algebra 2 work book answers

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.3538.

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. Mikes bus: 35 mi/h; Adams 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

56 4321 0 4321

0 5 6 7 8 9 104321

56 4321 0 4321

152

274

x 5c(a 1 b)

b 2 a

x 5 94g 2 3

w 5 S 2 h 1 h

r 5 L 2 SL

h 5 3Vpr2

Year Eligible Voters1988 180 million2012 242 million2020 263 million

32t

2 1 2t13a 119b

!4

!2!2

14

214952

59

132

12; 2

25

3 2 1

1

0 321

0.532 2

23

76

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

75All-In-One Answers Algebra 2

P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

54321 0 54321

23

223

42 0 2 4 6 161412108

54321 0 54321

20 10

16

0 20

22

3010

20 10

17

0 20

7

3010

54321 0 54321

54321 0 54321

54321 0 54321

4321 0 5 64321

54321 0 54321

4321 0 5 64321

0 5 6 7 8 9 104321

54321 0 54321

18 16 14 12 10 8 6

54321 0 54321

38

38

642 0 10 12 148642

54321 0 54321

12

212

56789 4321 0 1

56 4321 0 4321

72

272


P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

"5 x8

38

18

16

136

132 5 0.03125

144p5000 < 0.09

164 5 0.015625

516 5 0.3125

4770

1324

13

16

56

16

13

12

719

219

419

819

45

35

25

15

10 11291112

112

12

22072115

54321 0 54321

54321 0 54321

54321 0 54321

23

223

54321 0 54321

32

12

122

32

122

32


Pea

rso

n E

du

cati

on

, In

c., p

ub

lish

ing

as

Pear

son

Pre

nti

ce H

all.

All

rig

hts

res

erve

d.


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 68. 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 cm5. 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.

O

2

2

2

2x

y

O

2

4

6

42xy

O

2

4

2 4x

y

y 1 2 5 2(x 1 3)

y 2 23 5 212 ax 2 12by 2 1 5 213(x 2 0)

27213

322

12

32

25

43

103

27

10 0

1

4

9

123

1

2

3

2

3

4

5

O

2

2

2

2x

y

O

2

2

2

2x

y

O

2

6

22x

y

e22, 34, 312, 9 fO

2

6

10

2 4x

y

123; 116; 0; 21

132

12

1a


P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.


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 mi6. 417.9 gallons 7. 8a. y = 28x; 392 = 28 3 148b. 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

O

1

1 2 3

23456

x

y

O

2

4

2

2

4

2x

y

O

1

1 2 3 4 5 6 7 8 9 10

23456789

10

x

y

O

1

1 2 3 4 5 6 7 8 9 10

23456789

10

x

y

$0.056mi

5342

163

103

y 5 52xy 5 2356 xy 5

23x

y 5 37xy 513x

12; y 5

12x

35

49

916;

2716

232; 292

2 5132 513

13 2 (2

12)

223 232

a223, 13b(y2 2 y1)(x2 2 x1)a223, 13ba32, 212b

O

2

2

2

2x

y

O

2

2

2

2x

y

O

2

2

2

2x

y

O

2

2

2

2x

y

y 5 53x 243;

a2354 , 0b45;34;


Pea

rso

n E

du

cati

on

, In

c., p

ub

lish

ing

as

Pear

son

Pre

nti

ce H

all.

All

rig

hts

res

erve

d.


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.

21.

O

2

4

2 4x

y

O

2

2 2

2

x

y

O

2

2 2

2

4

x

y

O

2

2 2

2

x

y

O

2

4

x

y

2 4 6

O

2

4

2 24x

y

O

2

4

2 2x

y

O

2

2

2

4

2 x

y

O

2

4

2 4x

y

O

2

4

6

62 4x

y

O

2

4

2 24x

y

O

2

4

24

2

x

y

O

2

4

24x

y

O

2

4

2 4x

y

O

2

4

2 4x

y

y

x

40

30

20

10

200Calories

Fat (

g)

300 400 500 600 700O

O

8

8 10 12 14 16 18 20

101214161820

x

y



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

Guided Problem Solving 2-51. Graph the two equations. 2. Compare the graphs. Look forsimilarities 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 - 115. y = x + 2 + 1 16. y = -x + 217. y = -x + 2 18. y = -x - 1 - 219. y = 3x - 4 20. y = x - 221. y = 2x + 3 - 1

22.

23.

x

y

O

2

2

2

2

x

y

O

2

2

2

2

12

y 5 2 u x u 1 35

y 5 2 ` x 2 12 ` 2 32O

2

4

2 4x

y

O

2

4

2 4x

y

O

2

2

2

2x

y

O2 2

2

4

xy

O

2

4

24x

y

O

2

4

24 x

y

45

54321 1 2 3 54

321

12345

x

y

12x 1 6 5 y 1 3

12x 1 6 5 y 3,

4 4 8 12812O x

y

6

2

2

6

12x 2 6 5 2(y 2 3)

12x 2 6 5 y 2 3,2y 2 3 5 P 12x 1 6 P y 2 3 5 P

12x 2 6 P



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

24.

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

O

2

2 2

2

x

y

O

2

2

2

x

y

O

2

2 2

2

x

y

O

4

2

2 2x

y

O

2

2 2

2

x

y

O

2

2 2

2

x

y

O

2

2 2

2

x

y

O

2

2 2

2

x

y

O2 2

2

2

x

y

O2 2

2

2

x

y

O2 2

2

2

x

y

O2 2

2

2

x

y

O2 2

2

x

y

O

2

2 2

2

x

y

O

2

2

2

x

y

O

2

2

2

x

y

O

2

2

2

2x

y

O

2

2

2

2x

y

O

2

2

2

2x

y

O

2

2

2

2x

y

x

y

O

2

2

2

2



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

54

6

7

3

D

O

M

A

I

N

T R N S L A T I O N

L

O

P

E

R

E

L

T

I

O

N

F

U

C

T

I

O

NR A G E

L N E A R

410 5

x18

z7

O 4 8 12 16

4

8

12

16

x

y

O 50 100 150 200

50

100

150

200

x

y



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

O2 2

2

4

xy

6

O

2

2

2

2x

y

O

2

2 4 6x

y

O

2

2

2

2x

y

x

y

O4 6224

42

28

6

6

x

y

O4224

4

28

6

6

x

y

O424

4

42

8

6

6

O

2

2

2

2x

y

x

y

O4 62246

42

4

86

x

y

O42246

4

2

8

x

y

O42 626

46

46

2

x

y

O4 6426

46

46

2

e (x, y): y 5 2 15x 1 15 f

a5, 215b

10

5 10 15 20

20304050607080

x

y

O 2 4 6 8 1012x

y140

120

100

80

60

40

20


Algebra 2 All-In-One Answers 84

P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

1 2 3 4 5 6 7 8

2345678

x

y

O 1 3 5 j

s

5

3

1

O

2

24x

y

2

O

2

2

2

2x

y

O

2

24x

y

2

6

x

y

O42 6426

42

6

64

x

y

O42 6426

46

46

x

y

O42 6426

46

6

x

y

O42 6426

2

4

O

4

4

4

4

x

y

x

y

O4 6426

2

6

6

O

20

40

20 40 x

y

x 1 y # 30x $ 10y $ 5

O

4

4

4x

y

x 1 y $ 62x 1 5y # 20x $ 0y $ 0



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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.

(0,0) (4,0)

(3,2)

(0,5)

b

c

y

O4 6 71 3 5

21

4

6

3

5

7

x

y

(0, 5)

(1, 4)

(2, 0)

O1 2 3

2

3

x

y

(1, 0)

(0, 1)

( )3232 ,

O1 2 3 5 6 7

1

3

567

x

y

(2, 0)

(0, 2)

( )5656 ,

O1 2 3 4 6 7

1234567

x

y

(5, 0)

(0, 6)

(4, 2)

O1 2 3 4 5

123

567

x

y

(2, 3)(0, 4)

(5, 0)

O1 3 4 5 6

2

4567

x

y

(2, 2)

(2, 1)(4, 1)



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

9.

10.

11.

12.

13.

14.

15.

16.

y

z

x

5

5

5

55

y

z

x

5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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.

26.

27.

28.

29.

30.

31.

10

10

10

10 y

x

z

10

10

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

55

y

z

x

5

5

5

55



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

32.

33.

34.

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

36. x + 2y = 6, x + 3z = 6, 2y + 3z = 6;

37. x + 3y = 6, x + 2z = 6, 3y + 2z = 6;

38. 2x + 3y = 6, 2x + z = 6, 3y + z = 6;

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

y

z

x5

5

5

5

55

6

4

6

3

y

x

z

y

z

x5

5

5

5

5

y

z

x5

5

5

5

55



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

y

z

x

z

x6

6 y

3

y

z

x5

5

5

5

5

5

y

z

x5

5

5

5

5

5

y

z

x5

5

5

5

55

y

z

x5

5

5

5

5

y

z

x5

5

5

5

55



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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 3300400 150100 50

c17.6 8.3 5.4 8.7 4.0 6.6 3.59.5 5.1 4.5 6.4 2.6 5.1 2.7

d

ETDEPENDENTT

EDNEPEPPENNS

ORDEREDTEECT

EERHTCEDTHQN

IRDNFSNSRTEI

HSEPIEIHARSA

IQDNPSOSEENR

PEIENADONDHT

ANDOPALNIOES

DNCNOQEDLRCN

INELBISAEFPO

IEQUIVALENTC

12

x 1 5y 1 10z 5 96x 1 1 5 y 1 zx 1 y 1 z 5 23

x 1 y 1 z 5 223x 1 2y 1 z 5 9y 2 12z 5 10

a23, 212, 112ba21, 4, 12b



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

5. Week 1 Week 2 Week 3 Week 4Rock 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

d 34 234 21412 2

12 1

0 0.420.4 0.2

20.2 0c2 00 2

dc7 30 2

dc3 23 212 22 4

dc1620

d 0 222 1

21 0

c1 213 22

dc4 213 1

dc 4 123 7

dc6 226 0

dc240 230

35 8d

EnvelopesBoxes

Big Small

160 300 B 25 100REnvelopesBoxes

Big Small

120 270 B 60 108R

c2200 22200800 21000

d1 color3 color

Plastic Rubber 1200 3600 B1800 4800

R1 color3 color


R1 color3 color


R1 color3 color

Plastic Rubber 500 700B1300 1900

R

c 0 24 324 22 5

dc21 24

0 4d227 101 22219 93 21

28 21 20 8 1113 14

4 11

272423

22 226 524 22

8 25 263 28 124 212 218

c22 3

2 0dM 2 F 5 14 22293 26

87 68212 22

F 5 23 5893 82

0 3418 29

M 5 37 560 7687 102

6 27

z 5 72

c 5 53b 5 272

VanillaChocolateStrawberry

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

Flavor Day 1 Day 2 Day 3Vanilla 50 75 25Chocolate 175 125 150Strawberry 25 50 25

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



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

D T

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.

Practice 4-4

1. 2.

3. 4.

5. 6.

7. 8. 9.

10. 11.

12. 13.

14. 15.

16.

17.

18.

19.

Guided Problem Solving 4-4 1. 5 2. 1 3. subtract 5 from each x-coordinate4. add 1 to each y-coordinate

5. 6.

7. Yes, the graphs verify the answers.

8. c 7 2 826 28 0

d

c28 28 23 2321 23 21 23

dc25 25 25 251 1 1 1

d

c 0 2121 0

d c2 0 220 22 0

d 5 c 0 2 022 0 2

dc2 0 220 22 0

d 1 c 0 0 022 22 22

d 5 c 2 0 2222 24 22

d17 c 21 0 214 0214 27 0 7 d 5 c 3 0 22 022 21 0 1 d

O

4

4

4

4x

y

O

4

4

4

4x

y

O

4

4

4

4x

y

O

4

4

4

4

x

y

O

6

6

6

6x

y

c 4 4 2322 2 0

dc2 2 21.51 21 0

dc1 1 263 21 1

dc3 3 240 24 22

dc22 2 04 4 23

dc 2 22 024 24 3

dc2 22 04 4 23

dc 6 6 2124 28 26

dc6 6 24.53 23 0

dc5 5 226 2 4

dc44 44 23322 222 0

dSummer Winter

Cost 1,270,000 B1,010,000

R

150 130 160125 130 17560 52 80

C2 24 203

SD23 83

53 22

Tc 51 24117 55

d 8 14 14 1216 8 8 1018 18 20 14

11 1011 10

11 10c21 1 1

26 5 5d213 19 28224 42 214

25 8 23

72 2460 720 212

c4 55 4

dc71 3449 56

d 1 2 3 42 4 6 83 6 9 12



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

d22x 1 9y 2 2z 5 203x 2 y 1 2z 5 29

6x 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 13 162 13

13S

c2 212 2

dX 5 c 0840

d

a8, 43ba 317, 23317be x 1 y 5 50

425x 1 550y 5 25,000

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

9173xy

z 4 0 2112 2 0

1 21 12

c2924

dcxydc3 24

0 7d

c362dcx

ydc6 9

4 13d

23122

4253

20.4 20.4 20.10.2 0.5 0.220.1 0.2 20.1

20.6 0 20.20 20.5 020.4 0 0.2

0.65 21.45 20.220.8 1.4 0.4

0.4 20.2 20.2

29 11 191 21 225 26 210

3 21 2126 3 2

4 22 21 3 10 621 25 23

22 27 24

c5 12 22

dc1 230 1

dc 2 2721 4

dc4 71 2

dX 5 c4 251 21

dc 2 723 4

d

c34dc1

2d

2 310 225252 23

22 132 2

12

16 21618

18

c25 73 24

dc23 41 21

dc21 3

1 22dc 0 1

21 2d 12 12

21212

1 112 1



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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. a

3 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. (x) = x2 2. (x) = x2 + 4x + 8 3. (x) = -2x2 + 12 4. (x) = 2x2 - 1 5. (x) = x2 + 6x + 9 6. (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 8

4 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

29924



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

O23 2 31 1

1

32

y

x

2

y

456

O23 2 31 1

x1

32

3 31 1

y

45

1 O x

3

12

y

45

O23 2 31 1

x12

6

O

8

16

2 4x

y

(2, 16)

O

4

2

8

2 4x

y

(1, 9)

a1, 292bO2

4

2

2

1

4x

y

,( )92

O

2

2

2

4

2 x

y

(0, 3)

a212, 54b

O

2

4

12

24

2

2

,

x

y

( )54

O

2

2

2 4x

y

(2, 3)

a23, 43bO

2 23

2

2

2

,

x

y

( )43

O

2

2 24

4

xy

(1,5)

O

4

6

22 4x

y

(1 ,4)



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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

O42 28

24

2468x 1

(1, 1)x

y

O24

23

123

x 2

(2, 4)

x

y

O22

2468 4

246

x 1

(1, 3)

x

y

O11

12 3 4

123

x 1

(1, 2)

x

y

O1 21

1234

2

34x 1

(1, 1)

x

y

O3 41

1

12

2

234

x 6

(6, 6)

x

y

O2 4 6 82

2

210

468

10

x 2

(2, 3)

xy

O1 2 3 41

1

1234

5

5

y 5 2 1250x2 1 40

y 5 2 110x2 1 10

2 110

(0, 6)

x 0

x

y

O64 4 6

42

2468

(0, 3) x 0

x

y

O321 1 2 3

21

4

12

(1, 8)

x 1

x

y

O6428 2 4

642

10

2

(3, 13)

x 3x

y

O9 312 6

36

12963

(4, 16)

x 4x

yO

3 3 6 9 12 15

3

69

3

1215

(1, 7)

x 1x

y

O2648 2 4

42

42

8(3, 2)

x 3

x

y

O135 1

21

3

21

3

(4, 4)

x 4

x

y

O2 4 62 8 10

46

46

(1, 4)

x 1x

yO

2 21 41

1

345

c

p

O1 2 3 4 5 6 7 8

1000500

150020002500

y

xO8 242

46

46

4 521

y

112

x123

O

4



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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. bakerys 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 - y26. 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, 2142

14

16

12,

14

12

35, 2

35

12, 2

12

1112

122

19

254232

142

12, 2

15

2192214 , 2

354

23

122

32

2171

11

172

25

122

32

12

13

12

13

12

12,

132

12

213152

142

52

32

216

72

233

y 5 2ax 1 32b2 1 112y 5 ax 1 72b2 2 454

y 5 23ax 1 16b2 2 9512y 5 ax 1 52b2 2 254

x 1

(1, 2)

x

y

O12 1 2 3 4

123

23

x 1

(1, 5)

xy

O2468 2

2

810

2

x 2

(2, 0) x

y

O1 1 2 3 4 5

1

1234

x 3(3, 3)

x

y

O3 1 15

1234

12



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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. 516. 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 + 24i37. 13 38. 8 39. -9 + 7i 40. -1 + 6i 41.42. 43. 44. 2 + 4i 45. 15 - 8i46. 18 - 26i 47. 22 - 4i 48. 2 - 16i 49. 265 50. -2 + 8i 51. -5 + 16i 52. 169 53. 11 - 2i54. 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 - 9i24. 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 "292272 4

"5322

32 4

"4122

32 4

i"152

232 4"13

22 4 "53 1 5"15343

12 4

"1722

12 4

"216

25421 4"14

252

272 4"13

2232 4

"172

76 4

"1456

256 4"37

6254 4

i"154

212 4"11

2214 4

i"114

32 4

"192

54 4

"6541 4

i"62

238 4"41

8272 4

3"522

32 4

"172

1 4 i"232 4 "37272 4 "972214 4

"542

32 4

i"3222 4

"1062

232 4"23

212

1 4 "10245 4 i"1451 4 "3212 4 "5222 4 "312 4 "21226 4 4"2

a232, 234by 5 3ax 1 32b2 2 34a52, 32by 5 22ax 2 52b2 1 32

a252, 25by 5 ax 1 52b2 2 5

a12, 214by 5 23ax 2 12b2 2 14a223, 13by 5 23ax 1 23b2 1 13

a212, 0by 5 4ax 1 12b24414

94

494

4i"10 4i"5412i46i"242i"342i"544i"5

2i"2 23i"72i"115i"310i"3 4i"3

2i"22 2"10"103"5"173"2"5"13"29 "5"2

94, 2

94



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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 "212252

12, 2

432

14

25 4 3"510

6 4 "157

3 4 "3 5 4 i"7183 4 i"18341 4 i"21 4 i"34521 4 "6110

21 4 i"5910

21 4 2i5

3 4 i"474

22 4 i"113

5 4 i"1196

34

29 4 "1332

23 4 "32

23 4 2i"3323 4 "13

12

3 4 "172

21 4 i"798

21 4 i"232

54

32,

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



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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.

5F: Vocabulary Review Puzzle

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

12pr

2 1 48r

V 5 23pr3 1 10pr2

V 5 23pr34

3pr3V 5 10pr2

pr2h

213z5 1 1

12x

4 1 x 2 54s2 1 23

1V E

2R T E X

R4

T

S

B N O M I A L5P

6F

N

A C T R D

R M A

A R

DB

O

L

I

N

O

I

A

L

A

3

f(x) 5 ax2 1 bx 1 c,

1 23 45 6

c1 2 34 5 6

dO

2

2

2

2x

y (2, 3)

(3, 2)



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.


Algebra 2 All-In-One Answers 102

P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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 ft35. 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. -35. 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, 210. (x + 1)(x - 1)(x2 - 11); -1, 1,11. (x2 - 2)(x2 - 8);12. (x + 2)2(x - 2)2;-2, 213. (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"32"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, "22"2, "2, 2"8, "82"11, "11

23 4 3i"32

21 4 i"38

14

1 4 i"362

13

21 4 i"325 4 5i"3

2

3 4 3i"32

2 4 2i"323 4 3i"3

432

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

4 4 x

y

(5, 0) (2, 0)(0, 0)

O2 2

2

4

6

xy(2, 0) (3, 0)

O

2

2

2

2x

y

(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, 2i28. -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 "7381834

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

122

15

212, 0, 132

13, 0,

12

x4 1 10x2 1 9 5 0

15; 1

15

112

16

14

43

23

13

122

12

12

162

16

136

118

112

49

29

19

16

14

43

23

13

12

23, 2

14

234"132

3, 12, 21221 4 i"191 4 2i

2 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



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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 3 3V4p ; r 5 "3 6p2V2p3"3

a"3 12y

22x

25y23k

"3 4x"25uv2"4 u5r"3r6xy"3 x 4st3"4 s3xy5"z22a4"3 23k3"25z"3 y2z6x"x3x2"2

"3 6abc22bc

"2xy4y

"4 54x33x

"3 9x2y23y

"3y3

3"2x227"2y

"3 6x2"y"6

10 5 1.35"L8 5 1.35"L K 5 1.35"L247,

47

4x37

103

18

5b1g45b4g110b3g25C3 5 10b

3g2



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

Practice 7-31. -63 2. -6 3. 73 4. 11 5. 5 + 26. 3 - 7 7. 11 8. -2 - 9. 10 - 5

10. - 11. 12. 22 13. 4

14. 0 15. 13 16. -3 - 17. -38 + 718. 67 - 15 19. 28 - 16 20. 9 + 221. 30 + 12 22. 12 23. 1824. 41 - 3 25. 6 + 4 26. 10527. 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. (x) = 1.8x 1b. g(x) = 0.75x 1c. g(f(150)) = $202.501d. No; it doesnt 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. (x) = 0.75x 23b. g(x) = x - 5 23c. g((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 646 2

2

246

46

x

y

O 2 4 64

246

75

23x 1 25

245165

175

23a 1 25

14

2x2 1 34x 2 1

4x 2 12x2 1 3

#2A"33

2A"39

2A3"3s"32

RA 5 (2.7)

T

8033

(5ab)34n

45

(26)12b

342

13y

23(5y)

12m

13x

32

1"5 a81"7 t2"5 m12"4 ab"3 z2"5 b"a3"3 2y"3 x4

3x2y12x

13201

98a341

x2

21

y3140

b3

a41y6

9ab23

3

y16

x76

94

12y

32x

56

2243 1 525

21 1 52

1 2 521 1 51 1 52

270,000 1 90,000"32

(900 1 300"3 1 300"6)x 1 2"3 x2

x"2"5 2 2"23"5y"5 "x"

3 9"3 3"6"3 "10"7"6"14"3"7 "10"5"

4 3

"2"222 1 14"3133 1 "52"3"3"3 xy"3 x"7 "3"2"3



P

ears

on

Ed

uca

tio

n, I

nc.

, pu

blis

hin

g a

s Pe

arso

n P

ren

tice

Hal

l.A

ll ri

gh

ts r

eser

ved

.

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 62

246

246

8 10x

y

O2 4 6426

246

246

r 5 SP 2 1v264

v22g

f21(x) 5x 2 635,600

198,900212

O

2

2

2

2x

y

x 3 1 0 2

y 0 1

algebra 2 work book answers

Documents

answers mayvary

anirrational number

anatural number

aneven number

number of years

number of eligible voters

identity prop

p1 rt p answers