a2 aiotg07 ans 075-104 alg 2...chapter 1 practice 1-1 1.-4.2 2. 4 3. 4. ... 5. answers may vary....

Chapter 1

Practice 1-11. -4.2 2. 4 3. 4. 1 5. 6. 1.8 7. 6 8. 0.01 9. �

10. = 11. � 12. = 13. � 14. � 15. � 16. �17. integer, rational, real 18. whole, integer, rational, real19. irrational, real 20. rational, real 21. natural, whole,integer, rational, real 22. rational, real 23. irrational, real24. integer, rational, real 25. Comm. Prop. of Add.26. Identity Prop. of Add. 27. Assoc. Prop. of Add.28. Inv. Prop. of Mult. 29. Dist. Prop.30. Comm. Prop. of Mult. 31. Identity Prop. of Mult.32. Inv. Prop. of Mult. 33. Inv. Prop. of Add.34. Assoc. Prop. of Mult.35–38.

39. 40. -3; 41. ; 42. 4;

43. N: natural 44. H: rational; L: rational; n: natural45. t: rational; n: natural

Guided Problem Solving 1-11. An example that makes the statement false. 2. There maybe many valid counterexamples for each statement.3. Answers may vary. Sample: 4 is a whole number, but its

reciprocal is not a whole number. 4. Answers may vary.

Sample: 7 is a natural number, but its opposite -7 is not anatural number. 5. Answers may vary. Sample: 0 is a wholenumber, and since -0 = 0, the opposite of 0 is a wholenumber. 6. Answers may vary. Sample: The integer -1 has-1 as its reciprocal, so -1 is an integer whose reciprocal is aninteger. 7. Answers may vary. Sample: and - areirrational numbers, but their product -2 is a rational number.8. Answers may vary. They should be similar to counter-examples in (3) - (7). 9a. Answers may vary. Sample: 2 and5 are whole numbers but 2 - 5 =-3, which is not a wholenumber. 9b. Answers may vary. Sample: 5 is an integer, butits opposite -5 is not a whole number. 9c. Answers mayvary. Sample: 3 is a whole number but 32 = 9, which is not aneven number. 9d. Answers may vary. Sample:-1 is aninteger, but not a whole number. 9e. Answers may vary.Sample: 4 is a whole number and is 2, which is not anirrational number.

Practice 1-21. 7x 2. 14t - 5 3. -11a + b - 1 4. 2i + 7j 5. 12xy

6. 13x2 + 5x 7. 4m - 6 8. 9.

10. -a - 5 11. -8n2 - 16m 12. x2 - 2xy + y2

13a. 54 in.2 13b. 13.5 m2 14. $10.06 15. 85 16. 2617. -42 18. -1421 19. 10 20. 1 21. 32 22. 13

23. 186 24. 25 25. 0 26. -25 27. a + (a - b) + c + b +(a - 2c)+ b + c + (a - b); 4a

Guided Problem Solving 1-2 1. The number of eligible voters in millions in the UnitedStates from 1960 to 2000 2. The number of years since 19603. 28; about 180 million voters 4. 52, 60 5. about 242 millionvoters; about 263 million voters 6. -0.003y + 0.61 7. -0.0078y2 + 1.265y + 65.27 8. 20; about 87 million voters9. Answers may vary. Sample: Answers are reasonable.

10a. about 198 million eligible voters 10b. about 100 millionvoters

Practice 1-3

1.

2.

3.

4. ; no restrictions

5. ; a 2 b

6. x = t3 - 3; t 2 0 7. $20 and $35 8. 2.5 in., 6 in., 6.5 in.9. 41, 42, 43 10. 0 11. 1 12. 6 13. -1 14. 15. 1

16. 19 17. 18. Mike’s bus: 35 mi/h; Adam’s bus: 55 mi/h

19. slower train: 50 mi/h; faster train: 100 mi/h 20. 81, 83, 85, and 87 21. length: 17 cm; width: 12 cm

Guided Problem Solving 1-31. $5000 2. $2000; $3000 3. 6%; 8% 4. P = 2000, r = 0.06,t = 1 5. $2120 6. P = 3000, r = 0.08, t = 1 7. $3240 8. $360 9. $746.40 10. Answers may vary. Sample:I = P(1 + r)t - P; Answers verify. 11. $26; $52.86

Practice 1-41. t � -5

2. m � 8

3. x � -2

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Year Eligible Voters1988 180 million2012 242 million2020 263 million

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Algebra 2: All-In-One Answers (continued)

75All-In-One Answers Algebra 2

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4. a �

5. x � -8

6. x �

7. x � 12

8. x �

9. x � -16

10. -3 � x � 2

11. x � 2 or x � 8

12. x � -3 and x � 6, or -3 � x � 6

13. x � 1 or x � 2

14. -3 � x � 5

15. -2 � x � -1

16. x � -1 or x � 3

17. x � -1 and x � 2, or -1 � x � 2

18. at least $450019. less than 35 ft20. more than 15 years old21. at least 1072 questionnaires22. between 10.3 lb and 12.8 lb23. at least 7.75 in. and at most 8.25 in.24. between 4 h and 4.8 h, or between 4 h and 4 h 48 min

Guided Problem Solving 1-4 1. between $700,000 and $750,000 2. $496,0003. 700,000 � x + 496,000 � 750,000 4. 204,000 � x � 254,000 5. between $204,000 and $254,0006. $204,000 + $496,000 = $700,000; $254,000 + $496,000 =$750,000 7. between 18 hr and 25 hr

Practice 1-51. ∆h - 8.3« � 2 2. ∆a« � 2.5 3. ∆x - 27.5« � 5.54. x � -17 or x � 7

5. k � -16 and k � 22, or -16 � k � 22

6. all real numbers

7. t � -2 and t � 12, or -2 � t � 12

8. x � or x � 2

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Algebra 2 All-In-One Answers76

9. b � and b � , or � b �

10. w � or w � 2

11. all real numbers

12. u � -3 or u � 3

13. -7, 7 14. no solution 15. 2 16. -27, 3 17. -21, 21

18. , 1 19. no solution 20. , 4 21. -3, 3

22. -4, 2 23. 24. no solution

25. ∆x - 4.2« � 0.01; 4.19 � x � 4.2126. ∆x - 3.5« � 0.002; 3.498 � x � 3.502

27. ∆x - 10« � ; � x �

28. ∆T - 76« � 11; 65 � T � 8729. ∆w - 40« � 0.25; 39.75 � w � 40.2530. ∆d - 13.75« � 11.25; 2.5 � d � 25

Guided Problem Solving 1-5 1. Find a value for b that makes the equation true.2. distance 3. |4 - 8b| =-12 4. no 5. no solution6. For any value of b, the left side of the equality is negative.7. no solution

Practice 1-6

1a. , or 20% 1b. , or 40% 1c. , or 60%

1d. , or 80% 2a. < 0.42, or 42% 2b. < 0.21,

or 21% 2c. < 0.11, or 11% 2d. < 0.37, or 37%

3a. , or 50% 3b. < 0.33, or 33% 3c. < 0.17, or 17%

3d. < 0.83, or 83%

4a. {$6, $11, $15, $21, $25, $30}; 6 outcomes

4b. < 0.17, or 17% 4c. 0 4d. < 0.33, or 33%

5. < 0.54, or 54% 6. < 0.67, or 67%

7. Answers may vary.; The experimental probability is expect-ed to be close to the theoretical probability

< 0.31, or 31%

8. Answers may vary.; The experimental probability is expected to be close to the theoretical probability

< 0.02, or 2%

9. , or 9% 10. < 0.03, or 3%

Guided Problem Solving 1-6 1. 1, 2, 3, 4, 5, 6 2. Answers may vary. Sample: (3,2)3. (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4),(2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3),(4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2),

(6,3), (6,4), (6,5), (6,6) 4. 36 5. 1 6. 7. 6 8.

9. Answers may vary. Experimental probabilities should beclose to theoretical probabilities. 10a. (H,H,H), (H,H,T),(H,T,H), (T,H,H), (T,T,H), (T,H,T), (H,T,T), (T,T,T) 10b. 8

10c. 10d.

1A: Graphic Organizer1. Tools of Algebra 2. Answers may vary. Sample: propertiesof real numbers, solving equations, solving inequalities,probability 3. Check students’ work.

1B: Reading Comprehension1. temperature scales 2. degrees of temperature 3. 18 years4. degree 5. 32° (the freezing point of pure water) 6. Fahrenheit used a mixture of salt and ice; Celsius used thefreezing point of pure water. 7. Answers may vary. Sample:No. There were 96 degrees between 0° F and normal bodytemperature. There are almost the same number of degreesbetween the freezing and boiling points of water. Since thedifference between the high and low temperatures on theCelsius scale is greater, Celsius degrees must be significantlygreater than Fahrenheit degrees. 8. b

1C: Reading/Writing Math Symbols1. 5 multiplied by 9 or 5 times 9 2. 1, 2, 3 and the patterncontinues in the same way. 3. 12 divided by 0.4

4. the square root of 7 5. |–3| 6. x � 8 or 7. w = 29

8. x5 9. 10. 2, 4, 6, . . .

1D: Visual Vocabulary Practice1. variable 2. term 3. coefficient 4. opposite 5. absolutevalue 6. compound inequality 7. multiplicative inverse 8. algebraic expression 9. experimental probability

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Algebra 2: All-In-One Answers (continued)©

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1E: Vocabulary CheckOpposite: The additive inverse of any number, a, is -a.Reciprocal: The multiplicative inverse of any nonzero number,a, is .Absolute value of a real number: The distance from a realnumber to zero on the number line.Variable expression: An expression that contains one or morevariables.Solution of an equation: A number that makes the equationtrue.

1F: Vocabulary Review1. multiplicative inverse 2. solution 3. algebraic expression4. additive inverse 5. theoretical probability 6–8. Answersmay vary. Samples given. 6. The of a number is thedistance between that number and zero on a number line.7. The additive inverse of a number is its .8. The is the multiplicative inverse of a number.

Chapter 2

Practice 2-1

1. -8; ; 17; 37 2. 3. 7.8; 3.3;-7.2;-19.2

4. not a function 5. not a function 6. function

7. ; domain: {1, 2, 3, 5};

range:

8. ; domain: {-3, 0, 1};range: {-2, 4, 5}

9. ; domain: {-1, 2, 3};range: {2}

10. ; domain: {0.5};range: {-1, 0, 1, 3}

11. not a function 12. function 13. not a function14. ; not a function

15. ; function

16. 1 17. 3 18. 19.

Guided Problem Solving 2-1 1. The radius. 2. 10.5 cm 3. v(r) = 4/3pr3 4. 10.5 or 10.5 cm

5. cm3 6. about 4849 cm3 7. 4849 = pr3; r � 10.58. v(s) = s3; 1520.875 cm3

Practice 2-2

1. 2. 5 3. 4. 5. 6. 2 7. 8.

9. 10.

11.

12. 13.

14.

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15. 4x + y = 10 16. 2x - 5y = -17 17. y = -4

18. (0,-3); (4, 0) 19. 0; (0,-2); none

20. (0, 7); 21. undefined; none; (5, 0)

22. y = 2x + 5; 23.

24. x = -3; 25. y = 1;

Guided Problem Solving 2-2

1. , 2. The slope of the line through the

points 3. slope = 4.

5. slope = 6. 7. 8. 3

Practice 2-3

1. 2. 6; 18 3. 4. yes; 5. yes;-1.2

6. yes;-4 7. no 8. yes; 3 9. no 10. yes; 11. no

12. no 13. yes; 3; y = 3x 14. yes; 15. no

16. 17. y = -6x 18. y = -18x 19.

20. 21. 22. 23. y = 55x

24. 25. 26. 11 27. 28. y = 0.06x; 22 min

29. 46.08 in.

Guided Problem Solving 2-31. 392 mi 2. 14 gallons 3. k = 28 4. y = 28x 5. 103.6 mi

6. 417.9 gallons 7. 8a. y = 28x; 392 = 28 3 14

8b. 103.6 = 28x; x = 3.7 8c. y = 28 3 417.9; y ≈ 11,700 9a. y = 58x 9b. 145 mi 9c. 75 gallons

Practice 2-41. y = 0.6x - 2.1 2. y = -2.04x + 7.548 3. y = 1.2x + 200; $214.40 4. y = 58x; 464 words 5. y = 146x + 5000; 6460 subscribers6. ;

yes; using (3, 3.1) and (7, 5.2): y = 0.525x + 1.5257. ; no

8. ;

yes; using (-1,-1.8) and (1, 1.9): y = 1.85x + 0.059. ; no

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Algebra 2: All-In-One Answers (continued)©

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10a.

10b. using (9.4, 11.2) and (15.1, 19.1): y = 1.39x - 1.8310c. about 15.5% 10d. yes

Guided Problem Solving 2-4 1. Equation 2. Yes 3.

4. slope = 0.076 5. y = 0.076x - 10.04 6. about 15 g 7. Yes, it is a good fit. 8. about 606 Calories

Practice 2-51. E 2. C 3. A 4. F 5. B 6. D7. 8.

9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

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Guided Problem Solving 2-51. Graph the two equations. 2. Compare the graphs. Look for

similarities and differences. 3a.

3b. 4.

5.–6.

7. The graphs have the same size and shape. They havedifferent vertices, and one points up while the other pointsdown. 8. Test points should result in true statements.9.

The graphs have the same size and shape. They have differentvertices, and one points up while the other points down.

Practice 2-61. horizontal; 2. horizontal;

3. vertical; 4. combined;

5. combined; 6. horizontal;

7. y = ∆x + 2« + 1 8. y = ∆x - 4«

9. y = -∆x - 1« + 3 10.

11. y = ∆x + 3« - 2 12.

13. y = ∆x« - 3 14. y = ∆x - 1«

15. y = ∆x + 2« + 1 16. y = -∆x« + 2

17. y = -∆x + 2« 18. y = -∆x - 1« - 2

19. y = 3∆x« - 4 20. y = ∆x - 2«

21. y = 2∆x + 3« - 1

22.

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Guided Problem Solving 2-6 1. A translation shifts a graph horizontally, vertically, or both.2. years 3. x-axis 4. horizontal 5. left 6. horizontal 7. The graphs and answers agree. 8. Vertical; the graph isshifted up

Practice 2-71. y � x - 2 2. x - 2y � 4 3. y - 2x � 44. y � -2 5. x � 2 6. -2x - 3y � 6 7. 3x - y � 3 8. y - 3x � 39. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27. 28.

29a. x + y � 150, where x represents the number of tunasandwiches and y represents the number of ham sandwiches

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29b.

29c. Yes; the sum of 90 and 80 is more than 150.30a. 150x + 200y � 1800, where x represents the number of$150 models and y represents the number of $200 models30b.

30c. at least four $150 models

Guided Problem Solving 2-7 1. dashed 2. to the right or above 3. x =-34. not part 5. > 6. x � -3 7. 0 � -3; Yes 8. x � 2

2A: Graphic Organizer1. Functions, Equations, and Graphs 2. Answers may vary.Sample: linear equations, direct variation, absolute valuefunctions and graphs, two-variable inequalities 3. Check students’ work.

2B: Reading Comprehension1. graph paper, pencil, a ruler, and colored pencils or pens2. plot; make; classify 3. points plotted on the same graph asthe line 4. three lists of points; one for above, one for on,and one for below the line 5. a phrase that is one of the 3 choices: on the line, above the line, and below the line.6. Step IV asks about the equation while Step III asks aboutan inequality.

2C: Reading/Writing Math Symbols1. The theoretical probability of 3 occurring is 1 in 6.2. the theoretical probability of not taking Spanish3. a function f of x 4. f of 5, or the value of function fwhen 5 is the value of the variable 5. The function A (orArea) of s (or the side of a square) is equal to s2 (or the

length of the side squared). 6. x2 2 0 7. z : 7 or

8. P(red) 9. or 4 : 10 = x : 18 10. g(7)

2D: Visual Vocabulary Practice1. Constant of variation 2. Slope 3. Scatter plot 4. Translation 5. Standard form of a linear equation 6. Absolute value function 7. Trend line 8. Slope-interceptform 9. Point-slope form

2E: Vocabulary CheckRelation: A set of pairs of input and output values.Domain: The set of all inputs, or x-coordinates, of the orderedpairs of a relation.Range: The set of all outputs, or y-coordinates, of the orderedpairs of a relation.Function: A relation in which each element of the domain ispaired with exactly one element of the range.x-intercept: The point at which a line crosses the x-axis (or thex-coordinate of that point).

2F: Vocabulary Review Puzzle

Chapter 3

Practice 3-11. Independent 2. Inconsistent 3. Dependent 4. Independent 5. Dependent 6. Independent 7. Independent 8. Inconsistent 9. Independent 10. Inconsistent 11. Independent 12. Dependent13a. Income: y = 2000x - 500, where x = 1 represents May;Expenses: y = -2600x + 24000, where x = 1 represents May 13b. October (the sixth month) 14. (6, 4) 15. (5, 2) 16. (12, 1) 17. (2, 1) 18. (1,-2) 19. (2, 3) 20. (-4, 0)

21. (-1, 3) 22. 23. (-8,-1) 24. (2, 2)

25. (5, 1)

Guided Problem Solving 3-1 1. 6; 80 2. 4; 100 3. The number of flyers addressed after x minutes 4. y = 6x + 80 5. y = 4x + 100

a32, 24b

1 2

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6.

7. (10, 140) 8. 10 minutes 9. Yes; y = 6(10) + 80 = 140and y = 4(10) + 100 = 140 10. y = 3x + 5; y = 2x + 20;

After 15 minutes, thenumbers of newspapers isthe same at 50.

Practice 3-2

1. (6, 4) 2. (4, 1) 3. (5, 2) 4. (1, 2) 5. (4, 3) 6.

7. (1, 1) 8. (2,-2) 9. (5,-2) 10. C = 525 + 150p;I = 325p; three performances 11. (2, 3) 12. (4, 6) 13. (0, 3) 14. (-3, 5) 15. (4, 1) 16. (6, 3) 17. (2,-2) 18. (3, 0) 19. (-4,-4) 20. 8r + 1g = 4.60,6r + 3g = 4.80, where r represents number of oranges and g represents number of grapefruits; oranges = $.50,grapefruits = $.60 21. (1, 4) 22. (-2, 3) 23. (0, 3)

24. (1,-2) 25. 26. (-4, 5)

27. (-3, 2) 28. No solution 29. (2.25, 0)

Guided Problem Solving 3-2 1. $40,000 plus $2800 per performance 2. $36753. y = 40,000 + 2800x 4. y = 3675x5. 40,000 + 2800x = 3675x 6. x ≈ 45.7 7. 46 performances 8. Yes; y = 40,000 + 2800(46) = 168,800,y = 3675(46) = 169,050 9. 612 trips

Practice 3-31. 2.

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5. 6.

7. 8.

9. 10.

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Algebra 2 All-In-One Answers 84

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13a. ,

where x represents number of spiral notebooks and yrepresents number of three-ring notebooks13b.

Solutions correspond to points in shaded region with integercoordinates.

14a. ,

where x represents number of campers on the low trail and yrepresents number of campers on the high trail14b.

Solutions correspond to points in shaded region with integercoordinates.15. 16.

17. 18.

19. 20.

21. 22.

23.

Guided Problem Solving 3-31. 7, 8, 9, 10 2. more (or greater) 3. j � 0; s � 0; s � j;j + s � 7; j + s � 104.

5. (1, 6), (1, 7), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4),(3, 5), (3, 6), (3, 7), (4, 5), (4, 6) 6. Yes, substituting eachcombination listed in (8) into the inequalities of the systemresults in a true statement.7a. x � 0; y � 0; x + y � 5; x + y � 8; x � y or y � x7b. (3, 2), (4, 1), (4, 2), (4, 3),

(5, 0), (5, 1), (5, 2), (5, 3),(6, 0), (6, 1), (6, 2), (7, 0),(7, 1), (8, 0)

1

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Practice 3-41. ; (2, 1)

2. ; (0, 4)

3. ; (5, 0)

4. ; (2, 0)

5. ; (1, 0)

6. ; (0, 0)

7. (0, 10); 30 8. (4, 0); 4 9. (8, 8); 32 10a. Four loaves ofIrish soda bread and two Kugelhopf cakes 10b. $14 11a. 10 qt regular, 4 qt extra-rich 11b. $132

Guided Problem Solving 3-4 1. corn muffins: 4 c; bran muffins: 2 c; baker has 16 c2. corn muffins: 3 c; bran muffins: 3 c; baker has 15 c3. P = 3c + 2b4. c � 0, b � 0, 4c + 2b � 16 (milk), 3c + 3b � 15 (flour)5.

(0, 0), (0, 5), (4, 0), (3, 2) 6. At (0, 0), P = 0; At (0, 5),P = 10; At (4, 0), P = 12, At (3, 2), P = 13 maximized at (3, 2)7. 3 trays of cranberry muffins and 2 trays of bran muffins 8. Yes, other points in the feasible region result in P � 13.9. 40 Q, 60 R

Practice 3-51. From the origin, move forward three units. 2. From theorigin, move right two units. 3. From the origin, move for-ward three units, left two units, and down 4 units. 4. From theorigin, move back six units, left four units, and down one unit.5. From the origin, move up four units. 6. From the origin,move forward one unit, right two units, and up three units.7. From the origin, move forward three units, left one unit,and up six units. 8. From the origin, move right four units,and down one unit.

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17. (0, 0, 0) 18. (0, 0, 1) 19. (0, 2, 0) 20. (3, 0, 0)21. (0, 4,-2) 22. (0,-2, 3) 23. (-5, 0, 3) 24. (1,-1,-3)25.

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35. x + y = 3, x + z = 3, y + z = 3;

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39. -4x + 2y = 8,-4x - 4z = 8, 2y - 4z = 8;

40. 4x - 2y = 12, 4x + 6z = 12,-2y + 6z = 12;

41. 6x - 3y = 6, 6x + z = 6,-3y + z = 6;

42. 7x - 3y = 21, 7x + 7z = 21,-3y + 7z = 21;

43. 4x - 3y = -12, 4x + 6z = -12,-3y + 6z = -12;

Guided Problem Solving 3-5 1. y and z 2. x and z 3. x and y 4. x-intercept: (6, 0, 0);y-intercept: (0, 6, 0); z-intercept: (0, 0,-3) 5. x + y = 66. x - 2z = 6 7. y - 2z = 68.

9. The results are the same.10. xy-trace: 4x + 9y =-36;

xz-trace: 4x - 9z =-36;yz-trace: 9y - 9z =-36

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Practice 3-61. No unique solution 2. (4, 0,-1) 3. (3, 3, 3) 4. No solution 5. (-1, 1,-1) 6. (4, 1, 3) 7. (5,-1,-2)8. (-3,-2,-1) 9. (2,-2, 2) 10. (2,-1,-3) 11. (-2, 0, 5) 12. (4,-1,-2) 13. (1, 1, 2) 14. (3, 1,-6)

15. 16. 17. (-2,-1,-2)

18. (-1,-3,-4) 19. (0, 5, 0) 20. (8,-1,-2) 21. (1, 2, 3)22. (2,-3,-2) 23. No unique solution 24. (1, 1, 1)

25. ,

where x represents the first number, y represents the secondnumber, and z represents the third number; 3, 5,-10

26. ,

where x represents the number of $1 bills, y represents thenumber of $5 bills, and z represents the number of $10 bills;Eleven $1 bills, seven $5 bills, five $10 bills

Guided Problem Solving 3-6 1. weight of tail, weight of head, and weight of body 2. 9 lb 3. t = 9 4. h = t + b 5. b = h + t6. (h, b, t) = (27, 36, 9) 7. 72 lb (27 + 36 + 9) 8. Yes, thethree weights satisfy each of the statements in the originalproblem. 9. 11 hours (mathematics 1 hr, history report 4 hr,speech 6 hr)

3A: Graphic Organizer1. Linear Systems 2. Answers may vary. Sample: graphingsystems of equations, solving systems algebraically, systems ofinequalities, graphs in three dimensions 3. Check students’ work.

3B: Reading Comprehension1. alphabetical order 2. where to find the word in the text3. It repeats the word being defined. 4. an example of what isbeing defined 5. See if it is defined in the glossary. If not,look it up in a dictionary. 6. a

3C: Reading/Writing Math Symbols1. The most commonly used letter is f, but accept allreasonable responses. 2. The most commonly used letters are x and y, but accept all reasonable responses. 3. m 4. w5. l 6. the measure of angle A, usually in degrees 7. P(7)

3D: Visual Vocabulary Practice/High-UseAcademic Words1. Define 2. Evaluate 3. Approximate 4. Interpret 5. Model 6. Set 7. Compare 8. Property 9. Test

3E: Vocabulary CheckLinear system: This is a set of two or more linear equationsthat use the same variables.Dependent system: This is a system that does not have aunique solution.Linear programming: A technique that identifies theminimum or maximum value of some quantity. This quantity ismodeled with an objective function. Limits on the variables inthe objective function are constraints, written as linearinequalities.Objective function: In linear programming, this is a modelof the quantity that you want to make as larger or as small aspossible.Trace: This is a set of ordered pairs that results fromsubstituting 0 for one of the variables in the equation of aplane.

3F: Vocabulary Review Puzzle1. consistent 2. dependent 3. equivalent 4. inconsistent5. independent 6. three

Chapter 4

Practice 4-11. 3 � 1;-3 2. 3 � 4; 5 3. 2 � 3; 12 4. 3 � 3; q5. 3 � 2; 4 6. 1 � 4;-4

7.

8. 2 � 7 9. 9.5; percent unemployment in construction inJune, 1996 10. 6.6; percent unemployment in services in June, 1992 11. Answers may vary.

Sample: 12. 3 � 2

13. number of days lost to strikes per 1,000 employees inGreece in the given years 14. number of days lost to strikesper 1,000 employees in the United States from 1990 to 1994

M 5 £3900 3300

400 150100 50

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Guided Problem Solving 4-1 1. table 2. matrix 3. weeks 4. Estimates may vary. Sample:

5. Week 1 Week 2 Week 3 Week 4

Rock 165 150 200 180

R & B 100 94 110 98

Rap 96 90 110 100

Classical 98 97 97 1026. Columns represent the weeks in August and rows are thetype of CDs sold.7. The new bar graph should be the same as the one given.8a.

8b.

Columns represent the days of Labor Day Weekend androws are the flavors of ice cream.

Practice 4-2

1. a = 5; ; c = 12; d = 7 2. ; y = -7;

x = 4; ; a = -3; b = 0 3. x = 3; z = -2

4. ;

5. 6.

7. 8. 9.

10. 11. 12.

13. 14. not equal; dimensions are different

15. equal; dimensions and corresponding elements are equal

Guided Problem Solving 4-2 1. 2, 3 2. 2

3. Plant 1: ;

Plant 2:

4. Plant 1: ;

Plant 2:

5.

6. Plant 1; 8007. Plant 2; 22008. The answers check.

9a. Carrier A: ;

Carrier B:

9b. ; B; A

Practice 4-31. product undefined 2. 3.

4. difference undefined 5. 6.

7. product undefined 8. 9. product undefined

10. 11.

12. product undefined 13. 14.

15. product undefined 16.

17. 18. c0.5 20.5 22.52.5 22.5 25.5

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Day 1 Day 2 Day 3 50 75 25C175 125 150S 25 50 25

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Types of CD Wk 1 Wk2 Wk3 Wk4Rock 165 150 200 180R&B 100 94 110 98Rap 96 90 110 100Classical 98 97 97 102



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19. product undefined 20. product undefined

21. 3 3 4; 22. 2 3 2;

23. 2 3 2; 24.

25. 26. 27.

28. 29. 30.

31.

Guided Problem Solving 4-31. no 2. yes 3. [7 6 5] 4. 1 � 3

5. 6. 3 � 3 7. 1 � 3

Thurs Fri Sat8. Revenue [2100 1950 2570] 9. The answers check.

10.

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1. 2.

3. 4.

5. 6.

7. 8. 9.

10. 11.

12. 13.

14. 15.

16.

17.

18.

19.

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5. 6.

7. Yes, the graphs verify the answers.

8. c 7 2 826 28 0

d

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Tc 51 24117 55

d£8 14 14 12

16 8 8 1018 18 20 14

§

£11 1011 1011 10

§c21 1 126 5 5

d£213 19 28224 42 21425 8 23

§

£72 2460 720 212

§c4 55 4

d

c71 3449 56

d£1 2 3 42 4 6 83 6 9 12

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Practice 4-5

1. 2. 3. 4.

5. 6. 7.

8. No inverse; the determinant of the matrix is zero.

9. 10.

11. no inverse, cannot be solved 12. 13.

14. -1 15. -21 16. 14 17. -29 18. 9 19. 3620. yes 21. yes 22. yes


1. subtract from both sides of the equation

2. A-1 3. 4. 1

5. 6.

7. Yes, the equation is true.

8.

Practice 4-6

1. 2.

3. 4. no inverse

5. 6. no inverse

7. 8.

9. 10. 11. no inverse, cannot be solved

12. 39 13. -47 14. -7 15. 9 16. 26 17. -42 18. no 19. yes

Guided Problem Solving 4-6 1. No, the determinant is a number. 2. Any square matrix hasa determinant.3. (a1b2c3 + a2b3c1 + a3b1c2) - (a1b3c2 + a2b1c3 + a3b2c1)4. -30 5. Yes, the determinant is the same. 6. 52

Practice 4-71. (0.251, 0.3, 0.07) 2. (0.7,-0.3,-0.2) 3. (1, 5,-5) 4. (2, 1) 5. (2, 1,-9) 6. (3, 2) 7. (-5, 15, 21) 8. (-1, 0) 9. (0, 6, 2.8) 10. (-2,-1) 11. (-1, 7,-3) 12. (4, 2,-8)

coefficient variable constant

13. =

14. =

15. =

16. ;

(331,975.0482, 216,327.9518); about 331,975 doctors

17. ; (20, 30);

20 one-bedroom and 30 two-bedroom apartments

18. 19. 20. no unique solution

21. (4, –32) 22. det A = 10, has a unique solution23. det A = 0, no unique solution 24. det A = -5, has aunique solution

Guided Problem Solving 4-7 1. l = 2w 2. 840 ft

3. 4. 6

5. 6.

7. width = 140 ft, length = 280 ft 8. The answers check.9. 6 yards; 14 yards

Practice 4-8

1. 2.

3. 4. (2,-3) 5. (6, 2)

6. (-3, 2) 7. (0.9, 0.08, 0.3) 8. (0.25, 0.75, 0.5) 9. (3, 1,-2)

10. 11. c1 34 1

`2301dc23 4

2 28`2816

d

•22x 1 9y 2 2z 5 20

3x 2 y 1 2z 5 296x 1 5y 1 5z 5 24

e12x 1 6y 5 242x 5 2

e 4x 2 2y 5 36x 1 11y 5 9

c140280

dC 13

16

2 13

13S

c2 212 2

dX 5 c 0840

d

a8, 43ba 317, 233

17b

e x 1 y 5 50425x 1 550y 5 25,000

e x 1 y 5 548,3030.2553415x 1 0.1167209y 5 110,017

£9

173§£

xyz§£

4 0 2112 2 01 21 12

§

c2924

dcxydc3 24

0 7d

c362dcx

ydc6 9

4 13d

£23

122

§£4

253§

£20.4 20.4 20.1

0.2 0.5 0.220.1 0.2 20.1

§£20.6 0 20.2

0 20.5 020.4 0 0.2

§

£0.65 21.45 20.2

20.8 1.4 0.40.4 20.2 20.2

§

£29 11 19

1 21 225 26 210

§

£3 21 21

26 3 24 22 21

§£3 10 6

21 25 2322 27 24

§

c5 12 22

d

c1 230 1

dc 2 2721 4

dc4 71 2

dX 5 c4 251 21

dc 2 723 4

d

c34dc1

2d

≥2 3

10 225

252 23

¥£22 1

32 21

2§

≥16 21

6

18

18

¥c25 73 24

dc23 41 21

d

c21 31 22

dc 0 121 2

d≥12

12

212

12

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12 1

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12. 13. (-6,-8, 14) 14. (9,-3,-6)

15. (7, 1, 0) 16. (2, 6,-4) 17. (-1, 7, 0.5) 18. (-4, 3, 9)19. (5, 8,-2) 20. (1, 7,-9) 21. (-2, 3, 5)

Guided Problem Solving 4-81. 5 erasers and 2 pencils 2. 7 erasers and 5 pencils3. 5e + 2p = 0.23; 7e + 5p = 0.41

4. 5. 6.

7. e = 0.03, p = 0.04; one eraser is $0.03 and one pencil is$0.04 8. Yes, the prices match. 9. adult: $8; child: $5.50

4A: Graphic Organizer1. Matrices 2. Answers may vary. Sample: organizing datainto matrices, matrix multiplication, geometric transformationswith matrices, inverse matrices and systems 3. Check students’ work.

4B: Reading Comprehension1. They are to be taken together as a system. 2. 4 inequalities3. 6 elements 4. 2 rows 5. 3 columns 6. 2 by 3 or 2 3 37. -1 8. b

4C: Reading/Writing Math Symbols1. exponent 2. base 3. amn 4. a3 5. 6.7. a2 + b2

4D: Visual Vocabulary Practice1. matrix 2. zero matrix 3. matrix addition 4. dilation5. matrix multiplication 6. scalar multiplication 7. matrix element 8. matrix equation 9. rotation

4E: Vocabulary CheckSquare matrix: A matrix with equal numbers of columns and rows.Determinant: A real number ad – bc of a 2 � 2 matrix

.

Coefficient matrix: When representing a system ofequations with a matrix equation, this is the matrix containingthe coefficients of the system.Variable matrix: When representing a system of equationswith a matrix equation, this is the matrix containing thevariables of the system.Constant matrix: When representing a system of equationswith a matrix equation, this is the matrix containing theconstants of the system.

4F: Vocabulary Review

1. Answers may vary. Sample:

2. Answers may vary, but must have 3 rows and 2 columns.3. 9 4. Answers may vary.

Sample:

5. Answers may vary, but the two must be identical in everyway. 6. Answers may vary and can be of any dimensions, butevery element is zero.

Chapter 5

Practice 5-11. ƒ(x) = x2 2. ƒ(x) = x2 + 4x + 8 3. ƒ(x) = -2x2 + 12 4. ƒ(x) = 2x2 - 1 5. ƒ(x) = x2 + 6x + 9 6. ƒ(x) = x2 - 4x + 7 7. (0, 1); x = 0 8. (3, 0); x = 3 9. (-1,-2); x = -1 10. quadratic; quad: x2; lin: 2x; const:-8 11. quadratic;quad: 3x2; lin: 15x; const: none 12. linear; quad: none;lin:-25x; const: none 13. linear; quad: none; lin: 22x;const:-14 14. quadratic; quad: 3x2; lin:-4x; const: 8 15. quadratic; quad: 3x2; lin:-6x; const:-716. quadratic; quad: 3x2; lin: none; const:-12 17. quadratic;quad: 2x2; lin: x; const:-6 18. linear; quad: none; lin: 3x;const:-5 19. P9(0, 4), Q9(3, 1) 20. P9(-2,-2),Q9(-5,-5) 21. P9(2, 2), Q9(-1,-1) 22a. h = -16t2 + 272t 22b. 372 feet

Guided Problem Solving 5-11. 1974 2. (0, 10), (4, 15), (7, 18), (9, 20), (14, 25), (21, 32),(27, 34), (28, 37) 3. y =-0.0112x2 + 1.24x + 9.97 4. Answers may vary. Sample: Domain: whole numbers from 0 to 50, Range: whole numbers from 0 to 44. 5. x = 18; year1992 6. Answers may vary. Sample: The maximum value of thefunction is about (55, 44), so the first-class postage never reaches50¢. The quadratic model is useful over a limited number ofyears, but because it increases and then decreases, it does notmodel the data after 2021. 7. The quadratic model is usefulover a limited number of years, but because it increases and thendecreases, it does not model the data after 2021. 8. The answersare verified by the graph. 9a. y =-0.016x2 + 3.99x - 41.949b. Answers may vary. Sample: Domain: real numbers from 0 to100, Range: whole numbers from 0 to 200. 9c. 51 °F 9d. 118 °F; The sales may not follow this pattern when thetemperature gets so hot people do not leave their air-conditioned homes.

c 11 726 21

d 1 c21 02 5

d 5 c 10 724 4

d

£3 2 57 22 84 21 12

§

ca bc d

d

"3 a 1 b"4 b

` 5 0.237 0.41

` 5 0.44` 0.23 20.41 5

` 5 0.33` 5 27 5

` 5 11

£1 24 13 2 234 0 2

†29

924

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Practice 5-21. ; max. (1, 4)

2. ; min. (-1,-5)

3. ; max.

4. ; min. (2,-3)

5. ; max.

6. ; min. (0,-3)

7. ; min.

8. ; min. (1,-9)

9. ; min. (2,-16)

10. 11.

12. 13.4

�1

O�2�3 2 3�1 1

1

32

y

x

�2

y

456

O�2�3 2 3�1 1

x1

32

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y

�4�5

1 O x

�3

�1�2

y

45

O�2�3 2 3�1 1

x12

6

O

�8

�16

2 4x

y

(2, �16)

O

�4

�2

�8

2 4x

y

(1, �9)

a1, 292b

O�2

�4

�2

2

1

4x

y

�,( )92

O

2

�2

�2

�4

2 x

y

(0, �3)

a212, 54b

O

2

4

12

�2�4

�

�2

2

,

x

y

( )54

O

2

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2 4x

y

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a23, 43b

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2

,

x

y

( )43

O

�2

�2 2�4

�4

xy

(�1,�5)

O

4

6

2�2 4x

y

(1 ,4)



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14. 15.

16. 1.2 s; 24 ft 17. ; $6

18. $3.25 19. 81.125 ft; 156.25 ft 20. 20 fixtures per day21. 22.

23. 24.

25. 26.

27. 28.

29.


1. 10 ft 2. 10 ft 3. (0, 10), (10, 0) 4. a = , c = 10

5. 6. Yes, the graph verifies the model.

7.

Practice 5-31. y = x2 - 5 2. y = x2 + 2 3. y = (x - 2)2

4. y = -2x2 + 4 5. y = 2(x - 3)2 + 2 6. y = -2(x + 3)2 + 57. 8.

9. 10.

11. 12.

13. 14.x � �6

(�6, �2)

x

y

O�4�2 2�8

�2�4

2468x � �1

(�1, �1)x

y

O�2�4

�2�3

123

x � �2

(�2, 4)

x

y

O2�2

�2�4�6�8 4

246

x � 1

(1, 3)

x

y

O1�1

�1�2 3 4

123

x � �1

(�1, �2)

x

y

O1 2�1

�1�2�3�4

�2

34x � 1

(1, �1)

x

y

O3 4�1

1

�1�2

�2

234

x � 6

(6, 6)

x

y

O2 4 6 8�2

2

�210

468

10

x � 2

(2, �3)

xy

O1 2 3 4�1

1

�1�2�3�4

5

�5

y 5 2 1250x2 1 40

y 5 2 110x2 1 10

2 110

(0, �6)

x � 0

x

y

O�6�4 4 6

42

�2�4�6�8

(0, 3) x � 0

x

y

O�3�2�1 1 2 3

21

4

�1�2

(�1, 8)

x ��1

x

y

O�6�4�2�8 2 4

642

10

�2

(�3, �13)

x ��3x

y

O�9 �3�12 6

36

�12�9�6�3

(4, �16)

x � 4x

yO

�3 3 6 9 12 15

3

�6�9

�3

�12�15

(�1, �7)

x ��1x

y

O�2�6�4�8 2 4

42

�4�2

�8(�3, �2)

x ��3

x

y

O�1�3�5 1

21

3

�2�1

�3

(4, 4)

x � 4

x

y

O�2 4 62 8 10

46

�4�6

(1, �4)

x � 1x

yO

�2 21 4�1

1

�3�4�5

c

p

O1 2 3 4 5 6 7 8

1000500

150020002500

y

xO�8 2�4�2

�4�6

46

4 521

y

�1�1�2

x123

O

4



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15. 16.

17. 18.

19. y = (x + 2)2 - 4 20. y = 2(x + 2)2 - 5 21. y = -2(x + 2)2 + 8 22. y = -(x - 2)2 + 8

23. y = (x - 2)2 - 8 24.

25. y = 2(x - 0)2 - 6 26.

27. 28. y = (x + 4)2 - 13

29. 30. y = (x + 2)2 - 7

31. (2,-4); 8 32. (-6, 5);-7 33. (1,-1); 1

34. (-4,-3); 35. (1, 2); 3 36. (2, 4);-8 37. (5, 1); 101

38. (-5,-3);-53 39. (-2, 5);-15

Guided Problem Solving 5-31. price of a bagel in dollars 2. bakery’s daily profit in dollars3. The domain is all nonnegative numbers. 4. x cannot benegative because that would mean the bakery pays people totake the bagels. 5. $277.50; $210.00 6. (0.55, 300) 7. $.558. $300 9. The graph verifies the answers. 10a. The domainis all nonnegative numbers. x cannot be negative becausethat would mean the theater pays people to see a movie.10b. 140, 74.375 or about 74 10c. $6.50 10d. 150

Practice 5-41. (x + 2)2 2. (x - 5)(x - 2) 3. (x + 8)(x - 1) 4. x(x - 6) 5. (2x - 1)(x - 4) 6. (x + 7)(x - 5) 7. (x + 5)(x + 1) 8. (x + 3)(x - 3) 9. (x - 16)(x + 3)10. (x + 2)(x - 2) 11. x(4x + 1) 12. (x - 25)(x - 4)13. (x - 3)(x + 2) 14. (3x + 1)(3x - 1) 15. x(3x - 2)16. (x + 8)(x - 8) 17. (x + 5)(x - 5) 18. (x + 9)(x - 9) 19. (x + 6)(x - 6) 20. (x + 10)(x - 10) 21. (x + 1)(x - 1) 22. (2x + 1)(2x - 1) 23. 4(x + 3)(x - 3) 24. (3x + 2)(3x - 2) 25. (x - 8)(x + 1) 26. (x + 9)(x + 4) 27. (x - 3)(x - 2)

28. (x + 4)(x + 1) 29. (x - 22)(x + 1) 30. (x + 5)(x + 8) 31. (2x + 1)(x - 3) 32. (x + 11)(x - 1) 33. (x - 12)(x - 2) 34. (x + 2)(5x - 6) 35. (x + 1)(2x - 7) 36. (x + 5)(2x + 3) 37. (x - 3)(3x + 2) 38. (x + 3)(3x + 7) 39. (x + 8)(x - 3) 40. (x + 36)(x - 2) 41. x(x - 11) 42. 3x(x + 7)43. (x + 2)(x + 6) 44. (x - 6)(x - 4) 45. (x + 10)(x - 3) 46. (x - 14)(x + 12)47. (x - 9)(x + 8) 48. (2x + 5)(2x - 5) 49. (x + 11)(x - 11) 50. (x + 16)(x + 1) 51. (5x - 1)(2x - 3) 52. (2x + 3)(2x + 3) 53. (2x - 5)(2x + 3) 54. (3x + 2)(3x - 2)55. (x + 10)(x - 4) 56. 2(x + 2)(x - 2)57. (x + 11)(x + 7) 58. 2(x + 7)(x - 7)59. (x + 14)(x + 7) 60. (x + 6)(x + 14)61. (3x + 2)(3x + 8) 62. (2x + 3)(4x - 9)63. (x - 9)(x + 6) 64. (x + 13)(x - 13)65. (5x + 3)(5x - 3) 66. 7(x2 + 7) 67. 2(x - 7)(x + 2)68. (x + 6)(x + 2) 69. (x + 5)(x - 7) 70. (x + 9)(x - 7) 71. (5x + 1)(4x - 3)72. (2x - 1)(6x + 5) 73. (4x + 3)(x - 2)74. (4x - 3)(2x + 7) 75. 3(x + 7)(x - 8)

Guided Problem Solving 5-41. x + y 2. y 3. (x + y)2 4. y2 5. (x + y)2 - y2

6. x(x + 2y) 7. The expressions are correct. For example,4(4 + 2 2) = 32 and 62- 22 = 32. 8. (x + y)2 - 4y2;(x - y)(x + 3y)

Practice 5-5

1. 20,-2 2. 0, 3. 0, 3 4. 7,-1 5. 7,-7 6. -1

7. 1,-1 8. 4,-1 9. -4,-5 10. -9, 11. 1,-11

12. 0, 13. 2, 14. 1, 15. 1, 16. -1,

17. 2, 18. 19. -1, 20. -2, 21. 4, 2

22. -6,-1 23. 0,-3 24. , 5 25. 2, 26. , 1

27. 2, 28. 12,-12 29. , 1 30. -1, 31. -1,

32. 1, 2 33. 1, 34. -1, 35. -9,-1

36. 6.24,-2.24 37. 7, 1 38. 4,-4 39. -2,-4 40. 3, 1

41. -2, 42. , 43. 44. 1,

45. 46. -2, 47. 2, 48. -1,

49. -1, 50. -4, 51. -2,-1 52. -1,

53. 54. 0, 2 55. 56. ,-6 57.

58. -11,-1 59. 2, 60. 11,-11 61. 3, 62.

63. -8,-1 64. -2,-6 65. 4,-10 66. 2,-2 67. 3,-2

212, 21

4214

16

12, 14

12

35, 23

512, 21

2

11121

2219

254

2321

4212, 21

5

219221

4 , 2354

23

1223

2

217

111

1722

51223

2

12

13

12

13

12

12, 1321

2

213

1521

4252

32

216

72

233

y 5 2ax 1 32b

21 11

2

y 5 ax 1 72b

22 45

4

y 5 23ax 1 16b

22 95

12

y 5 ax 1 52b

22 25

4

x � 1

(1, �2)

x

y

O�1�2 1 2 3 4

�1�2�3

23

x � �1

(�1, �5)

xy

O�2�4�6�8 2

�2

�8�10

2

x � 2

(2, 0) x

y

O�1 1 2 3 4 5

�1

1234

x � �3(�3, �3)

x

y

O�3 �1 1�5

�1�2�3�4

12



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68. 1.65,-3.65 69. 3.46,-3.46 70. 0.9,-2.23

71. 3.87,-3.87 72. 73. -1,-4 74. -4,-9 75. 3, 2

Guided Problem Solving 5-51. 24 ft by 16 ft 2. 384 ft2 3. 276 ft2 4. length: (2x + 24),width: (2x + 16) 5. (2x + 24)(2x + 16) - 384 = 276 6. x =-23 or x = 3 7. 3 ft 8. Yes, the area of the borderis 276 ft2. 9. 5 ft

Practice 5-61. 2i,-4 + 2i, 12 - 14i 2. 1 + i, 1 + 3i,-7 + 7i3. -2 - 3i 4. 4 - i 5. -2i 6. 1 + i 7. 6i 8. -5 + 2i9. 2 - 3i 10. -4 11. 2 12. 13 13. 14. 15. 5

16. 17. 18. 19. 20. 3 21. 2

22. 23. 24. 25. 4 26.27. 28. -6i 29. 2 30. 0 31. 4 - 5i 32. -5 - 3i33. 26 34. 21 + 27i 35. 18 - 46i 36. -7 + 24i

37. 13 38. 8 39. -9 + 7i 40. -1 + 6i 41.42. 43. 44. 2 + 4i 45. 15 - 8i

46. 18 - 26i 47. 22 - 4i 48. 2 - 16i 49. 265

50. -2 + 8i 51. -5 + 16i 52. 169 53. 11 - 2i

54. 10 - 10i 55. -144 - 130i 56. 57.58. 59. -7 + 22i 60. 6 + 6i 61. 3 - 4i

62. 7 + 6i 63. 7 64. 5 + 12i 65. 2 + 8i 66. -3 + 14i

67. 26 68. 69. 410i 70. 71.

72. 45i 73. 74. 420i 75. 76.

77. 45i 78. 43i 79.

Guided Problem Solving 5-61. Yes 2. a2 + b2 3. x2 + 3ix - 3ix - 9i2 or x2 - 9i2

4. x2 + 9 5. 25 6. ±5 7. Yes,- 5 and 5 check and are bothsolutions. 8. x = ±7

Practice 5-7

1. 9 2. 3. 36 4. 5. 16 6. 64 7. 8. 1

9. y = (x + 2)2 - 10; (-2,-10)10. y = (x - 3)2 - 3; (3,-3) 11. y = 4(x + 1)2 - 8; (-1,-8)

12. ;

13. y = 2(x + 1)2 - 7; (-1,-7)

14. ;

15. ;

16. y = (x + 1)2; (-1, 0)17. y = -5(x - 1)2 + 6; (1, 6)

18. y = -2(x - 1)2 + 5; (1, 5)

19. ;

20. ;

21. y = 6(x - 1)2 - 5; (1,-5) 22. y = -2(x - 2)2 - 1; (2,-1)

23. ;

24. 25. 26.

27. 28. 29. 30.

31. 0,-11 32. 7,-2 33. ,-1 34.

35. 36. 37.

38. 1,-3 39. 40. 41.

42. 43. 44.

45. 46. 47. 48. 0, 3

49. 0, 8 50. 51.

52. 53. 54. 2,-1

55. 56. 57.

58. 0, 59. 0,-14 60. 61. 1,

62. 63. 4,-1 64. 65. -1,

66. 2,-4 67. 68. 69.

70. 71. 72.

73. 74.

Guided Problem Solving 5-71. height in feet 2. horizontal distance from the base of theleft side of the arch in feet3.

Ox

y600

300

300 500

3 4 "7232 4

"292

272 4

"53223

2 4"41

2232 4

i"152

232 4

"1322 4 "53 1

5"153

43

12 4

"17221

2 4"21

6

25421 4

"142

52

272 4

"13223

2 4"17

276 4

"1456

256 4

"37625

4 4i"15

4

212 4

"11221

4 4i"11

4

32 4

"192

54 4

"6541 4

i"62

238 4

"41827

2 43"5

2232 4

"172

1 4 i"232 4

"372

72 4

"972

214 4

"5423

2 4i"3

222 4"106

2

232 4

"232

12

1 4"10

245 4

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4. (315, 630) 5. The domain is real numbers from 0 to 630and the range is real numbers from 0 to 630. The distancesand heights must be nonnegative real numbers. 6. 630 ft7. 630 ft 8. vertex form: ; Yes,the answers verify.9a.

vertex (100, 50)9b. 50 ft 9c. 200 ft

Practice 5-81. 200; 2 real 2. 60; 2 real 3. 576; 2 real 4. 0; 1 real 5. 9; 2 real 6. -7; 2 imaginary 7. -7; 2 imaginary 8. 61; 2 real 9. -31; 2 imaginary 10. 9; 2 real 11. 0; 1 real 12. -8; 2 imaginary 13. 225; 2 real 14. -44; 2 imaginary

15. 0; 1 real 16. -3 17. 7, 8 18. , 1 19.

20. 21. , 1 22. -3,-5 23.

24. 25. 6,-2 26. 27. 2,

28. 29. 1 4 2i 30.

31. 32. -10,-8 33. 34. 4 4 3i

35. -4, 36. 37.

38. 39. 40.

41. 42. 43.

44. 45. 46. -5,-1 47. 4, 2

48. 49. No; When p = 4000, the discriminant is negative, so there are no real solutions. 50. 3,-1

51. -1,-4 52. 4,-2 53. ; 1.41, 0.30

54. ; 0.17,-1.17 55. -1, 56.

57. -3, 2 58. 16,-3 59. 0,

60. ; 0.79,-3.79 61. ; 3.73, 0.27

62. ; 1.28,-0.61 63. 7,-5 64. -5,-2

Guided Problem Solving 5-81. the year 1985 2. the amount of carbon monoxide releasedin a year in millions of tons 3.

4. Wherever y = 0.0721x2 - 2.8867x + 117.061 is below y = 100 is when less than 100 million tons were released.5. 0.0721x2 - 2.8867x + 117.061 < 100 6. Subtract 100 from each side. Then use the quadratic formula to solve.7. Answers may vary. 8. The results are the same.9a. Wherever is above y = 4500is when profit was greater than $4500. 9b. Solve -2x2 + 100x+ 4000 � 4500 by first subtracting 4500 from each side. Thenuse the quadratic formula to solve.

5A: Graphic Organizer1. Quadratic Equations and Functions 2. Answers may vary.Sample: properties of parabolas, transforming parabolas,quadratic equations, completing the square 3. Checkstudents’ work. Chapter: Quadratic Equations and Functions;Modeling Data with Quadratic Functions: using quadraticfunctions to model data; Properties of Parabolas: identifyingproperties of parabolas; Transforming Parabolas: translatingparabolas in the coordinate plane; Factoring QuadraticExpressions: factoring quadratic expressions; QuadraticEquations: working with quadratic equations; ComplexNumbers: defining and understanding complex numbers;Completing the Square: factoring quadratic expressions bycompleting the square; The Quadratic Formula: using thequadratic formula to solve quadratic equations

5B: Reading Comprehension1. factoring 2. ax2 + bx + c = 0 where a 2 0 3. because you need factors that have product ac and sum b4. (2x - 5) 5. Answers may vary. Sample: a(b + c) =ab + ac 6. Answers may vary. Sample: If two quantitieshave a product of zero, then one of them must be zero.7. Answers may vary. Sample: The Zero-Product Propertystates that one quantity must be zero. This means that onesolution or the other gives zero. “And” would mean bothsolutions satisfy the equation at the same time. 8. b.

y 5 22x2 1 100x 1 4000

100

200

x

y

5040302010

1 4 2"23

2 4 "323 4 "212

252

12, 24

3214

25 4 3"510

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21 4 "6110

21 4 i"5910

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432, 45

23 4 i"314

23

10

100 200

20

30

40

50

60

x

y

y 5 2 2315(x 2 315)2 1 630



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5C: Reading/Writing Math Symbols1. Answers may vary. Sample: (2, 3) means 2 units to the right along the x-axis and then 3 units up along the y-axis.(3, 2) means 3 units to the right along the x-axis and then2 units up along the y-axis. The x distance is always listed first.

2. Answers may vary. Sample: is a 2 3 3 matrix

with 2 rows and 3 columns.

is a 3 3 2 matrix with 3 rows and 2 columns.

3. 12 4 3 means 12 divided by 3, which equals 4, while 3 4 12means 3 divided by 12, which equals one-fourth. 4. 15 - 5means to subtract 5 from 15 to get 10, while 5 - 15 means5 minus 15, which is -10. 5. No; by the Symmetric Property ofEquality, a = b means b = a.

5D: Visual Vocabulary Practice1. absolute value of a complex number 2. parabola 3. difference of two squares 4. imaginary number 5. Quadratic Formula 6. vertex form of a quadratic function 7. standard form of a quadratic equation 8. complex numberplane 9. perfect square trinomial

5E: Vocabulary CheckQuadratic function: A function that can be written in theform where a � 0. Its graph is aparabola.Axis of symmetry: The line that divides a parabola into twoparts that are mirror images.Vertex of a parabola: The point at which the parabolaintersects the axis of symmetry.Factoring: Rewriting an expression as the product of itsfactors.Greatest common factor (GCF) of an expression: Thecommon factor of each term of the expression that has thegreatest coefficient and the greatest exponent.


Chapter 6

Practice 6-11. y = -0.0439814815x3 + 0.6507936508x2 - 2.935185185x+ 24.84126984; 21.098 2. y = 0.0130787037x3 -

0.1743055556x2 + 0.7951058201x + 3.125396825; 4.6362 3. 5x + 2; linear binomial 4. -3; constant monomial 5. 6x4 - 1; quartic binomial 6. 5s4 - 2s + 1; quartic trinomial 7. 2m2; quadratic monomial 8. -4x3 + x2 + 3x;cubic trinomial 9. 2x2 - 1; quadratic binomial 10. -3m3

+ 5m2; cubic binomial 11. -7x2 + 5x; quadratic binomial12. 3x3; cubic monomial 13. -x3 + 2; cubic binomial 14. -x; linear monomial 15. a5 + a4 + a3; quintic trinomial16. x2 - 25; quadratic binomial 17. p2 - 5p + 6;quadratic trinomial 18. 9c4; quartic monomial 19. b - 3; linear binomial 20. 12x - 6; linear binomial

21. ; quadratic binomial 22. ; quartic

trinomial 23. ; quintic binomial 24. 3x + 5 units

25. 0.0008797x3 + 0.2229900x2 - 3.1465532x + 29.0544437;about $1203.18 26. 0.0000006x3 - 0.0005101x2 + 0.1270416x + 2.0612682;about 12 yr

Guided Problem Solving 6-11. h = 10 cm 2. They are the same. 3.

4. 5. 6.

7. 8. Answers may vary.

9.

Practice 6-21. 5, multiplicity 3 2. 0; 8, multiplicity 2 3. 2;-7, multiplicity3 4. 0, multiplicity 2; 4, multiplicity 2 5. -3, 0, 3

6. ; 3, multiplicity 2 7. y = 2x3 - x2 - 50x + 25252

12pr2 1 48r

V 5 23pr3 1 10pr2

V 5 23pr34

3pr3V 5 10pr2

pr2h

213z5 1 1

12x4 1 x 2 5

4s2 1 23

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2R T E X

R4

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f(x) 5 ax2 1 bx 1 c,

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d

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2

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2x

y (2, 3)

(3, 2)



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8. y = -2x3 + 15x2 - 22x - 15 9. V = x3 + 54x2 + 936x + 5184 10. y = x3 - 6x2 + 5x + 12 11. y = x3 - 4x2 + 5x - 2 12. y = x4 - 2x3 - 15x2

13. y = x3 + 6x2 + 12x + 8 14. x3 - 2x2 + x15. x3 + 7x2 + 15x + 9 16. 2x4 + 23x3 + 60x2 - 125x - 500 17. y = 2x(x + 2)(x + 3) 18. y = x2(x + 2)(x - 3) 19. y = -3x(x - 3)2

20. -1, 1, 3;

21. -2, 3;

22. -5, 0, 2;

23. rel. max.: 4.06; rel. min.:-8.21; zeros: 0, 2, 524. rel. max.: 16.9; rel. min.:-5.05; zeros:-3, 1, 325. x(x + 2)(x - 8) 26. x(x + 3)(x + 4) 27. x(x - 3)(x - 5) 28a. V = x2(20 - x) 28b. about 1185 in. 3

Guided Problem Solving 6-21. 4 ft 2. The volume will be twice as much. 3. x ft 4. 60 ft3

5. 120 ft3 6. 7. 1 8. 1 ft 9. Answers may vary. 10. 2 in.

Practice 6-31. yes 2. yes 3. no 4. yes 5. x2 - 3x + 2 6. x2 + 3x - 7, R 5 7. -2x2 + 9x + 5 8. x2 + 6x + 99. x2 - x + 8, R -12 10. x2 - 7, R -10 11. x3 + x, R 112. x3 + 2x2 + 6 13. x3 - x2 + x + 11, R 32 14. 2x3 + 15x2 - 125 15. -1 16. -13 17. 0 18. 39

19. x - 16 20. 2x + 11, R 48 21. x2 + 6x + 3, R 2 22. 3x2 - 7x + 7, R -8 23. (x + 1)(x - 3)(x + 5) 24. (x - 2)(x + 3)(x - 4) 25. 2x2 - 2x - 1, R 16 26. x3 + 3x2 + 3x + 4, R 1 27. x3 + 2x2 - x, R 1 28. x4 + x3 + x2 + x + 1 29. x3 + 2x2 + x + 2, R -630. 3x2 - 3x + 3 31. width: x - 3; height: x - 5

Guided Problem Solving 6-31. x + 3 2. 3. 0 4. -3

5. 6. 0 7. yes

8. (x + 3)(3x2 + x - 4) + 0 = 3x3 + 10x2 - x - 129. 3(-3)3 + 10(-3)2 - (-3) - 12 = 0 10. no

Practice 6-4

1. (2x - 3)(4x2 + 6x + 9); ,

2. (x + 4)(x2 - 4x + 16);-4,

3. 2(x + 3)(x2 - 3x + 9);-3,

4. 2(x - 5)(x2 + 5x + 25); 5,

5. 4(x - 2)(x2 + 2x + 4); 2,

6. (3x + 1)(9x2 - 3x + 1); ,

7. (4x - 1)(16x2 + 4x + 1); ,

8. (x - 3)(x2 + 3x + 9); 3,

9. (x + 1)(x - 1)(x + 2)(x - 2);-2,-1, 1, 2

10. (x + 1)(x - 1)(x2 - 11); -1, 1,

11. (x2 - 2)(x2 - 8);12. (x + 2)2(x - 2)2;-2, 2

13. (x2 - 7)(x2 - 2);14. (x2 + 4)(x2 + 9);-2i, 2i,-3i, 3i15. (x + 1)(x - 1)(x + 3)(x - 3);-1, 1,-3, 316. (x + 1)(x - 1)(x2 + 4);-1, 1,-2i, 2i17. 5.52% 18. -2, 2,-0.71, 0.71 19. 0.06, 15.94 20. 0 21. -0.59, 0, 0.42 22. -0.67, 0, 1.4 23. -9, 0, 9 24. (n - 1)n(n + 1) = -336;-8,-7,-6 25. (x - 5)(x2 + 5x + 25) 26. (x2 - 3)(x2 - 5) 27. (x + 1)(x - 1)(x2 + 2) 28. (x + 1)(x2 - x + 1) 29. (x2 - 6)(x2 + 4) 30. (x2 + 1)(x2 + 9) 31. (x + 3)(x2 - 3x + 9) 32. (x2 - 2)(x2 + 9)

33. 0, 1, 34.

35. 36.37. -3, 3,-3i, 3i 38.39. 0,-2, 2, 40. 0, 2, 62i"3, i"3

2"5, "5, 2i"5, i"5

2i"2, i"2, 22i"2, 2i"22"14, "14, 2i, i

21, 1, 2"6, "621 4 i"32

2"7, "7, 2"2, "2

2"2, "2, 2"8, "8

2"11, "11

23 4 3i"32

21 4 i"38

14

1 4 i"3621

3

21 4 i"3

25 4 5i"32

3 4 3i"32

2 4 2i"3

23 4 3i"34

32

3 10 21 21229 23 12

3 1 24 0

23 k3x3 1 10x2 2 x 2 12

V(x) 5 (x 1 5)(x 1 4)(x 1 3)

O

10

20

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y

(�5, 0) (2, 0)(0, 0)

O�2 2

�2

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xy(�2, 0) (3, 0)

O

2

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(�1, 0) (1, 0)(3, 0)

Guided Problem Solving 6-41. 60 m3 2. the length of the box 3. width = x - 2 4. height = x - 1 5. V(x) = x(x - 1)(x - 2)6. x(x - 1)(x - 2) = 60 7. (5, 60). The length of the boxwhen the volume is 60 m3. 8. 5 meters 9. 5 4 3 = 60 10. 10 years old

Practice 6-51. 2. 3.4. 5. x4 - 8x3 + 21x2 - 32x + 686. x4 - 4x3 - x2 + 8x - 2 7. x4 + 3x2 - 54 8. x4 - 6x3 + 9x2 + 6x - 20 9. 4, 2,-1 10. 3, 1,-5

11. -4,-3, 12. 7,-2,-4 13. 3;

14. -2,-1, 1, 2 15. 2, 16. -1, 17. 1,18. -2, 19. 1,-1, 5 20. -4, 2 21. -2, 1, 3

22. 10, 23. 1,-3 24.

25. 2, 26. -3,

27. 41,43,45,415; none 28.41,42,44,4 ,4 ,4 ,

4 ,4 ,4 ,4 ,4 ,4 ,4 ,4 ,4 ;-4, ,

29. 41,4 ;-1, 30. 41,42,44,4 ,4 ,4 ,4 ,4 ,

4 ,4 ; none 31. 41,4 ; 32. 41,47,449; none

33. x3 - 7x2 + 17x - 15 = 0 34. x3 - 5x2 + 4x - 20 = 0 35. x3 - 5x2 + 4x + 10 = 0 36. x3 + 7x2 + x + 7 = 0 37. x3 + 4x2 + 16x + 64 = 0 38. x3 - 12x2 + 49x - 78 = 0

Guided Problem Solving 6-51. two 2. four 3. 3 - i 4. 2i5. (x - 2i)(x + 2i)(x - 3 + i)(x - 3 - i) 6. (x - 2i)(x + 2i)(x - 3 + 1)(x - 3 - i) =(x2 + 4)(x2 - 6x + 10) = x4 - 6x3 + 14x2 - 24x + 407. x4 - 6x3 + 14x2 - 24x + 40 = 08. Check students’ work. 9. Answers may vary.10.

Practice 6-6

1. -1, 0, 1 2. -4, 0, 4 3. 4.

5. -1, , 0 6. -5, 0, 5 7. 2; 2 or 0;41,43,4 ,4

8. 2; 2 or 0;41,42,45,410,4 ,4 ,4 ,4

9. 4; 4, 2, or 0;41,45,4 ,4 10. 3; 3 or 1;41,43,49,

4 ,4 ,4 ,4 ,4 ,4 11. 5; 5, 3, or 1;41,43,45,

415,4 ,4 ,4 ,4 ,4 ,4 ,4 ,4 12. 3; 3 or 1;

41,47 13. 3; 3 or 1;41,42,43,44,46,412

14. 4; 4, 2, or 0;41,42,43,46,4 ,4 15. 5; 5, 3, or 1;

41,42,43,46,4 ,4 ,4 ,4 16. 6; 6, 4, 2 or 0;41,42,

43,46,49,418,4 ,4 ,4 ,4 ,4 ,4 17. 5; 5, 3, or

1;41,45 18. 5; 5, 3, or 1;41,42,43,46,4 ,4 ,4 ,4 ,

4 ,4 19. 3 20. 4,-3i, 3i 21.

22. 2, 23. 1, 24. -3, 1, 4

25. -4, 26. -1, 27. -3, 3,-2i, 2i

28. -2, 2, 29.

30.

Guided Problem Solving 6-61. three 2. three 3. 41,42,43,44,46,49,412,418,436 4. 4 5. 6. 3i,-3i 7. 4,43i8. Answers may vary. 9. Answers may vary.10. -1,42i

Practice 6-71. combination 2. permutation 3. permutation 4. combina-tion 5. 12 6. 66 7. 792 8. 12 9. 1 10. 15 11. 1 12. 8413. 1 14. 252 15. 2002 16. 2,118,760 17. 40,320 18. 11019. 17,280 20. 360 21. 479,001,600 22. 239,500,800 23. 95,040 24. 12 25. 3024 26. 455 27. 60 28. 360 29. true, comm. prop. of mult. 30. false; Let a = 2. (22)! =24 2 4 = (2!)2 31. false, Let a = 2 and b = 3. 2 ? 3! =12 2 720 = (2 ? 3)! 32. true; identity prop. of add.33. false; Let a = 2 and b = 3. (2 + 3)! = 120 2 8 =

2! + 3! 34. false; Let a = 2. (2!)! = 2 2 4 = (2!)2

Guided Problem Solving 6-71. 2; 5; 3; 2 2. the number of different ratings possible 3. No; a particular television set will fall into one price rangeor the other. 4. 1 5. the Multiplication Counting Principle6. 2 5 3 2 7. 60 8. Answers may vary. 9. 240

Practice 6-81. x4 + 8x3 + 24x2 + 32x + 16 2. a7 + 14a6 + 84a5

+ 280a4 + 560a3 + 672a2 + 448a + 128 3. x7 + 7x6y+ 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7

4. d9 - 18d8 + 144d7 - 672d6 + 2016d5 - 4032d4

+ 5376d3 - 4608d2 + 2304d - 512 5. 256x8 - 3072x7

+ 16128x6 - 48384x5 + 90720x4 - 108864x3 + 81648x2

- 34992x + 6561 6. x9 - 9x8 + 36x7 - 84x6 + 126x5

- 126x4 + 84x3 - 36x2 + 9x - 1 7. 64x12 - 384x10y2

+ 960x8y4 - 1280x6y6 + 960x4y8 - 384x2y10 + 64y12

8. x35 + 14x30y + 84x25y2 + 280x20y3 + 560x15y4

+ 672x10y5 + 448x5y6 + 128y7 9. about 1% 10a. about 99% 10b. about 95% 10c. about 5% 11. about 3% 12. about 3% 13. about 8% 14. about 0.6% 15. n3 - 9n2 + 27n - 27 16. 16n4 + 64n3 + 96n2 + 64n + 16 17. n5 - 30n4

+ 360n3 - 2160n2 + 6480n - 7776 18. n6 - 6n5

+ 15n4 - 20n3 + 15n2 - 6n + 1

x2 1 9

2"3, "3, 212i, 12i

223, 23, 2i, i2"3, "3

21 4 i"32i"7, i"7

21 4 i"521 4 "5

22, 1 4 "738

18

34

14

32

12

187

97

67

37

27

17

34

14

32

12

32

12

56

16

53

13

152

52

32

12

94

34

14

92

32

12

52

12

103

53

23

13

32

1221

5

212, 0, 1321

3, 0, 12

x4 1 10x2 1 9 5 0

15; 11

5112

16

14

43

23

13

1221

212

1621

6136

118

112

49

29

19

16

14

43

23

13

12

23, 21

4234"13

2

3, 12, 21221 4 i"19

1 4 2i2 4 3i3 4 i2 4 i

2343"52

12

5 1 "6, 22 2 "10

4i, 6 1 i3 1 "2, 1 2 "32 2 3i, 2"7



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19. 8a3 + 24a2 + 24a + 8 20. x8 - 4x6y2 + 6x4y4 -

4x2y6 + y8 21. 32x5 + 240x4y + 720x3y2 + 1080x2y3 +

810xy4 + 243y5 22. 64x12 + 192x10y2 + 240x8y4 +

160x6y6 + 60x4y8 + 12x2y10 + y12 23. x6 - 3x4y2 +

3x2y4 - y6 24. 16b4 + 32b3c + 24b2c2 + 8bc3 + c4

25. 243m5 - 810m4n + 1080m3n2 - 720m2n3 + 240mn4

- 32n5 26. x18 - 6x15y4 + 15x12y8 - 20x9y12

+ 15x6y16 - 6x3y20 + y24 27. x7 + 7x6 + 21x5 + 35x4

+ 35x3 + 21x2 + 7x + 1 28. x8 + 32x7 + 448x6 +

3584x5 + 17920x4 + 57344x3 + 114688x2 + 131072x+ 65536 29. x6 - 18x5y + 135x4y2 - 540x3y3

+ 1215x2y4 - 1458xy5 + 729y6

30. x5 + 10x4 + 40x3 + 80x2 + 80x + 32 31. x10 - 5x8y2 + 10x6y4 - 10x4y6 + 5x2y8 - y10

32. y5 + 15y4 + 90y3 + 270y2 + 405y + 243 33. x12 + 18x10 + 135x8 + 540x6 + 1215x4

+ 1458x2 + 729 34. x7 - 35x6 + 525x5 - 4375x4

+ 21875x3 - 65625x2 + 109375x - 78125 35. x4 - 16x3y + 96x2y2 - 256xy3 + 256y4

Guided Problem Solving 6-81. 0.5 2. 5 3. 0.5 4. 2 5. 6. 7. 8. about 31% 9. 1 10. 11. about 16% 12. 13. about 16% 14. Answers may vary. 15a. 37.5% 15b. 25% 15c. 25%

6A: Graphic Organizer1. Polynomials and Polynomial Functions 2. Answers mayvary. Sample: polynomials and linear factors, dividingpolynomials, solving polynomial equations, the FundamentalTheorem of Algebra 3. Check students’ work.

6B: Reading Comprehension1. x 2. y 3. 1 unit 4. parabola 5. y-axis 6. downwards7. (0, 0) 8. upper right 9. a

6C: Reading/Writing Math Symbols1. subtract 2. inverse 3. zero 4. inverse; 5. 16. inverse 7. identity

6D: Visual Vocabulary Practice/High-UseAcademic Words1. symbol 2. always 3. table 4. explain 5. graph 6. formula 7. common 8. never 9. simplify

6E: Vocabulary CheckPolynomial: A monomial or the sum of monomials.Degree of a polynomial: The largest degree of any term.Remainder Theorem: If a polynomial P(x) of degree n � 1is divided by (x - a) where a is a constant, then the remainderis P(a).Multiplicity: The number of times the related linear factor isrepeated in the factored form of the polynomial.Relative maximum: The y-value of a point on the graph of afunction that is higher than other nearby points.

6F: Vocabulary Review Puzzle1. absolute 2. opposite 3. term 4. variable 5. evaluate6. complex

Chapter 7Practice 7-11. 12 2. -5 3. not a real number 4. 0.1 5. 0.3 6. 3

7.-3 8. 0.3 9. 6 10. -7 11. -0.4 12. 13. -20, 20

14. no real square roots 15. -100, 100 16. -0.25, 0.2517. no real fourth roots 18. -4, 4 19. -0.1, 0.1 20. -5, 521. 9x2 22. 11 ∆y5« 23. 2g2 24. 5x3 25. 3xy3

26. x - 9 27. 5(x + 2)2 28. 29. -2, 2 30. -3, 3

31. -0.4, 0.4 32. 33. 20 cm 34a. about 25.30 ft/sec

34b. about 10.48 ft/sec

Guided Problem Solving 7-11. K and L, respectively 2. length, L 3.4. ; L � 35 ft 5. ; L � 55 ft

6. � 20 ft longer 7. The answers check. 8a. � 72,000 cars

8b. � 6,500 cars

Practice 7-21. 2 2. 9xy2 3. 5yz2 4. 48x 5. 2xy

6. 7. 8. 9. 10.

11. 12. 13. 10 14. 54 15. 9 16. -3

17. 18. 2xy3 19. 20.

21. 22. 23. 24.

25. 26. 27. 28. 29.

30. 31. 32. 33.

34a. 34b. 2.88 in.

Guided Problem Solving 7-21. distance in miles from the satellite to the center of Earth2. 3950 mi 3. r = 3950 + 100 = 4050 4. 17,498 mi/h 5. r = 3950 + 200 = 4150 6. 17,286 mi/h 7. 212 mi/hgreater 8. The answers are reasonable. 9. 0.22 gram

r 5 Å3 3V4p ; r 5

"3 6p2V2p

3"3a

"3 12y2

2x25y2

3k

"3 4x"25uv2"4 u5r"3r6xy"3 x

4st3"4 s3xy5"z22a4"3 23k3"2

5z"3 y2z6x"x3x2"2

"3 6abc2

2bc"2xy

4y

"4 54x3

3x"3 9x2y2

3y"3y

33"2x

227"2y

"3 6x2"y"6

10 5 1.35"L8 5 1.35"L

K 5 1.35"L

247, 47

4x3

7

103

18

5b1g45b4g110b3g2

5C3 5 10b3g2



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Practice 7-31. -63 2. -6 3. 73 4. 11 5. 5 + 2

6. 3 - 7 7. 11 8. -2 - 9. 10 - 5

10. - 11. 12. 22 13. 4

14. 0 15. 13 16. -3 - 17. -38 + 7

18. 67 - 15 19. 28 - 16 20. 9 + 2

21. 30 + 12 22. 12 23. 18

24. 41 - 3 25. 6 + 4 26. 105

27. 26y 28. 6y + 13 - 25 29. x - 3

30. 31. 32.

33a. ft or about 2154 ft

33b. ft2 or about 212,942 ft2


1. 2. subtract 3. 4. 5.

6. 1 7. Yes, it equals the reciprocal of the golden ratio.

8.

Practice 7-41. 3 2. 81 3. 32 4. 256 5. 1 6. 4 7. -1 8. 9 9. 2

10. 11. 2 12. 4 13. 1 14. 15. 16. 0

17. 12 18. 19. 20. 21. 22.

23. 24. 25. 26. 27.

28. 10.1% 29. 30. 31. 32.

33. 34. 35. 36. 37.

38. 39. 40. 41. 42. 43.

44. 36a2 45. 46.


1. 39% 2. number of years ago that the organism died

3. fraction of A left after T years 4.

5. � 78% 6. � 61% 7. � 37% 8. Yes, the answers check.9. � 81%; � 65%; � 12%

Practice 7-51. 127 2. -8, 8 3. 9 4. 3 5. no solution 6. 25 7. 9 8. -14 9. 1 10. 27 11. 4, 2 12. 9 13. 7 14. 2 15. 4 16. 29,-25 17. 10 18. 16 19. 4 20. 13 21. 4

22. -27, 27 23. 64 24. 0,-1 25. no solution 26. 64 27. 23 28. 0 29. no solution 30. -2 31. 1 32. -123 33. 8 34. 12 35. 1 36. 16 37. 8 38. -6, 2 39. 2


1. 2. ; ; 3. about 8.8 in.

4. about 15.2 in. 5. Yes, the answer checks. 6a. about 10.7in. 6b. about 11.5 in.

Practice 7-61a. ƒ(x) = 1.8x 1b. g(x) = 0.75x 1c. g(f(150)) = $202.501d. No; it doesn’t matter whether you first multiply by 0.75 or by 1.8. 2. 2x2 + 4x + 2; all real numbers 3. -2x2 + 4x - 4; all real numbers 4. 8x3 - 2x2 + 12x - 3; all real numbers

5. ; all real numbers 6. 2x2 - 4x + 4; all real

numbers 7. ; all real numbers except 8. -4

9. -2 10. 7 11. 12. -4x + 7

13. 2x2 - 3x - 7 14. 15. 16. -8x + 6 17.

18. 19. 20. 3x2 - 13

21. 3x3 + 2x2 - 15x - 10 22. -2x2 + 3x + 1223a. ƒ(x) = 0.75x 23b. g(x) = x - 5 23c. g(ƒ(50)) = $32.50 23d. Yes; multiplying by 0.75 andthen subtracting by 5 is different than subtracting by 5 andthen multiplying by 0.75.

Guided Problem Solving 7-61. cost in dollars to produce x violins; income in dollars fromselling x violins 2. profit earned when he makes and sells xviolins 3. I(x) = 5995x 4. C(x) = 1000 + 700x 5. P(x) =5295x - 1000 6. 157,850 7. He made a profit of $157,850when he makes and sells 30 violins. 8. The answers match.9a. P(x) = 56x -30 9b. $13,970

Practice 7-71. 2.

x

y

O2 6�4�6 �2

2

�2�4�6

46

x

y

O 2 4 6�4

246

75

23x 1 25

245

165

175

23a 1 25

14

2x2 1 34x 2 1

4x 2 12x2 1 3

#2A"33

2A"39

2A3"3

s"32

RA 5 (2.7)–

T8033

(5ab)34n

45

(26)12b

342

13y

23(5y)

12m

13x

32

1"5 a8

1"7 t2

"5 m12"4 ab"3 z2

"5 b"a3"3 2y"3 x4

3x2y12x

13201

98a341

x2

21

y3140

b3

a41y69ab

23

3

y16

x76

94

12y

32x

56

224Í3 1 525

21 1 Í52

1 2 Í521 1 Í5

1 1 Í52

270,000 1 90,000"32

(900 1 300"3 1 300"6)

x 1 2"3 x2x"2"5 2 2"2

3

"5y"5

"x"3 9"3 3"6"3

"10"7"6

"14"3"7

"10"5"4 3

"2"222 1 14"313

3 1 "52

"3"3"3 xy"3 x"7

"3"2"3



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3. 4.

5. 6.

7. ; no 8. y = x - 2; yes

9. ; yes 10. ; no

11. ; yes 12. ; no

13. ; no 14. ; no

15. ; no 16. ; no

17. ; no 18. ; no

19. (x) = 6x; The domain and range of f and is theset of all real numbers; is a function.

20. ; The domain and range of f andis the set of all real numbers; is a function.

21. ; Domain of f = all real

numbers = range of ; Range of f = the set of real

numbers greater than or equal to -2 = domain of ;

is not a function.

22. ; Domain of f = all real

numbers = range of ; Range of f = all real numbers

greater than or equal to 4 = domain of ; is not a

function.

23. ; Domain of f = all real numbersgreater than or equal to 1 = range of ; Range of f = allreal numbers greater than or equal to 0 = domain of ;

is a function.

24. ; The domain and range of f and is

the set of all real numbers greater than or equal to 0; is a function.

25.

26.

27. -1 28. 3 29. 30. ; in 2009

Guided Problem Solving 7-71. v is the velocity of the water in feet per second; g is theacceleration due to gravity (32 ft/s2); x is the height of the

water in feet. 2. v2; ; 3. 25 4. 25 ft 5. 6.25 6. 6.25 ft

7. Yes, the answers check. 8. ; r � 8.4%

Practice 7-81. 2.

x

y

O2 4 6�2

246

�2�4�6

8 10x

y

O2 4 6�4�2�6

246

�2�4�6

r 5 Å SP 2 1

v2

64v2

2g

f21(x) 5x 2 635,600

198,900212

O

2

�2

�2

2x

y

x –3 –1 0 –2

y 0 1 2 3

O

2

�2

�2

2x

y

x –3 –2 –1 0

y –2 –1 0 1

f21

f21f21(x) 5 13x2

f21f21

f21f21(x) 5 x2 1 1

f21f21f21

f21(x) 5 4"x 2 4

f21

f21

f21

f21(x) 5 4"x 1 2

f21f21f21(x) 5 25x 1 10

f21f21f21

y 5 4"4 2 xy 5 4"x 1 4 2 4

y 5 4Äx 1 23y 5 4Äx 1 4

6

y 5 4"x 2 3y 5 4Äx5

y 5 4Ä1 2 x3y 5 1

2x 1 12

y 5 4"2x 2 3y 5 13x 2 1

y 5 4"x 2 2

x

y

O�2 21 3 4

�2

21

34

x

y

O�2�3 21 3

�2�3

123

x

y

O 4 5

345

x

y

O4�4�6 �2

2

�2�4�6


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3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

x�3�2�1 21 3

O

y

234

1

�2

x�1 4 521 3

Oy

1

�3�2

�5�4

x�4 �2�3 �1 1 2

O

y

23

1

�3�2

x�4 �2�3 �1 1 2

O

y21

�3�4

�2

x�1 4 52 3

O

y

23

1

�3�2

x�2�1 3 41 2

O

y

23

1

�3�2

xO1 2 3 4 5 6

y

45

321

x1 2�2�1 3 4

O

y

4

6

321

xO1 2 3 4 5

y

45

321

�1

x�3�2�1 2 3

O

y

23

1

�3�2

xO�1 1 2 3 4 5

y4321

�2

x

y

O6 8 1042

42

�2�4�6

�2

6

x

y

O6 842

4

�2�4�6

�2

6

x

y

O6 8 1042

24

�2

�6

�2

6

x

y

O6 8 1042

24

�4�2

�6

�2

6

x

y

O6 8 1042

24

�4�2

�6

�2

6

x

y

O642

24

�4�2

�6

�4

6

x

y

O642�2

24

�4�2

�6

8 10

6

x

y

O642�2

24

�4�2

�6

8 10

6

x

y

O642�2

24

�4�2

�6

�4 8

�8

x

y

O6�2

246

�4�6

8

x

y

O2 4 6�2

246

�2�4�6

8 10

x

y

O2 4 6�2

246

�2�4�6

8 10

x

y

O2 4 6�2

246

�2�4�6

8 10



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27.

28a. 28b. about 10.6 ft

29. 75 30. 7 31. no solution; is extraneous 32. 2.36

33. ; graph of shifted left

2 units 34. ; graph of

shifted left 5 units 35. ; graph of

shifted right 2 units 36. ; graph of

shifted left 3 units 37. ;

graph of shifted right 7 units and up 4 units

38. ; graph of shifted left

3 units and down 1 unit

39. 40.

41. 42.

43. 44.

Guided Problem Solving 7-81. length, in feet, of the trapeze 2. time, in seconds, for a

trapeze to complete one full cycle

3.

4. � 4.3; about 4.3 s 5. � 6.1; about 6.1 s 6. Yes, the answers

check.

7a.

7b. about 9.1 nautical miles; 11.7 nautical miles

7A: Graphic Organizer1. Radical Functions and Rational Exponents 2. Answersmay vary. Sample: roots and radical expressions, binomialradical expressions, rational exponents, inverse relations andfunctions 3. Answers may vary. Sample: packaging, art, spacetravel, solar energy 4. Check students’ work.

7B: Reading Comprehension1. cube 2. 12 edges 3. 8 vertices 4. sphere 5. They are not actually visible. 6. cube or polyhedron 7. inscribed 8. circumscribed 9. b

7C: Reading/Writing Math Symbols1. f, h 2. a 3. g 4. c 5. d 6. b 7. f 8. j 9. i, k

2 4 6

2

4

x

y

642O x

y4

2

O

2

�2�4

�2

2 x

y

O

2

�2

�2

2 x

y

O

2

�2

�2

2 x

y

O

2

�2

�2

2x

y

O

2

�2�4

�2

�4

2x

y

O

2

�2

�2

2 4x

y

y 5 5"xy 5 5"x 1 3 2 1

y 5 22"3 x

y 5 22"3 x 2 7 1 4y 5 28"x

y 5 28"x 1 3

y 5 5"3 xy 5 5"3 x 2 2

y 5 22"xy 5 22"x 1 5

y 5 9"xy 5 9"x 1 2

32

A

r

O100 200

4

8

300

12

xO1�1 2 3 4 5

y

45

321



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7D: Visual Vocabulary Practice1. nth root 2. like radicals 3. composite function 4. inverse relation 5. square root equation 6. radicalequation 7. square root function 8. radical function 9. inverse functions

7E: Vocabulary CheckRadicand: The number under a radical sign.Index: With a radical sign, this indicates the degree of the root.Principal root: When a number has two real roots, this is thepositive root.Rationalize the denominator: Rewrite the denominator ofan expression so there are no radicals in any denominator andno denominators in any radical.

Rational exponent: If the nth root of a is a real number and

m is an integer, then and .If m is negative, a � 0.

7F: Vocabulary Review Puzzle1. index 2. inverse 3. left 4. principal 5. radical 6. rational

Chapter 8

Practice 8-11. growth 2. decay 3. growth 4. decay5. ; y = 0

6. ; y = 0

7. ; y = 0

8. ; y = 0

9. y = 18,000(0.75)x; $5695.31 10. y = 29,000(0.88)x;$11,851.59 11. y = 1573(1.02)x; 1917 bears 12. y = 75,000(1.125)x; $2,568,247.87 13. y = 200,000(0.9925)x; 94,207 birds 14. y = 2(0.65)x

15. y = 10(0.8)x 16. y = 0.7(1.2)x 17. 1.45 18. 0.9 19. 0.6 20. 3 21. 25% decrease 22. 37.5% decrease23. 73% increase 24. $300,000

Guided Problem Solving 8-11. the intensity of sunlight beneath the surface of the ocean2. the depth beneath the ocean surface, in feet 3. percent ofsunlight that reaches a depth of x feet 4. 50 5. y � 5.63976205 6. about 5.6% 7. 370 8. y � 0.001708989. about 0.0017% 10. Answers may vary. 11. about 91.8%

Practice 8-21. 7.3891 2. 0.0821 3. 1.3956 4. 4.1133 5. $39,624.12

6. $21,557.68 7. ; about 5.5 mg

8. ; about 2.7 mg

9. ; about 34.6 mg 10. decay 11. growth

12. decay 13a. $9948.90 13b. $19.68 14. 9.9 yr

15. 16.

O

2

4

�2 2 x

y

O

2

4

�2 2 x

y

y 5 45a12b

113.2x

y 5 8a12b

164.9x

y 5 12a12b

164.1x

O

2

4

6

�2 2x

y

O

2

4

6

�2 2x

y

O

2

4

6

�2 2x

y

O

2

4

6

�2 2x

y

PRINCIPAL

LONOEGRVE

IACTEVIET

NRNRVNNEL

DEIOVARNA

EEOEICORC

XDRIHTGRI

TSDAELATD

ENNIEEIRA

NGROHFNRR

EEXEGTIIR

amn 5

nÍam 5 QnÍa Rma

1n 5

nÍa



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17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

Guided Problem Solving 8-21. to save $8000 2. 5 yr 3. a single deposit 4. continuously5. 0.052 6. 7. $6168.41 8. $6497.65,$6844.47, $7209.80, $7594.63, $8000. Answers may vary.9. Answer may vary. 10. $2556.43

Practice 8-31. 44 = 256 2. 70 = 1 3. 25 = 32 4. 101 = 10

5. 51 = 5 6. 8-2 = 7. 95 = 59,049 8. 172 = 289

9. 560 = 1 10. 12-2 = 11. 2-10 =

12. 38 = 6561 13. log981 = 2 14. log25625 = 2

15. log8512 = 3 16. log13169 = 2 17. log2512 = 9

18. log41024 = 5 19. log5625 = 4

20. log100.001 = -3 21. log4 = -3 22. log5 = -2

23. log8 = -1 24. log111 = 0 25. log66 = 1

26. log6 = -3 27. log171 = 0 28. log1717 = 1

29. 5 h 30. 4 31. 3 32. 2 33. 1 34. 0 35. -1 36. -2

37. -3 38. 1 39. 3 40. 2 41. -1 42. 0 43. 0 44. 3

45. 1 46. 1 47. 5 48. -2 49. -3 50. -2 51.

52. -2 53. 54. 6.3 3 10-8 55. 5.0 3 10-8

56. 6.3 3 10-9 57. 6.3 3 10-7 58. 2.5 3 10-6

59. 2.5 3 10-5 60. 1.0 3 10-7 61. 1.3 3 10-3

62. 63.

64. 65.

66. 67.

68. 69.

O

2

�2

2 4 6 x

y

O

2

�2

�2

2x

y

O

�2

�4

2 4x

y

O

2

�2

2 4x

y

x

y

O1 2 3 4 5

23

�1�2

4

�1

x

y

O2 3 4 5

123

�1�2�3

�1 1

x

y

O2 3 4 5�1

123

�1�2�3

1x

y

O1 2 3 4

123

�1�2�3

�1

12

52

1216

18

125

164

11024

1144

164

8000 5 Pe0.052(5)

O

2

4

�2�4x

y

O�2 2

�2

�4

xy

O

4

2

�2 2 x

y

O

4

2

�2 2 x

y

O�2 2

�2

�4

xy

O

4

�2 2 x

y

O�2 2

�2

�4

xy

O

2

4

�2 2 x

y

O

2

4

�2 2 x

y

O�2 2

�2

�4

xy



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70.

Guided Problem Solving 8-31. 2. = x; yes 3. 4. The error isin the second line. It should read . 5.6. 7. 1 = 3x 8. 9. Answers mayvary. 10. The error is in the third line. It should read

; the correct answer is

Practice 8-41. about 377.7 decibels 2. about 2.6 decibels 3. 1.07924.1.2042 5. -0.2219 6. -0.0969 7. 1.8751 8. 0.5052 9. 0 10. 1.7782 11. log512 12. log65 13. log21 = 0

14. log7x3 15. log415x 16. log 14 17. log 18. log

19. log3100xy2 20. log 8 21. log 3x 22. log 64 23. log

24. log x11 25. log6 26. log 27. log3

28. log2 29. log 30. log t24 31. log5

32. log x + log y + log z 33. log2x - log2y - log2z34. log 6 + 3 log x + log y 35. log 7 + 2 log (3x - 2)

36. log 2 + log r + log s + log t - log 5 - log w

37. log 5 + log x - log 4 - log y38. log55 - 5 log5x, or 1 - 5 log5x39. log 2 + 2 log x + log y - log 3 - 3 log k40. 2 log43 + 2 log4x + 2 log4y + 2 log4z 41. QuotientProp. 42. Power Prop. 43. Product Prop. 44. Power Prop.45. Power Prop. 46. Power and Quotient Prop.

Guided Problem Solving 8-41. W/m2 2. 6.31 W/m2 3. decibels 4. the decrease in apparent loudness

5. 6.

7.

8.

9.

10. 20 - 10 log 6.31 � 12 dB

11. dB, L2 � 68dB; dB

12. about 15 dB

Practice 8-51. 3.58 2. 3.36 3. 1.5 4. 0.68 5. 0 6. 1.43 7. 3 8. 1.63 9. 0.5 10. 0.53 11. 7.92 12. 1.28 13. 0.93 14. -0.47 15. 2.79 16. 0.39 17. 2.52 18. 2.04 19. 33.33 20. 10 21. 334 22. 0.22 23. 40 24. 4 25. 100 26. 100 27. 2528. 125 29. 10 30. 16.67 31. 2.26 32. 1.19 33. 0.48 34. -0.32 35. 1.48 36. 1.19 37. 3.85 38. 1.72 39. about 19 mo 40. about 27 yr 41. 3.16 42. 0.4 43. 0.0444. 4000 45. 20 46. 497.5 47. 47.5 48. 0.03 49. 5.48 50. 0.48 51. 0.23 52. 3.30 53. 0.86 54. 0.75 55. -2.54

Guided Problem Solving 8-51. 7.9 2. the magnitude of the Pennsylvania earthquake

3. 4. 5.

6. 7.

8.

9. 5.1 10. Answers may vary.

11. Answers may vary. 12. after 2 hours

Practice 8-61. 40.2 days 2. 35.7 days 3. 31.8 days 4. 6.36 km/s; no 5. 22.65 6. 25.79 7. 2.71 8. 0.92 9. 1.91 10. 0.41 11. 4.69 12. -1.15 13. 0 14. 17.33 15. 2.60 16. -2.2817. -0.02 18. 6.44 19. 1.61 20. 4 21. 21 22. no solution23. 0.61 24. 12.37 25. 1.58 26. 29,937.07 27. -0.11 28. 633.14 29. 2.12 30. 1.85 31. 1.84 32. 3 33. 2 34. 12 35. 1.83 36. 7.36 37. -0.93 38. 48.14 39. 151.4840. 4.19 41. ln 2 42. ln 243 43. ln 44. ln 45. ln 9x46. ln x4y3

Guided Problem Solving 8-61. maximum velocity of the rocket, in kilometers per second;the time in seconds that the booster rocket fires; velocity ofthe exhaust, in kilometers per second; the mass ratio of therocket 2. 6.9; 50; 3.1; unknown3.

4. 5.6. R � 10.8 7. Answers may vary. 8. Answers may vary.9. Answers may vary. 10. R � 20.0

8A: Graphic Organizer1. Exponential and Logarithmic Functions 2. Answers mayvary. Sample: properties of exponential functions, logarithmicfunctions as inverses, properties of logarithms, naturallogarithms 3. Reading Data 4. Testing Multiple Choices 5. Answers may vary. Sample: population, depreciation,medicine, investments 6. Check students’ work. Chapter:Exponential and Logarithmic Functions; ExploringExponential Models: modeling exponential growth and decay;Properties of Exponential Functions: exploring properties ofexponential functions; Logarithmic Functions as Inverses:

e6.910.0098(50)

3.1 5 R6.9 1 0.0098(50)

3.1 5 ln R

6.9 5 20.0098(50) 1 (3.1)ln R

zx3

4a

b

M 5 7.9 2log11,600

log30 ;

(7.9 2 M)log30 5 log11,600

log(307.92M) 5 log11,600307.92M 5 11,600

E ? 307.9

E ? 30M 5 11,600E ? 30ME ? 307.9

L1 2 L2 < 80 2 68 5 12L1 5 80

10 log1024 2 10 log(6.31 3 1026)

10(log1024 2 logI0) 2 10flog(6.31 3 1026) 2 logI0g

L1 2 L2 5 10 log1024

I02 10 log6.31 3 1026

I0

L2 5 10 log6.31 3 1026

I0L1 5 10 log1024

I0

3 10261024

12

12

12

12

12

12

yr4t8

x12y

13

z2x

13

y13

2xy5

87

12

38

r12s

13

t14

x2

y3

32.23 5 (22)x

log273 5 1331 5 33x

31 5 (33)x3 5 27x3 5 27xlog273log273

O

2

�2

2 4 6x

y



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write, evaluate, and graph logarithmic functions; Properties ofLogarithms: use properties of logarithms; Exponential andLogarithmic Equations: solve exponential and logarithmicequations; Natural Logarithms: evaluate natural logarithmicexpressions and solve equations using natural logarithms

8B: Reading Comprehension1. the current use of logarithms 2. common and natural 3. Answers may vary. Sample: The phrase “In the twentiethcentury” 4. 500 5. 39 6. log500 x = 39 7. a

8C: Reading/Writing Math Symbols1. 1; 13; no 2. 1; 5; no 3. (2,-3); (-3, 2); no 4. 5;-1; no 5. 64; 64; yes 6. -9,-9, 9; yes and no,-(b2) is the same as(-b2), but it is not the same as (-b)2.

8D: Visual Vocabulary Practice1. common logarithm 2. change of base formula 3. exponential equation 4. growth factor 5. logarithmicequation 6. continuously compounded interest 7. logarithmic function 8. decay factor 9. naturallogarithmic function

8E: Vocabulary CheckAsymptote: A line that a graph approaches but neverreaches.Logarithmic function: The inverse of an exponentialfunction.Exponential function: The general form is y = abx,where x is a real number, b � 0, and b � 1.Common Logarithm: A logarithm that uses base 10.Growth factor: The value b in y = abx, where b � 1.

8F: Vocabulary Review1. e 2. d 3. f 4. b 5. c 6. a 7. g 8. h

Chapter 9

Practice 9-11. 1 2. 1.2 3. 50 4. 5. 4.2 6. 7.

8. 9. 10. or

11. 12. 13. or

14. or 15. I varies inversely with R.16. A varies jointly with b and h. 17. h varies directly with Vand inversely with B. 18. V varies directly with the cube of r.19. 20. -4 21. 2 22. ; 1 23.

24. or ; 0.9 25. z = 2xy; 48

26. 27. inverse; 28. neither

29. direct; y = 6x 30. direct; y = 125x 31. neither

32. inverse;


1. directly 2. inversely 3. y = 8 4. the value of x when

y = 12 and z = 2 5. 6. 7. k = 1.5

8. 9. x = 32 10. Answers may vary.

11. Answers may vary. 12. a = 4

Practice 9-2

1. 2.

3. 4. 5.

6. 7.

8.

9. ; x = 1, y = 2

10. ; x = -1, y = 0

11. ; x = -3, y = -3

x

y

O�3�3

�6�9�12

�6�9

�12

x

y

O2 4

�2�6 6

�4

x

y

O2 4�2

24

�2�4�6 6

�4�6

y 5 2 3x 1 2 1 1

y 5 2 3x 1 3 2 1y 5 2 3

x 2 1 1 2

y 5 2 3x 2 3y 5 23

x 1 6y 5 2 3x 2 4 2 2

y 5 2 3x 1 1 1 3y 5 2 3

x 2 2 1 1

y 5 1.5xz2

8 5k(48)(3)2y 5 kx

z2

y 5 15x

y 5 20xz 5 3x

y3 ; 932

y 5 365xy 5 7.2

x

y 5 21x; 21

8y 5 8x

43

y 5 2 310xy 5 2 0.3

x

y 5 6310xy 5 6.3

xy 5 3xy 5 8

x

y 5 45xy 5 0.8

xy 5 230xy 5 224

x

y 5 36xy 5 14

x27



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12. ; x = 2, y = -2

13. ; x = 0, y = 3

14. ; x = -1, y = -2

15. ; x = 2, y = 1

16. ; x = 1, y = -1

17. ; x = 0, y = 0

18. ; x = 3, y = 1

19. ; x = -1, y = 2

20. ; x = 0, y = 0.5

21. ; x = -3, y = -1

22. ; x = 5, y = 0

23. ; x = 3, y = -2

x

y

O2 4

4

�26 8

�4�6�8

x

y

O4�2

246

�2�4�6

�4�6

x

y

O2 4�2

246

�2�4�6�8

�4�6

x

y

O1 2�1

123

�2�3

�3

x

y

O2 4�2

24

�2�4�6 6

x

y

O2�2

46

�2�4 6 8

�4

8

O

2

�2

�2

2 x

y

x

y

O21�1

1

�1�2

�2�3�4

2

x

y

O 2�1

1

�13 4 5

�2

234

xy

O1 2�1

1

�1�2�3�4

�2�3�4�5

x

y

O1 2�1

2

�2�3 3

34

x

y

O2 4

4

�26

�4�6

6



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24. ; x = 0, y = 0

25. ; x = 1, y = 1

26. ; x = 0, y = 0

27. ; x = 4, y = -2

28. ; x = 2, y = -0.5

29. 2.25 ft 30. 412.5 Hz 31. 825 Hz 32. 165 Hz 33. $7.5034. 324 keepsakes 35. $4.50 36. $36.00

Guided Problem Solving 9-21. 10,000 mi 2. mi/gal 3. g, gallons of gasoline used to drive

10,000 miles 4.

5. Check student’s table.

6. This will translate the graph 50 units to the right.

7. ;

8. 25 mi/gal; 28.57 mi/gal 9. Check students’ work.

10. ; or ; The graph of

the new mileage is a strech of the graph of the old mileage bya factor of 2.

Practice 9-31. -3, 4 2. 42 3. 2 4. 0,-2 5. -1 6. 0,43 7. y = 0

8. y = 1 9. 10. y = 2 11. y = 0 12. y = 1.5

13. 14.

x

y

O2�2

2

�2�4�6 4 6

�4�6

46

x

y

O2

2

�2�4 4 6 8

�4�6

46

y 5 12

m 520,000

gm 510,000

12g

m 510,000

g

100

80

60

40

20

300 400200Gasoline Used Later (gal)

Mile

age

(mi/g

al)

100O

m 510,000g 2 50

100

80

60

40

20

300 400200Gasoline Used (gal)

Mile

age

(mi/g

al)

100O

m 510,000

g

x

y

O1 2�1

2

�13 4 5

�2�3

3

x

y

O4

24

�26 8 10

�4�6�8

O

2

�2

�2

2 x

y

x

y

O1 2�1

12

�1�2 3 4

�2

34

O

2

�2

�2

2 x

y



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15. 16.

17. 18.

19. 20.

21.

22. vertical asymptote at x = -2; hole at x = 2 23. vertical asymptote at x = 1; hole at x = 0 24. verticalasymptotes at x = 1 and x = -1 25. vertical asymptote atx = -2 26. no vertical asymptotes or holes 27. verticalasymptote at x = 3; hole at x = -3 28. vertical asymptote

at x = 4 29. vertical asymptotes at and x = 3

30. vertical asymptotes at x = 2 and x = -2

31a. , where x = number of pages;

31b. at least 2365 pages 31c. 3571 pages 31d. 7292 pages31e. x = 0; y = 0.02

Guided Problem Solving 9-31. the player’s rate of success if she makes x more shots 2. an x-value; the number of free throws she needs to make3. Answers may vary.

4.

5. Answers may vary. 6. 6 free throws 7. 70%; answers may vary; 100%; answers may vary 8. 9. 20 assignments

Practice 9-4

1. ; x 2 0 2. 2; x 2 3. 3; y 2 1 or -1

4. ; x 2 -5 5. ; x 2 0 or -2 6. ; x 2 -2

7. ; y 2 0 or -6 8. ; x 2 5 or -5

9. ; x 2 6 or -6 10. ; x 2 7 or -5

11. ; x 2 3 or -2 12. ; x 2 -3 or -7

13. ; x 2 -5 or 14. ; x 2 1 or

15. ; x 2 4 or -4 16. ; x 2 -3

17. 10; a 2 -1, 0 18. -1; x 2 , 0,43

19. x2 - 1; x 2 -4, 2 20. x + 3; x 2 -4,-3,-1

21. ; y 2 -5,-4 22. ; x 2 0,45

23. ; y 2 -2,-1 24. ; x 2 -1, 2

25. ; y 2 2,49 26. ; y 2 46 27. ; y 2 0,47

28. ; x 2 , 2, 3, 5 29. ; x 2 41,43

30. 1; x 2 -3, 0, 5 31. ; x 2 -3,-2

32. ; x 2 0,46 33. x + 8; x 2 -2,48 34. ; x, y 2 0

35. ; x 2 0, , 5,44 36. ; x, y 2 0

37. 3x; x 2 0,-2 38. ; x 2 -6,-4, 2

39. ; x 2 -7,-3, 4

40. ; x 2 -2,41

Guided Problem Solving 9-41. The radius and height are both r. 2. cylinder or

hemisphere 3. 4. 5. VS.A. 5 2r

9S.A. 5 3pr2V 5 2

3pr3

x2 1 2x 1 1x2 1 x 2 2

x2 2 2x 1 1x2 1 14x 1 49

x3

x3

6y13

4x 2 163x

4y

1x

x2 2 5x 1 6x2 1 5x 1 6

x2 2 16x2 2 9

12

x 1 2x 2 2

y5

32

yy 2 2

3x 2 614

5y2 1 10y 1 536y 1 72

3x2 1 3xx 2 5

7y 2 286y 1 24

225

x 2 32

7x 1 4

23

2x 1 3x 2 122

32x 1 13x 1 2

4x 2 12x 1 7

3x 2 6x 2 3

x 1 8x 2 7

x 2 3x 2 6

xx 1 5

2y 1 6

35

x 1 1x 1 2

43

232

2x 1 1x

21 1 630 1 6 5 27

36 5 34 5 75%

WINDOW FORMATXmin=0Xmax=100X s c l =10Ymin=.5Ymax=1Y s c l =.1

y 5 0.02x 1 3500x

x 5 245

O

2

�2

�2

2x

y

O

2

�2

�2

2x

y

O

2

�2

�2

2

x

y

x

y

O3�3

3

�3�6 6 9 12

�6�9

69

x

y

O2�2

2

�2�4�6 4

�4�6

46

x

y

O�3

3

�3�6 6 9 12

�6�9

69

x

y

O2�2

2

�24 6 8 10

�4�6

46



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6. 7. 8. 9. The ratio

for the cylindrical tank is larger. 10. The cylindrical tank hasa larger volume. 11. yes; cylindrical tank holds more than ahemispherical tank; answers may vary. 12. cylindrical tank

Practice 9-51. 6x(x + 2)(2x - 3) 2. 6(x - 1)(x - 2)2(x + 10)

3. (2x + 3)2(2x - 3) 4. 10x(x + 3)2(x - 3) 5.

6. 7. 8. 9.

10. 11. 12.

13. 14.

15. 16. 17.

18.

19. 20.

21. 22.

23. 24. 25.

26. 27. 28. 29.

30. 31. 32. 33.

34. 35. 36. 37. 2x + 3

38. 39. 40.

41a. ohms 41b. ohms

Guided Problem Solving 9-51. 1 unit 2. unit 3. 1; 2 4. 5.

6. 2 7. 8. 9.

10. Check students’ work. 11.

Practice 9-6

1. 43 2. 44 3. 4. 5. 6. -2 7. -0.2

8. -0.5 9. 3 10. -2 11. 0 12. -17 13. 12 14. 6

15. 16. no solution 17. -9 18. 7 19. 11 20. 41

21. 5 22. -3 23. 0 24. 25. -3 26. 18 27.

28. -5 29. no solution 30. 12 31. 4 32.

33. no solution 34. 6 35. -5 36. -1 37. about 13 mi/htail wind 38. about 14 mi/h head wind 39. about 1.3 days 40. Tom: 125 min, Huck: 500 min

Guided Problem Solving 9-61. 700 miles 2. 360 mi/h 3. 4. h 5. faster 6. 7. 8.or 9. 90 mi/h 10. Answers may vary.11. 50 mi/h

Practice 9-71. no 2. yes 3. yes 4. no 5. dependent 6. independent7. independent 8. dependent 9. 20% 10a. 0.6 10b. 110c. 0.7 10d. 0.6 11a. 11b. 11c. 11d.

12. about 69.6% 13. 12.5% 14. 15. 0.16 16.

17. 18. 55% 19. 38%

Guided Problem Solving 9-71. a multiple-choice test 2. 3 3. 4 4. 1 5. 6. no

7. independent 8. ; ; 9. P(A) � P(B) � P(C) = � �

10. 11. Check students’ work. 12.

9A: Graphic Organizer1. Rational Functions 2. Answers may vary. Sample: inversevariation, rational functions and their graphs, rationalexpressions, solving rational equations 3. Check students’work.

9B: Reading Comprehension1. y-axis 2. when it is the ratio of two functions, written as afraction 3. The value 2, substituted for the variable x, resultsin a value of zero for the denominator, which makes the

function undefined. 4. 5. When the value 2

is substituted for the variable x, the denominator is zero andthe function is undefined. 6. a

9C: Reading/Writing Math Symbols1. 2. <2.718 3. <3.14 4. 7! means 7 factorial,or 7 3 6 3 5 3 4 3 3 3 2 3 1. 5. 3 : 5 means the ratio of3 to 5 or . 6. decimal point, read as “and,” separates units

and tenths 7. Multiply 7 times 9.

9D: Visual Vocabulary Practice/High-UseAcademic Words1. notation 2. composition 3. arrange 4. pattern 5. approach 6. equivalent 7. apply 8. exclude 9. solve

35

"21

x 2 2x 2 2 ?

(x 2 1)1

18

164

14

14

14

14

14

14

14

1112

120

120

16

23

23

23

3518 1 700

360 1 x 5 3.5

700360 1 700

360 1 x 5 3.5700360 1 x

dt 1 x or 360 1 x

3518t 5 d

s

143

607219

25

316

942 9

172 411

83

21a 1 1

b5 ab

ab ? 21a 1 1

b5 2ab

a 1 b23

35

43;

23

21a 1 1

b5 2

1 1 213

43

2417

3y(y 2 2)(y 2 6)(y 1 2)(y 2 4)

2y 1 6xyx

3x 2 35x 1 5

154

y 2 24y

x2x2 2 3x 2 2

x 1 24x 2 6

2y3x

x2 1 y2

x2 1 xy8r2

r2 2 4

2 6tt2 2 25

2gh

8c2

c2 2 95a2 1 2a

a2 2 4

5x 1 63x 2 1

5x2 2 25x 1 31x2 2 5x 1 6

3x2 1 14x2 1 5

4x2 2 36x 1 3x 2 9

4x 1 1(x 1 5)(x 1 1)(x 2 2)

2(x 1 2)x(x 2 3)

7x 1 52(3x 2 1)(2x 2 3)(2x 1 3)

(5x 1 1)(x 1 3)(x 2 3)(x 1 2)(x 1 5)(x 1 1)

3x 1 2

x2yx2 2 4

9y 1 4x21x2y2

10x 2 26(x 1 5)(x 2 5)(x 1 1)

3 2 2x2y2

8x3y3

12y 1 5x10x2y2

3(3y 2 1)y2 2 5

7y 1 53y

2x9

2 2 nn 2 4

3xy3

x2 1 2x 2 212

2x2

5

VS.A. 5 r

4S.A. 5 4pr2V 5 pr3



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9E: Vocabulary CheckBranch: A piece of a discontinuous graph.Inverse variation: An equation of the form or xy = k, where k � 0.

Rational function: where P(x) and Q(x) are

polynomial functions and Q(x) � 0.Joint variation: An equation of the form z = kxy,where k � 0.Point of discontinuity: Occurs at x = a, if a is a real numberfor which the denominator of a rational function f is zero.

9F: Vocabulary Review Puzzle1. simplest form 2. complex 3. extraneous solution 4. discontinuity 5. independent 6. branch 7. rational 8. dependent 9. combined 10. mutually exclusive

Chapter 10

Practice 10-11. (0, 0); (43, 0), (0, 43); {x∆-3 # x # 3}, {y∆-3 # y # 3} 2. (0, 0); (43, 0); {x∆x # -3 or x $ 3}, all real numbers 3. (0, 0); (41, 0), (0, 43); {x∆-1 # x # 1}, {y∆-3 # y # 3} 4. (0, 0); (43, 0), (0, 41); {x∆-3 # x # 3}, {y∆-1 # y # 1} 5. (0, 0); (43, 0), (0, 42); {x∆-3 # x # 3}, {y∆-2 # y # 2} 6. (0, 0); (45, 0), (0, 45); {x∆-5 # x # 5}, {y∆-5 # y # 5}7. ellipse;

x-axis, y-axis;{x∆-2 # x # 2},{y∆-1 # y # 1}

8. ellipse;x-axis, y-axis;{x∆-1 # x # 1},{y∆-2 # y # 2}


10. hyperbola;x-axis, y-axis;{x∆x # -2 or x $ 2},all real numbers



13. circle;all lines through center;{x∆-3 # x # 3},{y∆-3 # y # 3}

14. circle;all lines through center;{x∆ # x # },{y∆ # y # }

15. circle;all lines through center;{x∆ # x # },{y∆ # y # }"52"5

"52"5

y

�3 3

�3

O x

3

�1

1

1�1

"22"2"22"2

y

�3 3

�3

O x

3

1

2

2

�2

�2

y

O x

�1

1

1�1 2

2

�2

�2

y

�6 6

�6�4

O�2 2

x2

64

�2

y

�3

O x

3

�1

1

1�1 2

2

�2

�2

y

�3 3

�3

O x

3

�1

1

1�1

2

�2

y

�3 3O x

�1

1

1�1

2

�2

y

�3 3

�3

O x

3

1

1 2�2 �1

y

�3 3

�3

O x

3

2

2

�2

�2

f(x) 5P(x)Q(x) ,

y 5 kx



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16. ellipse;x-axis, y-axis;{x∆ # x # },{y∆-1 # y # 1}

17. hyperbola;x-axis, y-axis;{x∆x # or x $ },all real numbers

18.hyperbola;x-axis, y-axis;all real numbers,{y∆y # -1 or y $ 1}

19. hyperbola;x-axis, y-axis;{x∆x # or x $ },all real numbers



22. hyperbola;x-axis, y-axis;all real numbers,{y∆y # -3 or y $ 3}


24. circle;

all lines through center;

{x∆ # x # },

{y∆ # y # }




y

�6 6

�6

O x

6

4

4

�4

�4

y

�6 6

�6

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6

�2

2

2�2

y

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�9�6

�3 3x3

96

�6 6�3

1321

3

1321

3

y

O x

32

3�2

3�2

32

y

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�6�4

�2 2x2

64

�4 4�2

O

y

�6 6

�6�4

O�2 2

x2

64

�4 4�2

y

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�6

O x

6

�2

2

2�2

4

�4

y

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�6

O x

6

�2

2

2�2 4

4

�4

�4

"52"5

y

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3

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1

1�1 2

2

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�2

y

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O x

3

�1

1

1�1 2

2

�2

�2

"22"2

y

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�3

O x

3

�1

1

1�1 2

2

�2

�2

"22"2

y

�3 3

�3

O x

3

2

2

�2

�2



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39. circle;all lines through center;{x∆ # x # },{y∆ # y # }"32"3

"32"3

y

�3 3

�3

O x

3

�1

1

1�1 2�2

�2

y

�4O x

�2

2

2�2 4

4

�4

y

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�3

O x

3

�1

1

1�1

y

�6 6

�6�4

O�2 2

x2

64

�4 4�2

y

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�6�4

O�2 2

x2

64

�4 4�2

y

�6 6

�6�4

O�2 2

x2

64

�4 4

y

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�3

O x

3

�1

1

1�1 2

2

�2

�2

y

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�6

O x

6

2�2 4�4

y

�6 6

�6�4

�2 2x2

64

�4 4�2

y

�6 6O x

6

�2

2

2�2 4

4

�4

�4

�8 8

8

�8

y

�3 3

�3

O x

3

�1

1

1�1 2

2

�2

�2

y

�6 6

�6�4

x2

64

�4 4�2



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41. ellipse;x-axis, y-axis;{x∆ # x # },{y∆ # y # }


Guided Problem Solving 10-11. the lamp 2. the very edge of the shadow 3. a plane and adouble cone 4. The wall is like the plane and the lamp shadeis like the double cone. 5. parabola 6. hyperbola 7. circle8. Hold the lamp at an angle so that the light from the top ofthe shade gives a closed, curved oblong area of light on thewall. 9. Answers may vary. 10. Answers may vary.

Practice 10-2

1. left 2. downward 3. left 4. upward 5. upward

6. left 7. right 8. downward 9. (0,-8); y = 8

10. ; y =

11. 12.

13. 14.

15. 16.

17. (2,-3); x = -2 18.

19. (0, 2); y = -2 20.

21. x = 22. y = x2 23.

24. 25. 26.

27. 28. 29.

30. 31. 32.

33. 34. 35.

36. 37. 38.

39. 40. 41.

42. 43. 44.

45a. 45b. 12.5 in. 46. 47. y = x2

48. (3,-1); (3,-2); y = 0

O

�2

�4

�6

2 4xy

y 5 18x2y 5 1

40x2

x 5 112y2y 5 1

20x2x 5 120y2

y 5 2 112x2x 5 2 1

40y2x 5 214y2

x 5 2 112y2y 5 1

4x2y 5 2 116x2

x 5 124y2x 5 1

4y2y 5 132x2

y 5 128x2y 5 1

20x2x 5 2 120y2

x 5 2 124y2x 5 1

12y2y 5 112x2

x 5 18y2y 5 2 1

12x2y 5 2 116x2

x 5 2 112y21

16218y2

a0, 132b ; y 5 2 1

32

a 132, 0b ; x 5 2 1

32

a2 112, 0b ; x 5 1

12a0, 2234b; y 5 231

4

a 120, 0b ; x 5 2 1

20a0, 2 112b ; y 5 1

12

a 148, 0b ; x 5 2 1

48a34, 0b ; x 5 23

4

132a0, 2 1

32b

y

�3 3

�3

O x

�1

1

1 2

2

�2

�2

22"322"3"22"2

y

�3 3O x

�1

1

1�1 2

2

�2

�2

y

�3

O x

3

�1

1

1�1 2�2



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49. (0, 0); ; x = -

50. (-1, 1); (0, 1); x = -2

Guided Problem Solving 10-21. meters 2. speed of the wave, in meters per second 3. (0, 0) 4. a = upward 5. c = 2.5 6. (0, 2.5), y =-2.5 7. Answers may vary. Sample (10, 10), (0, 0), (-10, 10)8.

9. Check students’ work.10.

Practice 10-3

1. (x + 5)2 + (y + 2)2 = 16 2. (x - 1)2 + (y - 4)2 = 4

3. (x + 2)2 + (y - 5)2 = 1 4. (x + 4)2 + (y + 1)2 = 4

5. (x + 3)2 + (y + 4)2 = 9 6. (x - 4)2 + (y - 6)2 = 1

7. x2 + y2 = 9 8. x2 + (y - 1)2 = 4 9. (x + 1)2 + y2 = 36

10. (x - 2)2 + y2 = 1 11. x2 + (y + 3)2 = 25

12. (x - 4)2 + (y + 4)2 = 2.25 13. (x + 2)2 + (y - 6)2 = 16

14. (x - 5)2 + (y + 1)2 = 1.21 15. (x - 1)2 + (y + 5)2 = 6.25

16. (x - 2)2 + (y - 3)2 = 17. (x - 4)2 + (y + 2)2 = 9

18. (x + 2)2 + (y - 5)2 = 12 19. (x - 1)2 + (y - 7)2 = 49

20. (x - 5)2 + (y - 5)2 = 1 21. x2 + (y - 10)2 = 25

22. (x + 8)2 + (y + 6)2 = 36 23. (-1, 8); 1 24. (0,-3); 3

25. (-3,-1); 26. (6, 0); 27. (6, 9); 2 28. (0, 0); 12

29. 30.

31. 32.

33. 34.

35. 36.

x�4 161284�8

O

y

�12�8

�16

48

x�8 84�16

O

y

�8�12

84

12

x�8 84�16

O

y

�12�8

�16

48

x161284�8�4

O

y

�8

1284

16

x�12 �4 4�20

O

y

�8�12

84

12

x�4 84 12 16�8

O

y

�8�12�16

48

x�8�4 4 8 12�12

O

y

�8�12�16

48

x�12 �4 4�20

O

y

�8�12

84

12

"5"2

14

�4 0O

2

4

6

8

�8�12�16 161284

d

t

s

d

O

12

6

�6 6

110;

O

2

�2 2

�2

x

y4

O

2

�2

�2

2x

y

18a1

8, 0b



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Guided Problem Solving 10-31. the center and the radius of the circle 2. no

3.4.5.6.7.8. 3; 1; 9. The center is (3, 1). 10. The radius is .

11. Answers may vary. 12. (2, 3), 4

Practice 10-41. ; 2. ;

3. ; 4. (46, 0);

5. ; 6. ;

7. (44, 0); 8. ;

9. ; 10. ;

11. ; 12. ;

13. ; 14. ;

15. ; 16. ;

17. ; 18. ;

x

y

2 4 6�2�4�6

6

�6

x

y

O3 6�3�6

69

�9�6

Q0, 42"6RQ4"65, 0R

x

y

O2 4 6�2�4�6

42

�2�4

y

O1 2�1�2

23

�3�2

Q0, 4"11RQ4"15, 0R

x

y

O1 2�1�2

1

3

�3

�1

x

y

O1 3�1�3

12

�2�1

Q4"5, 0RQ0, 4"5R

x�2�1 21 3�3

O

y

�3�2

21

3

x�4�2 42 6�6

O

y

�6�4

42

6

Q4"5, 0RQ0, 44"3R

x�8�4 84 12�12

O

y

�12�8

84

12

x�6�3 63 9�9

O

y

�9�6

63

9

Q43"13, 0RQ46"2, 0R

x�4�2 42 6�6

O

y

�6�4

42

6

x�4�2 42 6�6

O

y

�6�4

42

6

Q0, 4"21R

x�8�4 84 12�12

O

y

�12�8

84

12

x�4�2 42 6�6

O

y

�6�4

42

6

Q0, 44"5RQ0, 472"3R

x�6�3 63 9�9

O

y

�9�6

63

9

x�6�3 63 9�9

O

y

�9�6

63

9

Q0, 4"91R

x�4�2 42 6�6

O

y

�6�4

42

6

x�6�3 63 9�9

O

y

�9�6

63

9

Q0, 4"35RQ0, 43"5R

"6"6

(x 2 h)2 1 (y 2 k)2 5 r2(x 2 3)2 1 (y 2 1)2 5 Í6

2(x2 2 6x 1 9) 1 (y2 2 2y 1 1) 5 2 4 1 9 1 1

(x2 2 6x 1 9) 1 y2 2 2y 5 2 4 1 9

(x2 2 6x) 1 (y2 2 2y) 5 24



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19. ; 20. ;

21. ;

22. 23.

24. 25. 26.

27. 28.

29. 30. 31.

32. 33.

34. 35.

36. 37.

38. 39. 40.

41. 42. 43.

44. 45. 46.

47. 48. 49.

50. or

Guided Problem Solving 10-41. eccentricity = 2. 10; 9 3. 0.9

4. ,

5. 10; � 9.95; 1; 0.1 6.

7. The shape is close to a circle; the shape is close to a line

segment. 8. No; since c � a, so .

9. Check students’ work.

Practice 10-5

1. ; 2. ;

3. ; 4. ;

5. ; 6. ;

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q42"17, 0RQ4"10, 0R

O

8

�8

�8

8x

y

O

8

�8

�8

8x

y

Q0, 42"10RQ4"85, 0R

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q0, 4"34RQ42"2, 0R

ca , 1c2 5 a2 2 b2,

�5O5

5

y

x

"99

�4 O

2

�8 84

y

x

Q0, – "19RQ0, "19R

ca

x2

2500 1y2

10,000 5 1x2

10,000 1y2

2500 5 1

x2

4 1 y2 5 1x2

49 1y2

25 5 1x2 1y2

5 5 1

x2

18 1y2

9 5 1x2

26 1y2

25 5 1x2

20 1y2

16 5 1

x2

121 1y2

100 5 1x2

81 1y2

36 5 1x2

20 1y2

4 5 1

x2

16 1y2

32 5 1x2

16 1y2

4 5 1x2 1y2

4 5 1

x2

36 1y2

20.25 5 1x2

400 1y2

625 5 1

x2

196 1y2

100 5 1x2

100 1y2

196 5 1

x2

49 1y2

100 5 1x2

36 1y2

25 5 1

x2

9 1y2

18 5 1x2

5 1y2

4 5 1x2

4 1 y2 5 1

x2

0.25 1y2

2.25 5 1x2

16 1y2

25 5 1

x2

10 1 y2 5 1x2 1y2

5 5 1x2

29 1y2

4 5 1

x2

16 1y2

4 5 1x2

81 1y2

16 5 1

xO1 3�1�3

12

�1�2

Q0, 42"2R

x

y

O1 3�1�3

32

�3�2

x

y

O2 3�2�3

32

�3�2

Q4"2, 0RQ4"2, 0R



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7. (0, 45); 8. ;

9. ; 10. (0, 45);

11. ; 12. ;

13. ; 14. ;

15. ; 16. ;

17. ; 18. ;

19. ; 20. ;

21. ; 22. ;

23. ; 24. ;

25. ; 26. ;

x

y

O4 62�4�6 �2

642

�6

�2�4

x

y

O4 62�4�6 �2

6

2

�6

�2

Q45"2, 0RQ0, 42"5R

x

y

O4 62�4�6 �2

6

2

�6

�2

x

y

O63�6�3

963

�9�6�3

Q0, 44"2RQ44"5, 0R

O

6

�6

�6

6

x

y

x

y

O64�6�4

642

�6�4�2

Q4"37, 0RQ42"5, 0R

x

y

642�6�4�2

64

�6�4

x

y

O642�6�4�2

64

�6�4

Q4"17, 0RQ0, 4"13R

x

y

O642�6�4�2

6

24

�6�4�2

x

y

64�6�4

6

24

�6�4�2

Q0, 4"41RQ0, 4"10R

x

y

O2 4�2�4

6

24

�6�4�2

O

8

�8

�8

8x

y

Q4"29, 0RQ4"26, 0R

2

�6

46

�4

�2�4 2 4x

y

O

4

�4

�4 2�2 4 6�6x

y

O

6

�6

Q0, 45"2RQ0, 4"29R

O

10

�10

�10

10x

y

4

�4

�12

812

�8

�8 4�4 8 12�12x

y

O

Q0, 42"26RQ4"73, 0R

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

a0, 45"52 b

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q4"13, 0R



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27. ; 28. (0, 45);

29. ; 30. ;

31. ; 32. ;

33. ; 34. ;

35. ; 36. ;

37. ; 38. (45, 0);

39. ; 40. ;

41. ; 42. ;

43. ; 44. ;

45. ;

x

y

O64�6�4

6

24

�6�4�2

Q42"17, 0R

x

y

O642�6�4�2

6

2

�6

�2

x

y

O642�6�4�2

42

�4�2

Q0, 42"5RQ0, 4"29R

x

y

O642�6�4�2

642

�6�4�2

x

y

6�6

642

�6�4�2

Q43"5, 0RQ0, 4"17R

x

y

O42 6�6�4�2

642

�6�4�2

x

y

O42 6�6�4�2

64

�6�4

Q4"41, 0RQ0, 42"5R

x

y

O42 6�6�4�2

6

24

�6�4�2

x

y

O42 6�6�4�2

6

2

�6

�2

Q0, 4"10R

x

y

O4 6�6�4

6

24

�6�4�2

x

y

O2 6�6 �2

6

24

�6�4�2

Q4"13, 0RQ4"13, 0R

x

y

O42 6�6�4�2

6

2

�6

�2

x

y

O42 6�6�4�2

642

�6�4�2

a0, 4254 ba0, 425

4 b

x

y

O4 6�6�4

642

�6�4�2

O

8

�8

�8

8x

y

Q42"5, 0RQ4"26, 0R

x

y

O2�2

642

�6

�2�4

x

y

O4 62�4�6 �2

64

�6�4

Q4"10, 0RQ0, 4"13R

x

y

O4 62�4�6 �2

64

�6�4

x

y

O4 6�4�6

642

�6

�2�4

Q4"29, 0R



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46.

47.

48. 49.

50. 51.

52. 53.

54. 55. 56.

57. 58. 59.

60. 61.


1. down 1 unit 2.

3.

4. subtract 5. add 6.

7.

8. Answers may vary.

9. ;

Practice 10-6

1. ellipse; (-1, 2); 2. hyperbola; (0, 2);

; ;

3. ellipse; (-4, 0); 4. circle; (4, 2); 1;

;

5. circle; (0,-3); 6; 6. hyperbola; (5,3); ;

7. hyperbola; (3, 2); 8. circle; (0, 0); ;(8, 2), (-2, 2);

2

�2

1

1

�1 2 3�3x

y

O

3

�3

6

y

6

2

2 8

4

4 10�2xO

8

�4

"7

4

4

2

62 8 10�2

x

y

O

8

�4

2

�6

�4

�4

2�2 4 6x

y

O

4

�8

Q5 4 "5, 3R

2

�2

31 2

1

4 5�1x

y

O

3

�3

6

�6

�6 6�12x

y

O

9

�9

Q24 4 4"3, 0R

4

�4

�4 2

2

�2 4 6�6x

y

O

6

�6

4

�4

�4 2

2

4 6�6x

y

O

6

�6

Q4"10, 2Ra21 42"30

5 , 2b

O

2

�2 2�4

�2

x

y4

(x 1 1)2

4 2(y 2 2)2

9 5 1

�3

�3

1O

x

y1

(x 2 1)2

4 – (y 1 1)2 5 1

�2

�4 4O x

y2

x2

4 2 y2 5 1

x2

81 2y2

63 5 1x2

64 2y2

36 5 1

x2

9 2y2

40 5 1x2 2y2

80 5 1x2

36 2y2

28 5 1

x2

36 2y2

64 5 1x2

36 2y2

45 5 1x2

64 2y2

336 5 1

x2

5625 2y2

26,775 5 1x2

4489 2y2

3975 5 1

x2

5.858 3 107 2y2

1.667 3 107 5 1x2

25 2y2

200 5 1

x2

8.582 3 1010 2y2

4.812 3 1010 5 1x2

49 2y2

32 5 1

x2

3.112 3 1010 2y2

3.907 3 1012 5 1

x2

1.869 3 1011 2y2

3.752 3 1012 5 1



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9. circle; (-1,-7); 9; 10. hyperbola; (-1,-1);

;

11. circle; (2, 2); 3; 12. ellipse; (2,-1);

;

13. circle; (5,-2); 6; 14. circle; (-1, 5); 8;

15. parabola; (1, 2); 16. parabola; (-3,-2);

17. circle; (-4,-1); 4; 18. hyperbola; (0, 0);

;

19. parabola; (2,-1); 20. parabola; (2,-1);

21. (x + 4)2 + (y - 5)2 = 36

22.

23. 24. x = (y + 2)2 + 1

25. 26.

27. (x + 1)2 + (y - 2)2 = 36 28. y = -(x + 1)2 + 5

29.

30.

31.

32.

Guided Problem Solving 10-61. hyperbola 2. (3,-2) 3. (-3,-2) 4. 6 5. (10.2,-2)

6. 7.2 7. b2 = (7.2)2 - 62 = 15.84 8. horizontal

9. 10.

11. Answers may vary. 12.

10A: Graphic Organizer1. Quadratic Relations 2. Answers may vary. Sample:parabolas, circles, ellipses, hyperbolas 3. Reading for ProblemSolving 4. Choosing Cannot Be Determined 5. Answers mayvary. Sample: design, solar energy, machinery, architecture 6. Check students’ work.

(y – 2)2 2 (x 2 3)2 5 1

(x 2 3)2

36 2(y 1 2)2

15.84 5 1(x 2 h)2

a2 2(y 2 k)2

b2 5 1

x2

2.25 1(y 1 2)2

6.25 5 1

(x 2 125)2

36 2y2

15,589 5 1

(x 2 2)2

25 1(y 1 5)2

16 5 1

(x 2 2)2

4 2(y 2 2)2

5 5 1

(x 1 4)2

9 1(y 1 5)2

4 5 1x2

9 1(y 2 2)2

4 5 1

12

(x 2 50)2

2304 2y2

196 5 1

(y 2 5)2

4 2(x 1 4)2

5 5 1

�2

2

4

4

6 8�4x

y

O64 8 10

xO2

�6

46

�4�2

y

4

�4

�4

2

�2 4 6�6x

y

O

6

�6

4

�4�2�6 2�10x

y

O

6

�6

Q42"2, 0R

�6 2 4�8x

6

y

O

8

�4

8

42

�4 2�2 4 6�6

y

xO

963

�3 6 9�9x

y

O

152

4

�6

62 8 10

y

xO

4

�8

1

�3

1 32 4 5�1

y

xO

2

�4

1

32

2

5�1

x

4

y

O

5

Q2 4 "6, 21R

2

�6

�6 �2

�4

4�8

y

xO

4

�8�12

y

�9�6

�6 3�3 9xO

3

�15

Q21 4 "34, 21R



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10B: Reading Comprehension1. y-axis 2. x-axis 3. upward; to the right 4. downward; tothe left 5. b

10C: Reading/Writing Math Symbols1. the set of all x such that x is a real number 2. the set of allx such that x is greater than zero 3. the set of all y such that yis less than negative 1 4. the set of all x such that x is between5 and 9 or the set of all x such that x is greater than 5 and lessthan 9 5. the set of all x and y such that x is equal to y 6. the set of all x and y such that y is equal to 3 times x

10D: Visual Vocabulary Practice1. vertices of a hyperbola 2. ellipse 3. foci of an ellipse 4. parabola 5. vertices of an ellipse 6. hyperbola 7. radius8. circle 9. foci of a hyperbola

10E: Vocabulary CheckRadius: The distance between the center of a circle and anypoint on the circumference.Conic section: A curve formed by the intersection of a planeand a double cone.Directrix: The fixed line used to define a parabola. Each pointof the parabola is the same distance from the focus and thisline.Circle: The set of all points in a plane at a distance r from agiven point.Center: The point that is the same distance from every pointon the circle.


Chapter 11

Practice 11-11. an = an-1 + 6 where a1 = -14; 16 2. an = an-1 - 0.3 where a1 = 6; 4.53. an = -2an-1 where a1 = 1;-32 4. an = 3an-1 where a1 = 1; 81

5. where a1 = 1;

6. where a1 = ;

7. an = an-1 + 3 where a1 = 36; 51 8. an = an-1 - 6 where a1 = 36; 6

9. where a1 = 9.6; 0.3 10. an = 7n; 140

11. an = 6n - 4; 116 12. an = n + 4; 2413. an = n - 2; 18 14. an = 2n + 1; 41

15. an = 0.8n; 16 16. 17.

18. 19. multiply by 2; 32, 64, 128

20. subtract 5; 19, 14, 9 21. add 0.1; 1.2, 1.3, 1.4 22. add 7; 39, 46, 53 23. multiply by 2; 40, 80, 160

24. subtract 3;-21,-24,-27 25. explicit;

26. explicit;-5,-2, 3, 10, 19 27. recursive; 5, 8, 17, 44, 125

28. explicit; 29. recursive; 5,-2, 5,-2, 5

30. recursive;-4,-8,-16,-32,-64 31a. 1, 6, 36, 216

31b. where a1 = 1 32a. 60° 32b.32c. No polygon has one or two angles.

Guided Problem Solving 11-11. 2 2. 7 3. 15 4. an = an- 1 + [2n + (n - 1)] 5. 26 6. 40

7.

8. Yes, the numbers of cards per level is correct.9.

Practice 11-21. 96 2. -406.9 3. 36.3 4. -99 5. 464 6. -231 7. 5.58. -10.5 9. 171 10. no 11. yes;-3 12. yes;-0.4 13. yes; 5 14. yes;-29 15. yes; 0.3 16. yes; 6 17. yes; 0.218. yes; 13 19. 36 20. 21 21. 31 22. 14.5 23. -42 24. -3.5 25. 0 26. -2 27. 21.5 28. -28.5 29. 227

30. 189.5 31. 4.5 32. 14.5 33. 9 34. 35. -1 36. -6.5

37a. where a1 = 32 37b. 32, 37, 42, 47, 52 37c. 37d. 127 people

Guided Problem Solving 11-21. 403, 417, 431 2. 403; 14 3.4. an= 495 5. n = 8 6. 501 7. 6 min 8. 3:20 P.M. = 920;1 min 9. 403, 417, 431, 445, 459, 473, 487, 501, …;501 - 495 = 6 min 10. 69

an 5 403 1 (n 2 1)(14)

an 5 32 1 5(n 2 1)an 5 an2 1 1 5

35

an 5 360nan 5 6an2 1

0, 12, 1, 112, 2

13, 23, 1, 43, 53

an 5 n 2 13; 192

3

an 5 12n; 1

40an 5 n4; 5

an 5 12an2 1

213

23an 5 an2 1 1 1

3

132an 5 1

2an2 1

E

H Y P E R

L

E

A

C

I

C

B O L A

L

L

I

P A R

A

D

A B O

T R I XD I

U

S

A

I

S

R E C

O C UF

S

E



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Levels 1 2 3 4 5

Cards Needed 2 7 15 26 40

Levels 1 2 3 4 5

Blocks Needed 1 3 6 10 15

Practice 11-31. 8 2. 12 3. 4 4. 6 5. 10 6. 4.8 7. yes; 3; 243, 7298. yes; 2; 64, 128 9. no 10. yes;-2; 64,-128 11. yes; 0.5; 0.0625, 0.03125 12. yes; 0.3; 0.81, 0.24313. no 14. yes;-0.5; 4,-2 15. no

16. geometric; 17. neither;-9,-14

18. geometric; 2,-2 19. arithmetic; 17, 2220. arithmetic;-11,-14 21. neither; 5,-622. an = 3(-2)n-1; 3,-6, 12,-24, 48 23. an = 5(3)n-1; 5, 15, 45, 135, 405 24. an =-1(4)n-1;-1,-4,-16,-64,-25625. an =-2(-3)n-1;-2, 6,-18, 54,-16226. an = 32(-0.5)n-1; 32,-16, 8,-4, 2

27. an = 2187 ; 2187, 729, 243, 81, 27

28. an = 9(2)n-1; 9, 18, 36, 72, 14429. an =-4(4)n-1;-4,-16,-64,-256,-102430. an = 0.1(-2)n-1; 0.1,-0.2, 0.4,-0.8, 1.631a. about 19.2 in. 31b. 9 mm 32a. an = 2537(1.025)n-1

32b. about 2732 33a. an = 1(1.5)n-1 33b. 1.5 in.33c. 2.25 in. 33d. about 86.5 in.

Guided Problem Solving 11-31. geometric mean =

2. 3–6. Answers may vary: A sample is

given 3. 3 and 12; 6 4. 3, 6, 12; 2 5. 768 6. 48 7. 5th term

8. The answers check. 9. Answers may vary. The answer to

step 7 is the same since halfway from the 1st term to the 9th

term is the 5th term.

Practice 11-41. 4; 0; 3; 6 2. 5; 3; 11; 35 3. 6; 28; 33; 183 4. 4; 13; 28; 825. 4; 2.5; 8.5; 22 6. 6; 2;-3;-3 7. 6; 5; 10; 45 8. 4;-4;-7;-22 9. 4; 11; 20; 6210. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15; 6411. 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26; 12412. 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44; 21613. 10 + 25 + 40 + 55 + 70 + 85; 285 14. 17 + 25 + 33 + 41 + 49 + 57 + 65; 28715. 125 + 126 + 127 + 128 + 129 + 130 + 131; 896

16. 17.

18. 19.

20. 21.

22. sequence; finite 23. series; infinite 24. sequence; infinite25. series; finite 26. sequence; infinite 27. series; finite28. -9 29. 39 30. -72 31. -51 32. 4.5 33. 60 34. 1025 stitches 35. 19 musicians; 84 musicians

Guided Problem Solving 11-41. 20 2. Front row of middle section has 10 seats; each of thetwo side sections has 4 seats 3. Last row of middle sectionhas 29 seats; each of the two side sections has 23 seats 4. Total seats in middle section is 390; each of the two side

sections has 270 5. 930 seats 6. middle section: ;

side section: 7. $46,950 8. The answers are

reasonable. 9. n = 24; d = 6

Practice 11-51. converges; yes 2. converges; yes 3. converges; yes4. diverges; no 5. converges; yes 6. diverges; no 7. 15

8. no sum 9. 10. no sum 11. 16 12. 1.5 13. 600

14. 4000 15. arithmetic; 126 16. geometric;

17. geometric; 1023 18. arithmetic; 240 19. 79.921875 20. 28,697,812 21. about 74.99 22. 40.5 23. 0.2222222224. 6300 25. $8553.71 26. $40,928.80 27. 5000 cm 28. about 177.78 mm 29. $2,319,367.05; $4,950,000

Guided Problem Solving 11-51. 4 2. 4 3.

4. 4, 16, 64 5. 4 6. 4 + 16 + 64 + 256 + 1024 + 4096 7. 5460 8. formula gives 5460 also 9a. $10, $20, $40 9b. $10 + $20 + $40 + $80 + $160 9c. $310

Practice 11-6For Exercises 1–19, answers are in units2.1a. 0.5(3.75) + 0.5(3) + 0.5(1.75) + 0.5(0); 4.251b. 0.5(4) + 0.5(3.75) + 0.5(3) + 0.5(1.75); 6.252a. 0.5(15.5) + 0.5(14) + 0.5(11.5) + 0.5(8); 24.52b. 0.5(16) + 0.5(15.5) + 0.5(14) + 0.5(11.5); 28.53a. 0.5(1.875) + 0.5(1.5) + 0.5(0.875) + 0.5(0); 2.1253b. 0.5(2) + 0.5(1.875) + 0.5(1.5) + 0.5(0.875); 3.1254a. 0.5(4) + 0.5(4.25) + 0.5(5) + 0.5(6.25); 9.754b. 0.5(4.25) + 0.5(5) + 0.5(6.25) + 0.5(8); 11.75

Stage 14

Stage 216

Stage 364

2551024

23

a20

n51(n 1 3)

a20

n51(n 1 9)

a7

n5 1(10n 1 5)a

8

n5 1(4n 2 1)

a6

n5 1(23n 1 13)a

4

n5 14n

a5

n5 1(0.3n 1 2)a

7

n5 1(2n 2 1)

an 5 a1 ? rn21!product of the two numbers

a13b

n21

19, 1

27



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5a. 0.5(6) + 0.5(6.5) + 0.5(8) + 0.5(10.5); 15.55b. 0.5(6.5) + 0.5(8) + 0.5(10.5) + 0.5(14); 19.56a. 0.5(2) + 0.5(2.125) + 0.5(2.5) + 0.5(3.125); 4.8756b. 0.5(2.125) + 0.5(2.5) + 0.5(3.125) + 0.5(4); 5.8757a. 0.5(14.25) + 0.5(12) + 0.5(8.25) + 0.5(3); 18.757b. 0.5(15) + 0.5(14.25) + 0.5(12) + 0.5(8.25); 24.758a. 0.5(2) + 0.5(2.75) + 0.5(5) + 0.5(8.75); 9.258b. 0.5(2.75) + 0.5(5) + 0.5(8.75) + 0.5(14); 15.259a. 0.5(9.75) + 0.5(9) + 0.5(7.75) + 0.5(6); 16.259b. 0.5(10) + 0.5(9.75) + 0.5(9) + 0.5(7.75); 18.2510a.

10b. 5.5 10c. 9.5 10d. 7.5; the mean 11. 6.75 12. 16.5 13. 9 14. 12 15. 2.25 16. 18 17. 918. 6 19. 20. total feet 21. total number of computers22. total miles 23. total gallons 24. total molecules 25. total price26. ; 3.25 units2

27. ; 4.25 units2

Guided Problem Solving 11-61. less 2. greater3–4.

5. 3 units2

6.

12 units2

7. 7.5 units2 8. The mean best approximates the area becauseit is between the other measures known to be larger and smaller

than the actual value. 9. , ;

10a–b.

area = 7 units2

10c.

area = 15 units2

10d. mean area = 11 units2; The mean best approximates thearea because it is between the other measures known tobe larger and smaller than the actual value.

11A: Graphic Organizer1. Sequences and Series 2. Answers may vary. Sample:arithmetic sequences, geometric sequences, arithmetic series,geometric series 3. Answers may vary. Sample: geometry,fund raising, design, crafts 4. Check students’ work.

8

6

4

2

1 3 42x

y

8

6

4

2

1 3 42x

y

11116

14716

7516

x

y8

4

42

x

y8

4

42

O

4

8

12

�4 4

x

y

O

2

4

2 4x

y

4.6

O

4

8

12

�4 4

x

y



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11B: Reading Comprehension1. terms in a geometric sequence 2. The recursive formula isbased on knowing the previous term. The explicit formula isbased on knowing the ratio. 3. In an-1, n - 1 is a subscriptthat tells which term you are finding. In r n-1, n - 1 is theexponent that tells you how many times to use the base, r, as afactor. 4. the recursive formula 5. the explicit formula 6. a

11C: Reading/Writing Math Symbols1. line AB 2. line segment CD 3. angle A 4. triangleXYZ 5. Answers may vary. Sample: In -5, the symbolmeans “negative” and is describing a kind of number, so it isan adjective. In 7 - 5, the symbol means “subtract” or“minus” and names a binary operation, so it is a verb thatdescribes an action. 6. Answers may vary. Sample: The letterm alone represents “line m.” The letter m in front of an anglerepresents “the measure of” angle A.

11D: Visual Vocabulary Practice1. arithmetic sequence 2. circumscribed rectangles 3. arithmetic mean 4. geometric mean 5. geometric series6. geometric sequence 7. arithmetic series 8. inscribedrectangles 9. explicit formula

11E: Vocabulary CheckSequence: An ordered list of numbers.Term: Each number in a sequence.Common ratio: The ratio of consecutive terms of ageometric sequence.Series: The sum of the terms of a sequence.Limit: The least and greatest integer values of n in summationnotation.

11F: Vocabulary Review1. Answers may vary. Sample: A sequence is an ordered list ofnumbers; a series is the sum of the terms of a sequence.2. Answers may vary. Sample: In calculating the area under partof a curve, circumscribed rectangles are partially above thecurve while inscribed rectangles are completely under the curve.3. Answers may vary. Sample: The common difference is thedifference between consecutive terms in an arithmeticsequence. The common ratio is the ratio between consecutiveterms in a geometric sequence.4. Answers may vary. Sample: An arithmetic sequence is anordered list of numbers in which the difference betweenconsecutive terms is constant. A geometric sequence is anordered list of numbers in which the ratio betweenconsecutive terms is constant.

Chapter 12

Practice 12-11a. about 0.66 1b. about 81 persons 1c. about 0.05 1d. about 0.15 1e. about 0.37

2a. Rolling Two Number Cubes

2b. Rolling Two Number Cubes

2c. Rolling Two Number Cubes

3a. Student Pizza Preferences

3b. sausage: 25.9%, cheese: 19.9%, pepperoni: 18.1%,supreme: 13.0%, other pizza: 14.4%, no pizza: 8.8%; 100.1%;There is a rounding error of 0.1%.3c.

3d.Cheese

Sausage or pepperoniSupreme or other

No pizza

0%

20%

40%

60%

80%

100%

Outcomes

Prob

abili

ty

0%

20%

40%

60%

80%

100% Pizza

No pizza

Outcomes

Pro

babi

lity

Sausage 56

Cheese 43

Pepperoni 39

Supreme 28

Other pizza 31

No pizza 19



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Only 1 Both cubes Cubes showNumbers Cube show same differentshowing shows 2 number numbers,

neither is 2

Frequency 10 6 20

Probability 2036

636

1036

Sum Prime Composite

Frequency 15 21

Probability 2136

1536

Sum 5 or less Greater than 5

Frequency 10 26

Probability 2636

1036

3e. The sum of the probabilities of pizza categories in part dequals the probability of pizza in part c. The overall total inboth is 100.1% (0.1% rounding error).4a. Check student’s work. 4b. Check student’s work.

Guided Problem Solving 12-11. the ratio of the number of times the event occurs to thenumber of times the event does not occur 2. A 1:4, B 2:3,C 1:3, D 1:7 3. the probability of each event 4. find the sumof the number of times it occurred and did not occur 5. P(A) = 0.2, P(B) = 0.4, P(C) = 0.25, P(D) = 0.125 6.

7. Yes, the answers are reasonable.8.

Practice 12-21a. 8.9% 1b. 24.6% 1c. 0.2% 1d. 1.1% 1e. 6.3% 1f. 4.0% 2a. 11.7% 2b. 36.8% 2c. 21.0% 2d. 47.2% 2e. 14.4% 2f. 16.0% 2g. 48.9% 2h. 51.1% 3. about58.2% 4. D = drizzle, F = fog without drizzle,C = cancelled game, P = played game

4a. 45% 4b. 6%5. M = male, F = female, C = attend concert,N = not attend concert

5a. about 47% 5b. about 25%

Guided Problem Solving 12-21. The occurrence of B has no effect on the probability of A.2. P(A) = 0.60; P(B) = 0.25 3. 0.15

4. 5. 0.6 6. P(A) is equal to

P(A|B). 7. The fact that P(A) = P(A|B) illustrates that theprobability of A is the same, regardless of the occurrence of B.8. Yes, the conclusions are the same. 9a. 9b.9c. They are not equal. The events are dependent.

Practice 12-31. 23 2. 78 3. 3 4. 110 5. about 93.3; 97; 97 6. about 47.6;48; 41, 49 7. about 2.6; 2.45; 2.4 8. about 15.7; 15.6; no mode9. about 418.8; 423; no mode 10. about 1021.9; 1023; 102311. about 0.019; 0.019; 0.018, 0.019 12. about 26.4; 27; 29 13. about 44.8; 45; 42, 45, 49 14. about 48.1; 50.5; no mode15. 18; 16.5; 15 16. about 1.5; 1.5; 1.3, 1.5 17. about 9.2; 9;no mode 18. about 116.2; 116; 114 19. about 4.29; 4.26; 4.2520. about 32.4; 34; no mode21.

22.

23.

24.

10 20 30 40 50 60

40 42 44 46 48 50 52

1000 1125 1250 1375 1500

0 5 10 15 20 25 3530

113

126

P(A|B) 5P(A and B)

P(B)

M

0.51

0.49

0.51

0.49

0.55

0.45

F

C

NC

N

D

0.3

0.7

0.7

0.3

0.2

0.8

F

C

PC

P

0.90.10

0.70.8

0.50.6

0.30.4

0.10.2

W YEvent

Pro

babi

lity

ZXx

y

0.4

0.3

0.2

0.1

Pro

bab

ility

EventA B DC



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25. 174; 188 26. 346; 368 27. 94; 98 28. 22; 86 29a. about 47.4 29b. 47.9 29c. 50.8 29d. 44.1, 47.9, 50.8;

Guided Problem Solving 12-31. 16 2. 1, 2, 4, 6, 7, 7, 8, 8, 9, 12, 13, 15, 16, 20, 22, 38 3. Q1 = 6.5, Q2 = median = 8.5, Q3 = 15.5, minimum = 1,maximum = 38 4.

5. 38 6. Q1 = 6, Q2 = median = 8, Q3 = 15,minimum = 1, maximum = 22 7.

8. The main effect of removing the outlier is a shortening ofthe long whisker. 9. The median decreases from 8.5 to 8.10. Yes, the answers are correct.11.

Practice 12-41. 295.7; 47.4 2. 30.3; 3.2 3. 2.4; 0.1 4. 74.3; 3.9 5. 66.8; 33.1 6. 8; 9.5; 4 7. 189; about 109.6; 114.5 8. 15; about 531.4; 6.5 9. 1.7; 2.3; 1.05 10. 4; 46.7; 2 11. 8; 100.5; 2.5 12. 5 13. 3 14a. about 3.49 14b. about 0.55 14c. 1.7 14d. 2; 1 15a. 33 15b. 18.515c. about 88.2 15d. about 10.5 15e. 3 15f. 2 16. +0.37517. +2.75


1. 2. 3. 5.5

4. 6.5,-2.5,-3.5,-1.5,-0.5, 1.5 5. 42.25, 6.25, 12.25,2.25, 0.25, 2.25 6. 6 7. 10.9 8. 3.3 9. The values match.10. = 41,000; = 202.5

Practice 12-51. It is most likely that Sample C was largest since it has thesmallest standard deviation, implying less variation thanSamples A and B. 2. This sample is likely to contain adisproportionate number of readers. Selecting students in

random classrooms would be more accurate. 3. The pizzarestaurant sells to many different groups of people. The classmight not like the same kinds of pizza as the population as awhole. The poll should be of class members. 4. The peopleeating in the restaurant probably are not indicative of thepopulation as a whole, either geographically or economically.The poll should be a random sample of the residents, possiblya random sample from each phone exchange to include peoplefrom all the different areas of the county. 5. This excludes thepeople who are working during the day. Contacting randomlyselected people, either from the phone book or voterregistration lists, would be more accurate. 6. This is fairlyaccurate usually. 7. about 44 8. about 2500 9. about 12,34610. about 27,778 11. 53%;416%; 37% to 69% 12. 72%;44%; 68% to 76% 13. 62%;48%; 54% to 70%14. 30%;46%; 24% to 36% 15. 42%;43%; 39% to 45%

Guided Problem Solving 12-51. 408 2. 258 3. sample proportion = 4. 63%

5. margin of error = 6. 5% 7. 58% to 68%

8. 63%; sample proportion; yes 9a. 17.2% 9b. 12.5% 9c. 4.7% to 29.7%

Practice 12-61.

1a. 87.5% 1b. 50% 1c. 37.5% 2. the weather outcome ona given day, acceptable weather; Check students’ work.3. asking a person chosen at random; favoring an early curfew;Check students’ work. 4. selecting a part; part is defective;Check students’ work. 5. about 1% 6. about 0.002% 7. about 25% 8. about 38% 9.

00 1 2 3 5

0.10.20.30.40.5

Prob

abili

ty

4Number of Successes

M

M

F

F

F

M 0.125

F 0.125

0.5

0.5

0.5

0.5

0.5

0.5

M 0.125

F 0.125

0.5

0.5

MM 0.125

F 0.125

0.5

0.5

0.5

0.5

M 0.125

F 0.125

0.5

0.5

4 1"n

xn

ss2

s 5 Å a (x 2 x)2

ns2 5 a (x 2 x)2

n

67 69 7371 75 77

0 10 3020

0 10 3020 40

44424038 4846 5250 54

Q1 Q2 Q3



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10.

11.

12.

13a. 68% 13b. 99% 13c. 97% 13d. 84% 14a. 18%14b. 6% 14c. 56%

Guided Problem Solving 12-61. 99% or 0.99 2. 1% or 0.01 3. 4. n = 10,x = 9 5. 0.0914 or 9.14% 6. n = 10, x = 7 7. 0.0001or 0.01% 8. There is a malfunction in the machinery thatmust be corrected. 9. 0.0042 or 0.42%; Yes, it is between9.14% and 0.01% 10. 0.25 or 25%

Practice 12-71. 53.3 2. 69.9 3. 36.7 4. 28.4 5.

6.

7.

8.

9.

10.

11. about 34% 12. about 13.5% 13. about 2.5% 14. about 68% 15. about 16% 16. about 50% 17a. about 6 students 17b. about 37 students 17c. about 156 students 18a. about 3 nails 18b. about 82 nails 18c. about 19 nails 19a. about 10%19b. about 5 bags 19c. about 40 bags

Guided Problem Solving 12-71. 63 min 2. 4 min 3. 2.5% 4. 13.5% 5. 16% 6. yes 7. 59 min 8. Yes, the z-score is less than -1. 9. 81.5%

12A: Graphic Organizer1. Probability and Statistics 2. Answers may vary. Sample:probability distributions, analyzing data, standard deviation,working with samples 3. Answers may vary. Sample: socialscience, genetics, market research, recycling 4. Checkstudents’ work.

12B: Reading Comprehension1. how probability is affected by a small number of cases2. probability of getting heads when tossing a coin

3. 4. experimental probability

5. 6. b

12C: Reading/Writing Math Symbols1. Answers may vary. Sample:-8, 3 2. no 3. yes 4. Answers may vary. Sample:-8, 4 5. yes 6. no 7. the probability of event R, given event Q 8. Answers mayvary. Sample: given that the event that follows takes place

12D: Visual Vocabulary Practice1. box-and-whisker plot 2. quartiles 3. mean 4. conditional probability 5. frequency table 6. probabilitydistribution 7. z-score 8. interquartile range 9. standarddeviation

12

12

91.178.866.541.929.617.3 54.2x

856796736496 556 616 676x

39.434.22918.613.48.2 23.8x

78726642 48 54 60x

130115 145857055 100x

131119107837159 95x

nCxpxqn2x

00 1 2 3

0.10.20.30.40.5

Prob

abili

ty

4Number of Successes

00 1 2 3

0.10.20.30.40.50.60.70.80.9

Prob

abili

ty

Number of Successes

00 1 2 3

0.10.20.30.40.5

Prob

abili

ty

Number of Successes



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12E: Vocabulary CheckMedian: The middle value in a data set.Outlier: An item of data with a substantially different valuefrom the rest of the items in the data set.Sample: Information gathered from only part of apopulation.Sample proportion: , where x is the number of times anevent occurs in a sample of size n.Margin of error: An estimate of error of a sampleproportion.

12F: Vocabulary Review Puzzle1. mean 2. outlier 3. quartiles 4. median 5. randomsample 6. mode

Chapter 13

Practice 13-11. not periodic 2. periodic; 2 3. periodic; 4. any two

points on the graph whose distance between them is one period;

sample: (0, 2) and (3 , 2); 5. any two points on the graph

whose distance between them is one period; sample: (0, 0) and

(4 , 0); 4 6. any two points on the graph whose distance

between them is one period; sample: (0, 2) and (4, 2); 4 7. ; 1

8. 3; 2 9. 2; 3 10. 6; 2 11. 6; 12. 13. 4; 2

14. 5; 15. ; 2 16. 4; 17. 5; 18.

Guided Problem Solving 13-11. 0.2 s 2. 0.5 mV 3. Yes; the y-values repeat in a regularpattern. 4. 5 cycles 5. 5 units 6. 1 sec 7. 1 sec 8. 6 units9. 3 mV 10. 1.5 mV 11. Check students’ work. 12. Theperiod is 0.5 s and the amplitude is 1.5 mV.

Practice 13-21. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

Ox

y

315°

Ox

y

�45°

Ox

y

�330°O

x

y

�150°

Ox

y

�190°O

x

y

�90°

Ox

y

�30°Ox

y

330°

Ox

y

270°

O

x

y

210°

Ox

y

135°

Ox

y

100°

Ox

y

60°

Ox

y

30°

212, 15

811221

212315

8

123; 13

4134

18

218

14

14

313

13

314

xn



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15. 16.

17. 18.

19. 20.

21. 260° 22. 300° 23. 135° 24. 215° 25. 12° 26. 345°27. 122° 28. 124° 29. 340° 30. 61° 31. 49° 32. 322°33. 16° 34. 150° 35. 27° 36. 30° 37. 300° 38. 80°39. 190° 40. 10° 41. 20° 42. 98° 43. 120° 44. 46°45. 240° 46. 100° 47. 138° 48. 30° 49. 233° 50. 17°

51. ; (0.71, 0.71)

52. ; (-0.71,-0.71)

53. ; (-0.71, 0.71)

54. ; (0.71,-0.71)

55. ; (0.87,-0.5) 56. ; (0.87, 0.5)

57. ; (-0.87, 0.5)

58. ; (-0.87,-0.5)

59. ; (0.5,-0.87) 60. ; (0.5, 0.87)

61. ; (-0.5,-0.87) 62. ; (-0.5, 0.87)

63. (0,-1); (0,-1) 64. (1, 0); (1, 0) 65. (1, 0); (1, 0)

66. (0, 1); (0, 1) 67. ; (-0.71, 0.71)

68. ; (-0.5, 0.87) 69. -60° 70. 120° 71. 315°

Guided Problem Solving 13-21. Quadrant I 2. negative 3. positive 4. (cos θ, sin θ) 5. cos θ =-, sin θ =+ 6. -;-;+;- 7. II and III 8. II 9. If the terminal side of an angle is in Quadrants I orII, then the sine of the angle is positive; otherwise it is not.If the terminal side of an angle is in Quadrants I or IV, thenthe cosine of the angle is positive; otherwise it is not.10. Check students’ work. 11. positive

Practice 13-31. 2. 3. 4. 5. p 6. 7.

8. 9. 2p 10. 11. 12. 13. 14.

15. 16. 180° 17. 360° 18. 150° 19. 135° 20. 270°

21. 30° 22. 210° 23. 330° 24. 60° 25. 240° 26. 225°

27. 315° 28. 120° 29. 20° 30. 40° 31.

32. 33. 34.

35. 36. 37.

38. 39. 11.0 in. 40. 39.8 cm 41. 10.5 cm

42. 92.2 cm 43. 2.1 ft 44. 15.7 m 45. about 17.8 in.

46. 1.2 m


1. 24 2. 360º 3. 4. 2π radians

5. radians 6. radians

7. mi 8. radians

9. mi 10. C = 2π (3960) �

24,881 mi; � 1036.7 mi 11. C= 2π (1580) � 9927 mi;

� 413.6 mi 12. more; Check students’ work. 13. 8 o’clock

Practice 13-4

1. 4; 2p; y = 4 sin u 2. 1.5; ; y = 1.5 sin 4u

3. 2; 3p; y = -2 sin u 4. 1; 6p; y = sin u

5. 2.5; p; y = -2.5 sin 2u 6. 4; p; y = -4 sin 2u

13

23

p2

992724

24,88124

1580 ?p12 5 395p

3 < 413.6

p123960 ?

p12 5 330p < 1036.7

p12

2p24 5 p

12

360+

24 5 30+

2 5 15+

212; "3

2

"32 ; 21

22 12; 2"3

22 "32 ; 12

"22 2 "2

22 "22 ; 2 "2

212; "3

2

"32 ; 12

11p9

10p9

8p9

11p18

4p9

2p9

5p3

3p2

4p3

5p6

p6

p2

p4

a212, "3

2 ba 2 "2

2 , "22 b

a212, "3

2 ba 2 12, 2 "32 b

a12, "3

2 ba12, 2 "3

2 ba 2 "3

2 , 2 12ba 2

"32 , 12b

a"32 , 1

2ba"32 , 21

2ba"2

2 , 2 "22 b

a 2"2

2 , "22 b

a 2"2

2 , 2"2

2 ba"2

2 , "22 b

O x

y

�355°O

x

y

�145°

Ox

y

145°

Ox

y

�120°

Ox

y

120°

Ox

y

�180°



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7. ; y = 2 sin 2u

8. ; y = 3 sin u

9. ; y = 2 sin 4u

10. ; y = 2 sin 8u

11. ; y = 1.5 sin 6u

12. ; y = 2.5 sin u

13.

14.

15.

16.

17.

18.

19.

20.

O

4

5�4

3pp

u

y

52p5

O

4

2�4

p 3pp

u

y

2

O

4

3�4

p2pp

u

y

3

O

2

�2

p

u

y

23pp2

O

4

�4

2p 3pp

u

y

O

2

�2

p

u

y

23pp2

O

2

2�2

p 3pp

u

y

2

O

2

�2

2p 3pp

u

y

O

2

�2

2p 3pp

u

y

O

2

6 3�2

p

u

y

p p8

O

2

8 4�2

3pp

u

y

p8

O

2

4 2�2

3pp

u

y

p4

O

2

�2

2p 3pp

u

y

O

2

2�2

p 3pp

u

y

2



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21.

22. about -0.1 23. about 0.2 24. about 0.2 25. 0.3 26. about 0.1 27. about 0.2 28. -0.3 29. about -0.2

Guided Problem Solving 13-41. the sound wave for the note A above middle C 2. 0.001; 880π 3. the amplitude 4. the number of cycles in 0 to 2π 5. period = 6. 0.001 7. 8. 9. 880π10. Answers may vary. 11. 480; 1

Practice 13-51.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

O

2

2�2

p 3pp

u

y

2

O

2

�2

62 4

y

u

O

4

�4

62 4

y

u

O

4

2�4

p 3pp

u

y

2

O

2

�2

2p 3pp

u

y

O

4

2�4

p 3pp

u

y

2

O

2

�2

2p 3pp

u

y

O

2

�2

62 4

y

u

O

4

�4

2p 3pp

u

y

O

2

�2

2p 3pp

u

y

O

4

�4

2p 3pp

u

y

O

2

�2

62 4u

y

O

2

�2

2p 3pp

u

y

1440

2p880p

2pb

O

4

�4

2p 3pp u

y



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14.

15.

16. y = 6 cos t 17. y = -5 cos u

18. y = 4 cos 2u 19. y = 3 cos 4u 20. 2p; 1; p; 0, 2p; ,

21. p; 4; 0, p, 2p; ,

22. 2p; 5; p; 0, 2p; 23. 0.24, 1.85, 2.34, 3.95, 4.43, 6.04

24. 2.36 25. 1.00, 3.00, 5.00 26. 1.34 27. 0.84, 5.44 28. 0

29. 2.67, 5.33 30. 4.19 31. 3.14 32. y = 2p cos 2pu

33. y = cos 2u

Guided Problem Solving 13-51. 7 ft 2. 5.5 ft 3. 1.5 ft 4. 12 h 22 min 5. 742 min 6. 7. less 8. y =-0.5 9. 225.632,516.368, 967.632, 1258.368 10. 12:17 A.M.- 7:49 A.M.,12:39 P.M.- 8:11 P.M. 11. Answers may vary.12.

Practice 13-6

1. p; 2. 2p; p 3. 4p; 2p 4.

5. 2; 1, 3, 5 6. 1; 7.

8. 9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

O

4

4�4

3pp

y

2p

4

u

O

4

6�4

p

u

y

3p

O

4

1 2 3

�4

u

y

O

4

4�4

3pp

y

4u

2p

O

4

2�4

p 3pp

u

y

2

O

4

4�4

3pp u

y

2p

4

O

4

2�4

p 3pp u

y

2

O

4

2�4

p 3pp u

y

2

O

4

2�4

p 3pp

u

y

2

O

4

2�4

p 3pp

y

2

u

1; 12, 32, 52, 72, 92, 112p; p2 , 3p2

p2 ; p4 , 3p4 , 5p4 , 7p4

12, 32, 52, 72, 92, 11

2

p2 ; p4 , 3p4 , 5p4 , 7p4

p2 , 3p2

y 5 2 cos 2p720t

y 5 1.5 cos 2p742t

12

p2 , 3p2

3p2 ; p4 , 3p4 , 5p4 , 7p4

p2

3p2

p2

2p5

O

4

�4

62 4

y

u

O

4

�4

62 4

y

u



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20.

21.

22.

23.

24.

25.

26.

27.

28. 29. p 30. 2p 31. undefined 32. 1 33. -1

34. undefined

35. ; 200, undefined,-2200

36. ;-14.9,-31.1,-50.1

37. ;-50, undefined, 50

Guided Problem Solving 13-61. θ is the measure of one of the base angles of the isoscelestriangular tiles 2. 140.4 ft2

3.

4. about 1.732 in. 5. about 5.196 in.2 6. about 15.588 in.2

7. 20,217.6 in.2 8. 3891; 1297 9. 27.714; 3891; fewer.10. 3216

Practice 13-71.

O

2

2�2

p 3pp

y

2

x

30 60O

y

4

�

Xmin=0Xmax=470Xscl=50

Ymin=–300Ymax=300Yscl=100





p4

O

4

8�4

p

u

y

4p

83p

O

4

2�4

3 93

u

y

2

O

4

2�4

p 3pp

y

2u

O

4

8�4

1 u

y

41

83

O

4

6�4

p

y

3p

2p u

O

4

8�4

p

y

4p

83p u

O

4

4�4

1

y

21

43 u

O

4

1 2 3

�4

y

u



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2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16. y = sin x - 2 17. y = cos (x + p) 18. y = cos x +

19. y = sin (x - 3.2) 20. 3; 2p; none; 2 units up

21. 2; 2p; units left; none 22. 1; p; none; 1 unit up

23. 1; 2p; units right; none 24. ; 2p; none; 3 units down 12

p3

p2

p4

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

2

2�2

p 3pp

y

2

x

O

4

2�4

p 3pp

y

2

x



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25. 1; 4p; none; 2 units down

26.

27.

28.

29

30.

31.

32. -2; 2 units to the left 33. 1; 1 unit to the right 34. -1.5; 1.5 units to the left 35. 1; 1 unit to the right

36. units to the right 37. -p; p units to the left

Guided Problem Solving 13-71. cosine graph and sine graph 2. horizontal 3. units 4. right 5. positive; 6. 7. left 8. negative;- 9. 10. Answers mayvary. 11. 12.

Practice 13-81. 0.86 2. 2 3. -1.10 4. -1 5. undefined 6. -1.07 7. 0.58 8. 14.14 9. -1.00 10. undefined 11. -1.01

12. 1.41 13. ; 1.41 14. undefined 15.

16. 2 17. undefined 18. - ;-1.41 19. undefined 20. 1

21. undefined 22. ; 1.15 23. - ;-1.15 24. 2

25. 26. 27. 28. -

29.

30.

31.

32.

33.

34.

O

4

2�4

p 3pp

u

y

2

O

2

2�2

p 3pp

y

2

uu

O

2

2�2

p 3pp

y

2

u

O

2

2�2

p 3pp

y

2

u

O

2

2�2

p 3pp

y

2

u

O

2

2�2

p 3pp

y

2

u

32

107

52

32

2"33

2"33

"2

2"33 ; 1.15"2

T 5 65 sin ( p12x 1 p2) 1 6p

2

cos x 5 sin (x 1 p2)p

2

sin x 5 cos (x 2 p2)p

2

p2

p2, p2

O

4

2 4

�4

y

x

O

2

�2

42

y

x

O

2

�2

42

y

x

O

4

�4�2

2

42

y

x

O

2

�2

42

y

x

O

4

2 4

�4

y

x



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35.

36.

37.

38. 1.73 39. undefined 40. 0.36 41. -5.76 42. 1.56 43. 1.02 44. 2.75 45. -2 46a.

46b. about 14.14 ft 46c. 10 ft

Guided Problem Solving 13-81. cotangent and tangent 2.

3. Domain is all real numbers except odd multiples of ; rangeis all real numbers; asymptotes occur every π units at x = . . .- ,- , , , . . . 4. Domain is all real numbers exceptmultiples of p; range is all real numbers; asymptotes occur everyπ units at x = . . .,-π, 0, π, 2π, 3π... 5. The graphs have thesame period and range. 6. Their asymptotes are shifted by .

7. x = ; x = 8. Check students’ work. 9. x = ; x =

13A: Graphic Organizer1. Periodic Functions and Trigonometry 2. Answers mayvary. Sample: exploring periodic data, angles and the unitcircle, radian measure, sine function, cosine function, tangentfunction 3. Check students’ work.

13B: Reading Comprehension1. converting between two units of angle measure:degrees and radians 2. the meaning of a radian: 2p radians �a complete circle, or 360° 3. 30° and 60° 4. 5. 6. a

13C: Reading/Writing Math Symbols1. p 2. pi 3. S 4. sigma 5. p 6. u 7. theta

13D: Visual Vocabulary Practice1. sine function 2. secant 3. phase shift 4. cosecant 5. coterminal angles 6. cosine function 7. periodic function8. cotangent 9. unit circle

13E: Vocabulary CheckPeriodic function: Repeats a pattern of y-values at regularintervals.Cosine θ : The x-coordinate of the point at which the terminalside of the angle θ intersects the unit circle.Central angle: An angle whose vertex is at the center of acircle.Intercepted arc: The portion of a circle whose endpoints areon the sides of a central angle of the circle and whoseremaining points lie in the interior angle.Radian: The measure of a central angle of a circle thatintercepts an arc of equal length to a radius of the circle.

13F: Vocabulary Review Puzzle1. amplitude 2. clockwise 3. cosine 4. cycle 5. period6. sine 7. tangent

CLOCKWISE

TNEGNATDT

CRNRICUPI

NYDEOTWEN

EICSIYNRU

TDILZERIO

WNPOEIEOO

EMTRWSRDY

AMIEPSUEI

p2

12

5p2

p2

5p4

p4

p2

3p2

p2

p2

3p2

p2

y2

π π2πx

O

10

2�10

1 31

y

2

t

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp

u

y

2

O

2

2�2

p 3pp

u

y

2



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Chapter 14

Practice 14-11.–18. Answers will vary 19. -tan2 u 20. csc u 21. sec u22. cos u 23. 1 24. cos2 u 25. 1 26. csc u 27. sin u28. 1 29. sec2 u 30. csc u 31. 1 32. 1 33. -1 34. cos u

Guided Problem Solving 14-11. To verify an identity, you should transform one side of theequation until it is the same as the other side.

2. 3.

4. 5.

6. 7. 8. Yes, it verifies.9.

Practice 14-21. 2. 3. 4. 5. 0.85, 2.29

6. 3.99, 5.44 7. 8.

9. 10. 0.93, 5.36 11.

12. 13. 14.

15a. 15.7° 15b. 11.5° 16. 1.19 + 2pn, 4.33 + 2pn17. 0.85 + 2pn, 2.29 + 2pn 18. 1.81 + 2pn, 4.47 + 2pn19. 1.10 + 2pn, 5.18 + 2pn20. 45° + n ? 360°, 135° + n ? 360°21. 45° + n ? 360°, 225° + n ? 360°22. 45° + n ? 360°, 315° + n ? 360° 23. 90° + n ? 360°24. p 25.

Guided Problem Solving 14-21. I = the current in amps 2. t = seconds3. 4. t = 0.0028 5. 0.0028 sec

6. t =-0.0028 7. 8. Yes, check

the answers. 9. 0.0045 sec; 0.0212 sec

Practice 14-31. 2. 3. 4. 5. 6. 7. 8.

9. d = 17;&F = 28.1°;&E = 61.9°10. e = 1.7;&F = 30°;&E = 60°11. d = 2.2;&F = 26.6°;&E = 63.4°12. d = 2.2;&F = 63.4°;&E = 26.6°13. f = 500;&F = 0.1°;&E = 89.9°14. f = 19.4;&F = 67.6°;&E = 22.4°15. f = 10.4;&F = 60°;&E = 30°

16. d = 5.1;&F = 11.3°;&E = 78.7°17. 771.7 ft 18. 270.9 ft 19a. 3.8° 19b. 4.8° 19c. 2.4°

19d. 5.1° 19e. 7.2° 19f. 11.2° 20a.

20b. 20c. 20d.

20e. 20f. 21. 45° 22. 60° 23. 60°

24. 18.9° 25. 36.9° 26. 45° 27. 66.4° 28. 73.0° 29. 48.6°30. 26.6° 31. 85.2° 32. 6.0°

Guided Problem Solving 14-31. 90 ft 2. 60.5 ft 3. 4. x � 127.28 ft

5. about 67 ft 6. 6 ft 7. 8. θ � 3.4°

9. Yes, the answers are reasonable. 10. 100.6 ft

Practice 14-41. 14.9° 2. 15.9 3. 15.0 4. 43.9° 5. 136.6 6. 32.6°7. 27.8° 8. 14.8 9. 11.5 10. 38.2° 11. 12.8° 12. 90.413. 32.0° 14. 30.0 15. 69.8 in2 16. 33.3 ft2 17. 1.7 cm2

18. 164.4 in.2 19. 1025.5 ft 20. 2542.4 yd and 1866.4 yd

Guided Problem Solving 14-41. triangle with two equal sides 2. 180°

3. 4. x = 47.05; 47.05°

5. 6. c = 204; 204 ft 7. Yes, the

answers check. 8. 31.1 yd

Practice 14-51. 5.3 2. 3.1 3. 43.0° 4. 12.5 5. 21.8° 6. 35.9° 7. 18.5 8. 32.5° 9. 439.3 10. 72.5° 11. 5.8 12. 3.2 13. 14.5 14. 15.2 15. 77.9 16. 18.2° 17. 66.7° 18. 102.4° 19. 28.7°20. 73.4° 21. 70.3° 22. 28.7 mi

Guided Problem Solving 14-51. 85 mi 2. 20 mi 3. 65 mi 4. 20 mi 5. 6. d � 45.4;

about 45.4 mi 7. ; x � 14.4° or x �

180° -14.4° = 165.6° 8. Turn 14.4° left. 9. 4.4° 10. Yes,the answers are reasonable. 11. 8.7 mi

Practice 14-6

1. 2. 3. 4.

5. 6. 7. 8. 1 9.

10. 11. 12.

13.–16. Answers may vary 17. cot A 18. sin A

22 2 "3"32

"32

"32"2

2"2

2"6 2 "2

4

"6 1 "24

2"6 2 "24"32

"32

sin10°45.4 5 sinx°

65

d2 5 652 1 202 2 2(65)(20)cos10°

sin 47.05°150 5 sin 85.9°

c

x° 1 x° 1 85.9° 5 180°

tan u 5 6100

x2 5 902 1 902

"133 ; 1.2"13

3 ; 1.2

23; 0.72"13

13 ; 0.632; 1.5

3"1313 ; 0.8

45

53

54

34

43

34

35

45

160 1 0.0028 < 0.019 sec

I40; sin21 I

40 ; 160p sin21 I

40

p2 , 3p2

0, p4 , p, 5p40, p3 , 5p30, 3p4 , p, 7p4

0, p3 , 5p3 , pp2 , 3p2 , 2p3 , 4p3

0, p3 , 2p3 , p5p6 , 7p6 , 2p3 , 4p3

p3 , 4p3

5p6 , 7p6

p3 , 5p3

3p4 , 7p4

5 sin 2ua cos

2u sin

2ub 5 cos

2u

sin2ucsc2u 2 sin2u 5 sin2u(csc2u 2 1) 5 sin2u(cot2u) tan

2u 2 sin 2u sin

2u; sin2u cos 2u

sin 2u 2 sin

2u cos 2u(1 2 cos

2u)a sin 2u

cos 2ub

a sinu cos ub

2 or sin

2u cos

2u tan u 5 sin u

cos u; cotu 5 cos u sin u



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19. 20. 21. 22.

23. 24. 0 25. No solution 26.

27. 28. 29. 1 30. -1 31. 0 32.

Guided Problem Solving 14-61. 2.3.4. =

5.6.7. =

8.9. ( , )10. Yes, the coordinates are the same.11. sin 3θ

Practice 14-7

1. 2. 3. 7 4. 5. 6. 7.

8. 9. 10. 11. 12.

13.–20. Answers may vary. 21. 22. 23.

24. 25. Undefined 26. 0 27. 28.

29. 30. 31.

32. 33.

34. 35. 36. 37. 1 38. 0

Guided Problem Solving 14-71. 2. or

or 3.4. 5. 6.7. 8. Yes, the answers check.

9. ;

14A: Graphic Organizer1. Trigonometric Identities and Equations 2. Answers mayvary. Sample: trigonometric identities, solving trigonometricequations using inverses, right triangles and trigonometricratios, area and the laws of sines, the law of cosines 3. Answers may vary. Sample: physics, construction, surveying,sailing 4. Check students’ work. Chapter: TrigonometricIdentities and Equations; Trigonometric Identities: verifytrigonometric identities; Solving Trigonometric Equations

Using Inverses: evaluate inverses of trigonometric functionsand solve trigonometric equations; Right Triangles andTrigonometric Ratios: find lengths of sides, and the measuresof angles of right triangles; Area and the Law of Sines: find thearea of any triangle and use the Law of Sines; Law of Cosines:use the Law of Cosines in finding the area of a triangle; AngleIdentities: verify angle identities, and sum and differenceidentities; Double-Angle and Half-Angle Identities: verifydouble- and half-angle identities

14B: Reading Comprehension1. early history of trigonometry2. 150 A.D. 3. 1600 B.C. 4. Hipparchus, Ptolemy, Menelaus,Copernicus 5. astronomy 6. b

14C: Reading/Writing Math Symbols1. 25 2. -25 3. 4. 5. 6. x + 5

7.

14D: Visual Vocabulary Practice1. cosine 2. secant 3. cotangent 4. trigonometric identity5. Law of Sines 6. Transitive Property of Equality 7. Lawof Cosines 8. cosecant 9. sine function

14E: Vocabulary CheckTrigonometric identity: A trigonometric equation that istrue for all values except those for which an expression oneither side of the equal sign is undefined.Radian: The measure of a central angle of a circle thatintercepts an arc equal in length to a radius of the circle.Function: A relation in which each element of the domain ispaired with exactly one element of the range.Tangent function: A function that matches the measure θ ofan angle in standard position with the y-coordinate of the pointat which the line containing the terminal side of a central angleof the unit circle intersects the tangent line x = 1.Trigonometric ratios for a right triangle: The sixdifferent ratios of the sides of a right triangle.

14F: Vocabulary Review1. h, i 2. e 3. c, g 4. d, f 5. b 6. a 7. m 8. k 9. j 10. l

p6 1 2pn and 5p6 1 2pn

14

14

12

u 5 0, 2p3 , 4p32cos2u 2 cosu 2 1 5 0

u 5 p2, 3p2 , 0.384, 2.758

8sinu 2 38sinu 2 38sinucosu

2sinucosucos2u 5 1 2 2sin2ucos2u 5 2cos2u 2 1cos2u 5 cos2u 2 sin2usin2u 5 2sinucosu

#2 1 "22Å2 2 "2

2 1 "2"2

2

#2 2 "2 1 !32Å2 2 "2 1 !3

2 1 "2 1 !3

#2 1 "2 1 !32

"2 1 !32

2"3

2"3

22"312

2"3

2"3"32

2"34

3"34

525323

523"34

34

5"3434

17

5"275"27"2

10"210

5sinu 1 5"3cosu5cosu 2 5"3sinu

5sinu 1 5"3cosu

10(sinucos60° 1 cosusin60°)10sin(u 1 60°)

sin(A 1 B) 5 sinAcosB 1 cosAsinB

5cosu 2 5"3sinu

10(cosucos60° 2 sinusin60°)10cos(u 1 60°)

cos(A 1 B) 5 cosAcosB 2 sinAsinB

10sin(u 1 60°)10cos(u 1 60°)

"22

p2 , 3p2

p3, 5p3

0, 2p3 , p, 4p3p6, 7p6

0, p, 7p6 , 11p6

p4 , 5p4p

p6 , 5p6



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a2 aiotg07 ans 075-104 alg 2...chapter 1 practice 1-1 1.-4.2 2. 4 3. 4. ... 5. answers may vary....

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