine
wh
eth
er t
he
rela
tion
is
a fu
nct
ion
.
Dis
tan
ce (
mile
s)2
10
43
y
x5
67
89
10
Cost ($)
68 4 21016 14 12
2. T
EXT
MES
SAG
ING
Man
y ce
ll p
hon
es
hav
e a
text
mes
sagi
ng
opti
on i
n a
ddit
ion
to
reg
ula
r ce
ll p
hon
e se
rvic
e. T
he
fun
ctio
n f
or t
he
mon
thly
cos
t of
tex
t m
essa
gin
g se
rvic
e fr
om N
olin
e W
irel
ess
Com
pan
y is
f(x
) =
0.
10x
+ 2,
wh
ere
x is
th
e n
um
ber
of t
ext
mes
sage
s th
at a
re
sen
t. F
ind
f(10
) an
d f(
30),
the
cost
of
10
text
mes
sage
s in
a m
onth
an
d th
e co
st o
f 30
tex
t m
essa
ges
in a
mon
th.
3.G
EOM
ETRY
Th
e ar
ea f
or a
ny
squ
are
is
give
n b
y th
e fu
nct
ion
y =
x2 ,
wh
ere
x is
th
e le
ngt
h o
f a
side
of
the
squ
are
and
y is
th
e ar
ea o
f th
e sq
uar
e. W
rite
th
e eq
uat
ion
in
fu
nct
ion
not
atio
n a
nd
fin
d th
e ar
ea o
f a
squ
are
wit
h a
sid
e le
ngt
h o
f 3.
5 in
ches
.
4.TR
AV
EL T
he
cost
for
car
s en
teri
ng
Pre
side
nt
Geo
rge
Bu
sh T
urn
pike
at
Bel
tlin
e ro
ad i
s gi
ven
by
the
rela
tion
x
= 0.
75, w
her
e x
is t
he
doll
ar a
mou
nt
for
entr
ance
to
the
toll
roa
d an
d y
is t
he
nu
mbe
r of
pas
sen
gers
. Det
erm
ine
if t
his
re
lati
on i
s a
fun
ctio
n. E
xpla
in.
5. C
ON
SUM
ER C
HO
ICES
Ais
ha
just
re
ceiv
ed a
$40
pay
chec
k fr
om h
er n
ew
job.
Sh
e sp
ends
som
e of
it
buyi
ng
mu
sic
onli
ne
and
save
s th
e re
st i
n a
ban
k ac
cou
nt.
Her
sav
ings
is
give
n b
y f(
x) =
40 –
1.2
5x, w
her
e x
is t
he
nu
mbe
r of
so
ngs
sh
e do
wn
load
s at
$1.
25 p
er s
ong.
a. G
raph
th
e fu
nct
ion
.
Son
gs
Purc
has
ed10
50
2015
x25
3035
40
Savings ($)
1520 10 52540 35 30
f (x)
b.
Fin
d f(
3), f
(18)
, an
d f(
36).
Wh
at d
o th
ese
valu
es r
epre
sen
t?
c. H
ow m
any
son
gs c
an A
ish
a bu
y if
sh
e w
ants
to
save
$30
?
1-7
Wor
d Pr
oble
m P
ract
ice
Fu
ncti
on
s
yes
f(10
) = $
3; f
(30)
= $
5
Th
is r
elat
ion
is n
ot
a fu
nct
ion
. T
he
gra
ph
wo
uld
be
a ve
rtic
al li
ne,
w
hic
h w
ou
ld n
ot
pas
s th
e ve
rtic
al
line
test
.
f(3)
= 3
6.25
; bu
ys 3
so
ng
s,
save
s $3
6.25
f(18
) =
17.
50;
buys
18
son
gs,
sa
ves
$17.
50f(
36)
= -
5; s
amp
le a
nsw
er:
if s
he
wan
ts t
o b
uy 3
6 so
ng
s,
she
nee
ds
$5 e
xtra 8
son
gs
f
(x)
= x
2 f(
3.5)
= (3
.5)2
=
12
.25
in2
042_
054_
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An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A23 Glencoe Algebra 1
Answers (Lesson 1-7 and Lesson 1-8)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
48
Gle
ncoe
Alg
ebra
1
Co
mp
osit
e F
un
cti
on
s
Th
ree
thin
gs a
re n
eede
d to
hav
e a
fun
ctio
n—
a se
t ca
lled
th
e do
mai
n,
a se
t ca
lled
th
e ra
nge
, an
d a
rule
th
at m
atch
es e
ach
ele
men
t in
th
e do
mai
n w
ith
on
ly o
ne
elem
ent
in t
he
ran
ge. H
ere
is a
n e
xam
ple.
Ru
le: f
(x)
= 2
x +
1
3
-5
f(x)
5
x 21
-3
f(
x) =
2x
+ 1
f(
1) =
2(1
) +
1 =
2 +
1 =
3
f(
2) =
2(2
) +
1 =
4 +
1 =
5
f(
-3)
=
2(
-3)
+ 1
= -
6 +
1 =
-5
Su
ppos
e w
e h
ave
thre
e se
ts A
, B, a
nd
C a
nd
two
fun
ctio
ns
desc
ribe
d as
sh
own
bel
ow.
Ru
le: f
(x)
= 2
x +
1
Ru
le: g
(y)
= 3
y -
4
AB
C
f(x) 3
5
x 1
g[f(x
)]
g(
y) =
3y
- 4
g(3)
= 3
(3)
- 4
= 5
Let
’s f
ind
a ru
le t
hat
wil
l m
atch
ele
men
ts o
f se
t A
wit
h e
lem
ents
of
set
C w
ith
out
fin
din
g an
y el
emen
ts i
n s
et B
. In
oth
er w
ords
, let
’s f
ind
a ru
le f
or t
he
com
pos
ite
fun
ctio
n g
[f(x
)].
Sin
ce f
(x)
= 2
x +
1, g
[f(x
)] =
g(2
x +
1).
Sin
ce g
(y)
= 3
y -
4, g
(2x
+ 1
) =
3(2
x +
1)
- 4
, or
6x -
1.
Th
eref
ore,
g[f
(x)]
= 6
x -
1.
Fin
d a
ru
le f
or t
he
com
pos
ite
fun
ctio
n g
[f(x
)].
1. f
(x)
= 3
x an
d g(
y) =
2y
+ 1
2.
f(x
) =
x2
+ 1
an
d g(
y) =
4y
3. f
(x)
= -
2x a
nd
g(y)
= y
2 -
3y
4. f
(x)
=
1 −
x -
3 a
nd
g(y)
= y
-1
5. I
s it
alw
ays
the
case
th
at g
[f(x
)] =
f[g
(x)]
? Ju
stif
y yo
ur
answ
er.
Enri
chm
ent
1-7
g
[f(x
)] =
6x +
1
g
[f(x
)] =
4x
2 +
4
g
[f(x
)] =
4x
2 +
6x
g
[f(x
)] =
x -
3
N
o. F
or
exam
ple
, in
Exe
rcis
e 1,
f[g
(x)]
= f
(2x +
1)
= 3
(2x +
1)
+ 6
x +
3, n
ot
6x +
1.
042_
054_
ALG
1_A
_CR
M_C
01_C
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6049
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5:21
PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Lesson 1-8
Cha
pte
r 1
49
Gle
ncoe
Alg
ebra
1
1-8
Stud
y G
uide
and
Inte
rven
tion
Inte
rpre
tin
g G
rap
hs o
f Fu
ncti
on
s
Inte
rpre
t In
terc
epts
an
d S
ymm
etry
Th
e in
terc
epts
of
a gr
aph
are
poi
nts
wh
ere
the
grap
h i
nte
rsec
ts a
n a
xis.
Th
e y-
coor
din
ate
of t
he
poin
t at
wh
ich
th
e gr
aph
in
ters
ects
th
e y-
axis
is
call
ed a
y-
inte
rcep
t. S
imil
arly
, th
e x-
coor
din
ate
of t
he
poin
t at
wh
ich
a g
raph
in
ters
ects
th
e x-
axis
is
call
ed a
n x
-in
terc
ept.
A
gra
ph p
osse
sses
lin
e sy
mm
etry
in
a l
ine
if e
ach
hal
f of
th
e gr
aph
on
eit
her
sid
e of
th
e li
ne
mat
ches
exa
ctly
.
AR
CH
ITEC
TUR
E T
he
grap
h s
how
s a
fun
ctio
n t
hat
ap
pro
xim
ates
th
e sh
ape
of t
he
Gat
eway
Arc
h, w
her
e x
is t
he
dis
tan
ce f
rom
th
e ce
nte
r p
oin
t in
fee
t an
d y
is
the
hei
ght
in f
eet.
Id
enti
fy t
he
fun
ctio
n a
s li
nea
r or
n
onli
nea
r. T
hen
est
imat
e an
d i
nte
rpre
t th
e in
terc
epts
, an
d d
escr
ibe
and
in
terp
ret
any
sym
met
ry.
Lin
ear
or N
onli
nea
r: S
ince
th
e gr
aph
is
a cu
rve
and
not
a
lin
e, t
he
grap
h i
s n
onli
nea
r.y-
Inte
rcep
t: T
he
grap
h i
nte
rsec
ts t
he
y-ax
is a
t ab
out
(0, 6
30),
so t
he
y-in
terc
ept
of t
he
grap
h i
s ab
out
630.
Th
is m
ean
s th
at
the
hei
ght
of t
he
arch
is
630
feet
at
the
cen
ter
poin
t.x-
Inte
rcep
t(s)
: T
he
grap
h i
nte
rsec
ts t
he
x-ax
is a
t ab
out
(-32
0, 0
) an
d (3
20, 0
). S
o th
e x-
inte
rcep
ts a
re a
bou
t -
320
and
320.
Th
is m
ean
s th
at t
he
obje
ct t
ouch
es t
he
grou
nd
to t
he
left
an
d ri
ght
of t
he
cen
ter
poin
t.S
ymm
etry
: T
he
righ
t h
alf
of t
he
grap
h i
s th
e m
irro
r im
age
of t
he
left
hal
f in
th
e y-
axis
. In
th
e co
nte
xt o
f th
e si
tuat
ion
, th
e sy
mm
etry
of
the
grap
h t
ells
you
th
at t
he
arch
is
sym
met
ric.
T
he
hei
ght
of t
he
arch
at
any
dist
ance
to
the
righ
t of
th
e ce
nte
r is
th
e sa
me
as i
ts h
eigh
t th
at s
ame
dist
ance
to
the
left
.
Iden
tify
th
e fu
nct
ion
gra
ph
ed a
s li
nea
r or
non
lin
ear.
Th
en e
stim
ate
and
in
terp
ret
the
inte
rcep
ts o
f th
e gr
aph
an
d a
ny
sym
met
ry.
1.
Righ
t Wha
le P
opul
atio
n
Population80 0
160
240
Gene
ratio
ns S
ince
200
74
812
y
x
2.
St
ock
Pric
e
Price Variation (points)
-22 0 Ti
me
Sinc
e O
peni
ng B
ell (
h)
24
6
y
x
3.
y
x
Ave
rage
Gas
olin
ePr
ice
Price ($ per gallon)
23 1 0456
Year
s Si
nce
1987
1510
525
2030
L
inea
r; t
he
y-i
nte
rcep
t is
250
, so
th
ere
wer
e 25
0 ri
gh
t w
hal
es in
19
87;
x-in
terc
ept
is 1
0, s
o t
her
e w
ill b
e n
o r
igh
t w
hal
es a
fter
10
gen
erat
ion
s; n
o li
ne
sym
met
ry.
N
on
linea
r; y
-in
terc
ept
is 0
, so
th
eres
n
o c
han
ge
in t
he
sto
ck v
alu
e at
th
e o
pen
ing
bel
l; x-
inte
rcep
ts a
re 0
an
d
abo
ut
5.3,
so
th
ere
is n
o c
han
ge
in
the
valu
e af
ter
0 h
ou
rs a
nd
ab
ou
t 5.
3 h
ou
rs a
fter
op
enin
g;
no
lin
e sy
mm
etry
.
No
nlin
ear;
y-in
terc
ept
abo
ut
1,
so t
he
aver
age
pri
ce o
f g
as
was
ab
ou
t $1
per
gal
lon
in
1987
; no
x-in
terc
epts
, so
th
ere
is n
o t
ime
wh
en g
as w
as f
ree;
n
o li
ne
sym
met
ry.
Exam
ple
O
y
x
y -in
terc
ept
x -in
terc
ept
Gate
way
Arc
h
Height (ft)
0Di
stan
ce (f
t)80
-80
-24
024
0
160
240 80320
400
480
560y
x
042_
054_
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PM
A15_A26_ALG1_A_CRM_C01_AN_660498.indd A23A15_A26_ALG1_A_CRM_C01_AN_660498.indd A23 12/21/10 6:44 PM12/21/10 6:44 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A24 Glencoe Algebra 1
Answers (Lesson 1-8)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
50
Gle
ncoe
Alg
ebra
1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Inte
rpre
tin
g G
rap
hs o
f Fu
ncti
on
s
1-8
Inte
rpre
t Ex
trem
a an
d E
nd
Beh
avio
r In
terp
reti
ng
a gr
aph
als
o in
volv
es
esti
mat
ing
and
inte
rpre
tin
g w
her
e th
e fu
nct
ion
is
incr
easi
ng,
dec
reas
ing,
pos
itiv
e, o
r n
egat
ive,
an
d w
her
e th
e fu
nct
ion
has
an
y ex
trem
e va
lues
, eit
her
hig
h o
r lo
w.
Exam
ple
HEA
LTH
Th
e ou
tbre
ak o
f th
e H
1N1
viru
s ca
n b
e m
odel
ed b
y th
e fu
nct
ion
gra
ph
ed a
t th
e ri
ght.
Est
imat
e an
d i
nte
rpre
t w
her
e th
e fu
nct
ion
is
pos
itiv
e, n
egat
ive,
in
crea
sin
g, a
nd
d
ecre
asin
g, t
he
x-co
ord
inat
es o
f an
y re
lati
ve e
xtre
ma,
an
d
the
end
beh
avio
r of
th
e gr
aph
.
Pos
itiv
e: f
or x
bet
wee
n 0
an
d 42
N
egat
ive:
no
part
s of
dom
ain
Th
is m
ean
s th
at t
he
nu
mbe
r of
rep
orte
d ca
ses
was
alw
ays
posi
tive
. Th
is i
s re
ason
able
bec
ause
a n
egat
ive
nu
mbe
r of
cas
es
can
not
exi
st i
n t
he
con
text
of
the
situ
atio
n.
Incr
easi
ng:
for
x b
etw
een
0 a
nd
42
Dec
reas
ing:
no
part
s of
dom
ain
Th
e n
um
ber
of r
epor
ted
case
s in
crea
sed
each
day
fro
m t
he
firs
t da
y of
th
e ou
tbre
ak.
Rel
ativ
e M
axim
um
: at
abo
ut
x =
42
Rel
ativ
e M
inim
um
: at
x =
0T
he e
xtre
ma
of t
he g
raph
ind
icat
e th
at t
he n
umbe
r of
rep
orte
d ca
ses
peak
ed a
t ab
out
day
42.
En
d B
ehav
ior:
As
x in
crea
ses,
y a
ppea
rs t
o ap
proa
ch 1
1,00
0. A
s x
decr
ease
s, y
dec
reas
es.
Th
e en
d be
hav
ior
of t
he
grap
h i
ndi
cate
s a
max
imu
m n
um
ber
of r
epor
ted
case
s of
11,
000.
Est
imat
e an
d i
nte
rpre
t w
her
e th
e fu
nct
ion
is
pos
itiv
e, n
egat
ive,
in
crea
sin
g, a
nd
d
ecre
asin
g, t
he
x-co
ord
inat
e of
an
y re
lati
ve e
xtre
ma,
an
d t
he
end
beh
avio
r of
th
e gr
aph
.
1.
Righ
t Wha
le P
opul
atio
n
Population
80 0
160
240
Gene
ratio
ns S
ince
200
74
812
y
x
2.
Stoc
k Pr
ice
Price Variation (points)
-22 0 Ti
me
Sinc
e O
peni
ng B
ell (
h)
24
6
y
x
3.
y
x
Ave
rage
Gas
olin
ePr
ice
Price ($ per gallon)
23 1 0456
Year
s Si
nce
1987
1510
525
2030
y
x
Wor
ldw
ide
H1N
1
Reported Cases
4000 0
8000
12,0
00
Day
s Si
nce
Out
brea
k21
147
3528
42
Th
e p
op
ula
tio
n is
ab
ove
0 fo
r th
e fi
rst
10 g
ener
atio
ns,
an
d t
hen
bel
ow
0. A
neg
ativ
e p
op
ula
tio
n is
no
t re
aso
nab
le. T
he
po
pu
lati
on
is
go
ing
do
wn
fo
r th
e en
tire
ti
me.
Th
ere
are
no
ext
rem
a.
As
the
tim
e in
crea
ses,
th
e p
op
ula
tio
n w
ill c
on
tin
ue
to
dro
p.
Th
e st
ock
wen
t d
own
in v
alu
e fo
r th
e fi
rst
3.2
ho
urs
, an
d t
hen
ro
se
un
til t
he
end
of
the
day
. Th
e st
ock
va
lue
dec
reas
es in
val
ue
for
the
fi rs
t 3.
2 h
ou
rs, a
nd
th
en g
oes
up
in
val
ue
for
the
rem
ain
der
of
the
day
. Th
e st
ock
had
a r
elat
ive
low
va
lue
afte
r 3.
2 h
ou
rs a
nd
th
en a
re
lativ
e h
igh
val
ue
at t
he
end
of
the
day
. As
the
day
go
es o
n, t
he
sto
ck in
crea
ses
in v
alu
e.
Th
e av
erag
e g
aso
line
pri
ce is
alw
ays
po
siti
ve. I
t in
crea
ses
for
the
fi rs
t fe
w
year
s, d
ecre
ases
un
til
abo
ut
the
11th
yea
r, th
en
incr
ease
s. T
he
rela
tive
m
inim
a ar
e at
1 a
nd
ab
ou
t 11
. Th
e av
erag
e p
rice
ap
pea
rs t
o in
crea
se a
s ti
me
pas
ses.
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NA
ME
DAT
E
P
ER
IOD
Lesson 1-8
Cha
pte
r 1
51
Gle
ncoe
Alg
ebra
1
Skill
s Pr
acti
ceIn
terp
reti
ng
Gra
ph
s o
f Fu
ncti
on
s
1-8
Iden
tify
th
e fu
nct
ion
gra
ph
ed a
s li
nea
r or
non
lin
ear.
Th
en e
stim
ate
and
in
terp
ret
the
inte
rcep
ts o
f th
e gr
aph
, an
y sy
mm
etry
, wh
ere
the
fun
ctio
n i
s p
osit
ive,
n
egat
ive,
in
crea
sin
g, a
nd
dec
reas
ing,
th
e x-
coor
din
ate
of a
ny
rela
tive
ext
rem
a,
and
th
e en
d b
ehav
ior
of t
he
grap
h.
1.
Dav
id’s
Sav
ings
for
Car
Savings ($) 1400
1200 0
1600
1800
2000
2200
Wee
ks2
46
810
y
x
3.
y
x
Hei
ght o
f Gol
f Bal
l
Height (ft)
40 080120
160
Dist
ance
from
Tee
(yd)
4080
120
160
2.
y
x
Baki
ng S
uppl
ies
Flour (c)
4 08121620
Batc
hes
of C
ooki
es4
812
4.
Sola
r Re
flect
or
Height (ft)
Wid
th (f
t)
y
xO16 8
−8
−16
−8
−16
816
focu
s
linea
r; y
-in
terc
ept
= 1
400;
no
x-i
nte
rcep
t; n
o li
ne
sym
met
ry;
po
siti
ve a
nd
incr
easi
ng
fo
r x >
0;
min
imu
m is
$14
00
at t
ime
0;
savi
ng
s w
ill c
on
tin
ue
to in
crea
se;
see
stu
den
ts’ w
ork
fo
r in
terp
reta
tio
ns.
linea
r; y
-inte
rcep
t =
20;
x-in
terc
ept
= 1
0; n
o li
ne
sym
met
ry;
po
sitiv
e an
d
dec
reas
ing
fo
r x >
0; m
axim
um
is
20 c
up
s at
tim
e 0;
am
ou
nt
of
fl ou
r w
ill d
ecre
ase
un
til it
is g
on
e; s
ee
stu
den
ts’ w
ork
fo
r in
terp
reta
tion
s.
nonl
inea
r; y
-inte
rcep
t ≈
0;
x-in
terc
epts
≈ 0
and
120
; lin
e sy
mm
etry
x ≈
60;
hei
ght
was
al
way
s po
sitiv
e an
d in
crea
sed
until
it
was
60
yard
s fr
om t
he te
e an
d
decr
ease
d 60
to 1
20 y
ards
fro
m t
he
tee;
see
stu
dent
s’ w
ork
for
inte
rpre
tatio
ns.
no
nlin
ear;
y-i
nte
rcep
t =
-6.
25;
x-i
nte
rcep
ts =
-12
.5 a
nd
12.
5;
line
sym
met
ry a
bo
ut
the
y-a
xis;
p
osi
tive
fo
r x <
12.
5 an
d x
> 1
2.5;
th
e m
inim
um
is -
6.25
at
0;
see
stu
den
ts’ w
ork
fo
r in
terp
reta
tio
ns.
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An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A25 Glencoe Algebra 1
Answers (Lesson 1-8)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
52
Gle
ncoe
Alg
ebra
1
Prac
tice
Inte
rpre
tin
g G
rap
hs o
f Fu
ncti
on
s
1-8
Iden
tify
th
e fu
nct
ion
gra
ph
ed a
s li
nea
r or
non
lin
ear.
Th
en e
stim
ate
and
in
terp
ret
the
inte
rcep
ts o
f th
e gr
aph
, an
y sy
mm
etry
, wh
ere
the
fun
ctio
n i
s p
osit
ive,
n
egat
ive,
in
crea
sin
g, a
nd
dec
reas
ing,
th
e x-
coor
din
ate
of a
ny
rela
tive
ext
rem
a,
and
th
e en
d b
ehav
ior
of t
he
grap
h.
1.
y
x
Who
lesa
le T
-Shi
rt O
rder
Total Cost ($)
200 0
400
600
800
1000
Shirt
s (d
ozen
s)2
46
810
3.
y
x
Hei
ght o
f Div
er
Height Above Water (m)
2 04681012
Tim
e (s
)0.
51
1.5
22.
5
2.
y
x
Wat
er L
evel
Water Level (cm)
28 032364044
Tim
e (s
econ
ds)
4080
120
160
200
240
4.
y
x
Boys
’ Ave
rage
Hei
ght
Height (in.)
24 04872
Age
(yr)
48
1216
20
Lin
ear;
y-i
nte
rcep
t is
50,
so
th
e se
t u
p c
ost
is
$50;
no
x-i
nte
rcep
t, so
at
no
tim
e is
th
e co
st $
0;
no
lin
e sy
mm
etry
; p
osi
tive
an
d in
crea
sin
g f
or
x
> 0
, so
th
e co
st is
alw
ays
po
siti
ve w
ill in
crea
se
as m
ore
sh
irts
are
ord
ered
.
No
nlin
ear;
y-in
terc
ept
is a
bo
ut
43, s
o w
ater
leve
l w
as a
bo
ut
43 c
m w
hen
tim
e st
arte
d; n
o
x-in
terc
ept,
so t
he
wat
er le
vel d
id n
ot
reac
h 0
; no
lin
e sy
mm
etry
; wat
er le
vel w
as a
lway
s p
osi
tive
and
dec
reas
ed t
he
entir
e tim
e; g
rap
h a
pp
ears
to
le
vel o
ff o
r b
egin
to
incr
ease
as
x in
crea
ses.
No
nlin
ear;
y-i
nte
rcep
t is
24,
so
th
e av
erag
e b
oy
is 2
4 in
ches
at
bir
th;
no
x-i
nte
rcep
t; n
o li
ne
sym
met
ry;
alw
ays
po
siti
ve, s
o h
eig
hts
are
al
way
s p
osi
tive
; ap
pea
rs t
o b
e a
max
imu
m o
f ab
ou
t 72
at
abo
ut
19, t
his
mea
ns
that
an
av
erag
e b
oy r
each
es h
is m
axim
um
hei
gh
t o
f 72
in
ches
at
age
19.
No
nlin
ear;
y-i
nte
rcep
t is
10,
so
div
er s
tart
ed a
t 10
m;
x-i
nte
rcep
t o
f ab
ou
t 1.
8, s
o d
iver
en
tere
d
the
wat
er a
fter
ab
ou
t 1.
8 se
c.;
no
lin
e sy
mm
etry
; h
eig
ht
was
po
siti
ve f
or
x <
1.8
an
d n
egat
ive
for
x >
1.8
, so
div
er w
as a
bov
e th
e w
ater
un
til 1
.8
sec.
; th
e h
eig
ht
incr
ease
d u
nti
l max
. of
10.5
at
0.3
sec.
, th
en it
dec
reas
ed;
div
er w
ou
ld c
on
tin
ue
to g
o d
ow
n f
or
som
e ti
me,
th
en w
ou
ld c
om
e u
p.
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NA
ME
DAT
E
P
ER
IOD
Lesson 1-8
Cha
pte
r 1
53
Gle
ncoe
Alg
ebra
1
1-8
Wor
d Pr
oble
m P
ract
ice
Inte
rpre
tin
g G
rap
hs o
f Fu
ncti
on
s
1.H
EALT
H T
he g
raph
sho
ws
the
Cal
orie
s y
burn
ed b
y a
130-
poun
d pe
rson
sw
imm
ing
free
styl
e la
ps a
s a
func
tion
of t
ime
x.
Iden
tify
the
func
tion
as
line
ar o
r no
nlin
ear.
T
hen
esti
mat
e an
d in
terp
ret
the
inte
rcep
ts.
y
x
Calo
ries
Bur
ned
Swim
min
g
Calories (kC)
800
1200 400 0
1600
2000
2400
2800
Tim
e (h
)3
21
57
46
8
2. T
ECH
NO
LOG
Y T
he
grap
h b
elow
sh
ows
the
resu
lts
of a
pol
l th
at a
sks
Am
eric
ans
wh
eth
er t
hey
use
d th
e In
tern
et
yest
erda
y. E
stim
ate
and
inte
rpre
t w
her
e th
e fu
nct
ion
is
posi
tive
, neg
ativ
e,
incr
easi
ng,
an
d de
crea
sin
g, t
he
x-co
ordi
nat
es o
f an
y re
lati
ve e
xtre
ma,
an
d th
e en
d be
hav
ior
of t
he
grap
h.
y
x
Did
you
use
the
Inte
rnet
yes
terd
ay?
Yes Responses(percent of polled)
60 070
Mon
ths
Sinc
e Ja
nuar
y 20
0512
2436
4860
3.G
EOM
ETRY
Th
e gr
aph
sh
ows
the
area
yin
squ
are
cen
tim
eter
s of
a r
ecta
ngl
e w
ith
pe
rim
eter
20
cen
tim
eter
s an
d w
idth
xce
nti
met
ers.
Des
crib
e an
d in
terp
ret
any
sym
met
ry i
n t
he
grap
h.
Are
a (c
m2 )
Area (cm2)
Wid
th (c
m)
10
-102030 0
24
68
10
y
x
4. E
DU
CATI
ON
Ide
ntify
the
func
tion
gra
phed
as
line
ar o
r no
nlin
ear.
The
n es
tim
ate
and
inte
rpre
t th
e in
terc
epts
of t
he g
raph
, any
sy
mm
etry
, whe
re t
he fu
ncti
on is
pos
itiv
e,
nega
tive
, inc
reas
ing,
and
dec
reas
ing,
the
x-
coor
dina
te o
f any
rel
ativ
e ex
trem
a, a
nd
the
end
beha
vior
of t
he g
raph
.
U.S.
Edu
catio
n Sp
endi
ng
Spending (billions of $)
200 0
400
600
800
1000
Year
s Si
nce
1949
3020
1050
7040
60
y
x
Lin
ear;
th
e x-
an
d y
-in
terc
epts
are
0. T
his
m
ean
s th
at n
o C
alo
ries
are
bu
rned
wh
en n
o
tim
e is
sp
ent
swim
min
g.
Th
e g
rap
h is
sym
met
ric
in t
he
line
x =
5. I
n
the
con
text
of
the
situ
atio
n, t
he
sym
met
ry
mea
ns
that
th
e ar
ea is
th
e sa
me
wh
en w
idth
is
a n
um
ber
less
th
an o
r g
reat
er t
han
5.
No
nlin
ear;
y-i
nte
rcep
t is
ab
ou
t 10
, so
sp
end
ing
was
ab
ou
t $1
0 b
illio
n in
194
9; n
o
x-in
terc
ept;
fu
nct
ion
is p
osi
tive
fo
r al
l val
ues
o
f x, s
o e
du
cati
on
sp
end
ing
has
nev
er b
een
$0
; fu
nct
ion
is in
crea
sin
g f
or
all v
alu
es o
f x,
wit
h n
o r
elat
ive
max
ima
or
min
ima;
as
x-in
crea
ses,
y-i
ncr
ease
s, s
o t
he
up
war
d
tren
d in
sp
end
ing
is e
xpec
ted
to
co
nti
nu
e.
Th
e fu
nct
ion
is p
osi
tive
an
d in
crea
sin
g f
or
x >
0, s
o In
tern
et u
se is
incr
easi
ng
am
on
g
tho
se p
olle
d. T
her
e ar
e n
o e
xtre
ma.
As
x
incr
ease
s, y
incr
ease
s, s
o In
tern
et u
se is
ex
pec
ted
to
co
nti
nu
e to
incr
ease
. Ho
wev
er
sin
ce t
he
dat
a ar
e p
erce
nts
, 10
0 is
th
e m
axim
um
it c
ou
ld e
ver
reac
h.
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Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF 2nd
Chapter 1 A26 Glencoe Algebra 1
Answers (Lesson 1-8)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DAT
E
P
ER
IOD
Cha
pte
r 1
54
Gle
ncoe
Alg
ebra
1
1-8
Enri
chm
ent
Sym
metr
y i
n G
rap
hs o
f Fu
ncti
on
sYo
u h
ave
seen
th
at t
he
grap
hs
of s
ome
fun
ctio
ns
hav
e li
ne
sym
met
ry. F
un
ctio
ns
that
hav
e li
ne
sym
met
ry i
n t
he
y-ax
is a
re c
alle
d ev
en f
un
ctio
ns.
Th
e gr
aph
of
a fu
nct
ion
can
als
o h
ave
poin
t sy
mm
etry
. Rec
all
that
a f
igu
re h
as p
oin
t sy
mm
etry
if
it c
an b
e ro
tate
d le
ss t
han
36
0° a
bou
t th
e po
int
so t
hat
th
e im
age
mat
ches
th
e or
igin
al f
igu
re. F
un
ctio
ns
that
are
sy
mm
etri
c ab
out
the
orig
in a
re c
alle
d od
d f
un
ctio
ns.
Eve
n F
un
ctio
ns
Od
d F
un
ctio
ns
Nei
ther
Eve
n n
or
Od
d
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
Th
e gr
aph
of
a fu
nct
ion
can
not
be
sym
met
ric
abou
t th
e x-
axis
bec
ause
th
e gr
aph
wou
ld f
ail
the
Ver
tica
l L
ine
Tes
t.
Exer
cise
sId
enti
fy t
he
fun
ctio
n g
rap
hed
as
even
, od
d, o
r n
eith
er.
1.
y
xO
2.
y
x
3.
y
xO
4.
y
xO
od
dev
en
even
n
eith
er
5.
y
xO
6.
y
xO
7.
y
xO
8.
y
xO
even
od
dn
eith
erev
en
042_
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Chapter 1 Assessment Answer KeyQuiz 1 (Lessons 1-1 and 1-2) Quiz 3 (Lesson 1-5 and 1-6) Mid-Chapter TestPage 57 Page 58 Page 59
Quiz 4 (Lessons 1-7 and 1-8)
Page 58
Quiz 2 (Lessons 1-3 and 1-4)
Page 57
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A27 Glencoe Algebra 1
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
84 + 6
Multiplicative Property of Zero; 0
Substitiution
7(100-2); 686
B
two plus the product of 5 and p
1
8
B
= 7 · 7 · 2 · 5 Commutative (×)
= (7 · 7) · (2 · 5) Associative (×)
= 49 · 10 = 490 Substitution
1.
2.
3.
4.
11
X Y
56843
3-4
21
D = {–4, 1, 2, 3}R = {3, 4, 5, 6, 8}
B
t = 1000 _
40 ; t = 25 min
1.
2.
3.
4.
Nonlinear; see students’ work.
A
30
function
8.
9.
10.
11.
12.
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7.
18 times p
G
C
F
D
x squared minus 5
Sample answer: Mult. Iden. and Mult. Inv.
6(10) + 6(2); 72
13b + 2b2
= 6.4 + 1.6 + 2.7 + 5.3 Commutative (+)
= (6.4 + 1.6) + (2.7 + 5.3)Associative (+)
= 8 + 8 Substitution
= 16 Substitution
D
D
J
= 4
_ 3 � 3 � 7 � 10 Commutative (×)
= ( 4
_ 3 � 3) �
(7 � 10) Associative (×)
= 4 � 70 Substitution
= 280 Substitution
$2375
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Chapter 1 Assessment Answer KeyVocabulary Test Form 1Page 60 Page 61 Page 62
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Chapter 1 A28 Glencoe Algebra 1
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Sample answer: The solution set of an open sentence is the set of elements from the replacement set that make an open sentence true.
coefficient
function
domain
like terms
continuous function
power
open sentence
variable
the behavior of the values of a function at the positive and negative extremes in its domain
range
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G 20.
C
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B
B: 12x + 6
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Chapter 1 Assessment Answer KeyForm 2A Form 2BPage 63 Page 64 Page 65 Page 66
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Chapter 1 A29 Glencoe Algebra 1
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B: 8a2
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Chapter 1 Assessment Answer KeyForm 2CPage 67 Page 68
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PDF 2nd
Chapter 1 A30 Glencoe Algebra 1
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4(5 · 1 ÷ 20)
= 4(5 ÷ 20) (Mult. Identity)
= 4 ( 1 _ 4 ) (Substitution)
= 1 (Mult. Inverse)
n2 + 34
60
Substitution; 10
Additive Identity; 5
18
5(2x)
128
3(14) - 3(5); 27
9w + 14w 2
17y + 7
6
5
7
4 times n cubed plus 6
(5.0, 4.20), (6.0, 5.05), (7.0, 5.90), (8.0, 6.75)
time; temperature
(8, 87); at 8 A.M. the temperature is 87°.
B: a.
b.
c.
- (1 � 9) + 8 + 7
198 � 7
1 + (9 - 8) + 7
As the weight of the letter increases, the cost increases.
16.
17.
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19.
Weight (oz)
Rat
e ($
)
0
1
2
3
4
5
6
7
5.0 6.0 7.0 8.0
20.
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Chapter 1 Assessment Answer KeyForm 2DPage 69 Page 70
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Chapter 1 A31 Glencoe Algebra 1
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23x + 8
11w 2 + 7z 2
10(5) + 3(5); 65
Refl exive Property; 3
Multiplicative
Inverse; 1
_ 11
20
36
6(6 · 1 ÷ 36) = 6(6 ÷ 36) (Mult. Identity)
= 6 (
1 _ 6 )
(Substitution)
= 1 (Mult. Inverse)
5 times a number cubed plus 9
1 _ 3 n + 27
4n 2
6
8
40
260
16.
17.
18.
19.
20.
Weight (oz)
Rat
e ($
)
0
1
2
3
4
5
6
1.0 2.0 3.0 4.0 5.0
(2.0, 1.80), (3.0, 2.75), (4.0,
3.70), and (5.0, 4.65)
game; score
Sample answer:
Between the fi rst and
third game Robert
becomes comfortable
with the lane. Robert is
tired for the fourth game.
As the weight of the letter increases, the rate increases.
B: 2[(5 - 1) ÷ 4 +
1]
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Chapter 1 Assessment Answer KeyForm 3Page 71 Page 72
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Chapter 1 A32 Glencoe Algebra 1
n3 + 12 1.
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2 _ 3 (3 ÷ 2) + (9 - 9) (Subst.)
= 2 _ 3 ( 3 _ 2 ) + 0 (Subst.)
= 1 + 0 (Mult. Inverse)
= 1 (Add. Identity)
42 + 2nsix times a numbersquared divided by 5
45
200
88
(2)(x) + (2)(3y)
- (2)(2z);
2x + 6y - 4z
3 + 30a + 33an
simplifi ed
105
100
Multi. Iden.; 1
Substitution; 9
5
_ 4
1
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
year; number of newspapers soldThe number of
newspapers sold was
decreasing during the
years 2006–2010.
Dis
tan
ce
Time
The population of Ohio
was about 4 million in
1900.
function
t = 50 + 4(8); t = 82
The population of Ohio will approach about 13 million.
-6r 2 - 4r + 2
10
Sample answer:
The puppy goes a
distance on the trail, stays
there for a while, goes
ahead some more, stays
there for a while, then
goes back to the
beginning of the trail. The
function is continuous.
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Chapter 1 Assessment Answer Key Page 73, Extended-Response Test
Scoring Rubric
Score General Description Specifi c Criteria
4 Superior
A correct solution that
is supported by well-
developed, accurate
explanations
• Shows thorough understanding of the concepts of translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.
• Uses appropriate strategies to solve problems.
• Computations are correct.
• Written explanations are exemplary.
• Graphs are accurate and appropriate.
• Goes beyond requirements of some or all problems.
3 Satisfactory
A generally correct solution,
but may contain minor fl aws
in reasoning or computation
• Shows an understanding of most of the concepts of translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.
• Uses appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are effective.
• Graphs are mostly accurate and appropriate.
• Satisfi es all requirements of problems.
2 Nearly Satisfactory
A partially correct
interpretation and/or
solution to the problem
• Shows an understanding of most of the concepts of
translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.
• May not use appropriate strategies to solve problems.
• Computations are mostly correct.
• Written explanations are satisfactory.
• Graphs are mostly accurate.
• Satisfi es the requirements of most of the problems.
1 Nearly Unsatisfactory
A correct solution with no
supporting evidence or
explanation
• Final computation is correct.
• No written explanations or work shown to substantiate the
fi nal computation.
• Graphs may be accurate but lack detail or explanation.
• Satisfi es minimal requirements of some of the problems.
0 Unsatisfactory
An incorrect solution
indicating no mathematical
understanding of the
concept or task, or no
solution is given
• Shows little or no understanding of most of the concepts
of translating between verbal and algebraic expressions, open sentence equations, algebraic properties, and graphs of functions.
• Does not use appropriate strategies to solve problems.
• Computations are incorrect.
• Written explanations are unsatisfactory.
• Graphs are inaccurate or inappropriate.
• Does not satisfy requirements of problems.
• No answer may be given.
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Chapter 1 A33 Glencoe Algebra 1
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Chapter 1 Assessment Answer Key Page 73, Extended-Response Test
Sample Answers
In addition to the scoring rubric found on page A33, the following sample answers may be used as guidance in evaluating extended response assessment items.
1a. Sample answer: 2x + 1; two times x plus 1
1b. Sample answer: the quotient of x
minus 1 and 2; x - 1 _____ 2
2. The student should explain that a replacement set is a set of possible values for the variable in an open sentence. The solution set is the set of values for the variable in an open sentence that makes the open sentence true.
3a. The student should write an equation that represents the Additive Identity Property, the Multiplicative Identity Property, the Multiplicative Property of Zero, or the Multiplicative Inverse Property. The student should also name the property that is illustrated. Sample answer: 1 + 0 = 1; Additive Identity Property
3b. Since 23 is the sum of 20 and 3, the Distributive Property allows the product of 7 and 23 to be found by calculating the sum of the products of 7 and 20, and 7 and 3.
3c. The student should explain that the Commutative and Associative Properties allow the terms in the expression 18 + 33 + 82 + 67 to be moved and regrouped so that sums of consecutive terms are multiples of 10. Thus, after the first step of addition the remaining sums are easier to accomplish.
18 + 33 + 82 + 67= 18 + 82 + 33 + 67 Commutative (+)= (18 + 82) + (33 + 67) Associative (+)= 100 + 100 Substitution = 200 Substitution
4. Sample answer: The distance a boy is from his home as a function of time. Label the vertical axis as distance and
the horizontal axis as time. The boy rides his bike to the post office to drop off a letter. He rides to his high school which is a bit closer to his house. He jogs twice around the track, then rides his bike straight home.
5a. Sample answer: {(-1, -3), (0, -1), (1, 4), (2, 5)}
5b. Sample answer:
x y
-1 -1
0 -3
0 -1
1 4
2 5
5c. The student should identify in their relation where they used the same domain element with two or more different range elements.
6. Nonlinear; y-intercept about 2.9, so about 2.9% of polled accessed the Internet away from home several times a day in March 2004. No x-intercept, so no time when no one accessed the Internet away from home several times a day; no symmetry; positive for x > 0; increasing between x = 0 and x ≈ 15 and between about x ≈ 38 and x ≈ 72, it is slightly decreasing between x ≈ 15 and x ≈ 38, away from home Internet use increased from March 2004 for about 15 months to about 4%, decreased slightly until March 2007 when it began to increase; appears to continue to increase.
X Y
-1012
-3-1
45
y
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Chapter 1 A34 Glencoe Algebra 1
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Chapter 1 Assessment Answer KeyStandardized Test Practice
Page 74 Page 75
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Chapter 1 A35 Glencoe Algebra 1
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10. F G H J
A B C D
F G H J
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
A B C D
11.
12.
13.
14.
15.
F G H J
A B C D
A B C D
F G H J
A B C D
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Chapter 1 Assessment Answer KeyStandardized Test PracticePage 76
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Chapter 1 A36 Glencoe Algebra 1
18.
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31.
32.
33a.
1000 computers were affected when time started.
33b.
The number of affected computers is expected to continue to increase.
Time
Dis
tan
ce
Sample answer:
x =
18
11y +
3
11n
8
4
22
11
four times m squared plus two
2x - 6
5.04
12
136
1 _ 6
{2}
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