Alg 2 Practice Answers

Practice Workbook Answer Key

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Practice — Chapter 1Lesson 1.1

1. yes 2. yes 3. no 4. yes 5. no6. yes 7. yes 8. no 9. yes 10. no

11. no 12. yes13.

14.

15.

16. (6, 19) 17. (4, 20) 18. not linear19. (�4, 23) 20. (8, �29) 21. (5, �14)

Lesson 1.21. 2.3. 4.5. 6. 7.8. 9. 1 10. 3

11. 12.13. 14.15. 16.

Lesson 1.31. 2.3. 4.5. 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. y� �

14x�154

y� �13xy�

43x�83

y� �43x� 2y� x� 2

y� �14x�

72y� �12x� 4

y�12x� 10y� �

13x� 2y� �2x� 8y� �3x� 3

y�12x� 3y� 3x� 4

y� �12x� 1y� 4x� 16

y� �3x� 5y� 2x� 15y�

34x� 5y� �4x� 5y� �3x� 7y� �

14x� 8y� �2x� 1y� 4x� 13

y�34x� 5y� �

12x� 1y� xy�

45x�1110y� �9x� 13

y� �12x� 1y� �

15x�85

y� �x� 2y� x� 2

y� �34x� 3y�

56x� 3m� �3, b� �7m� �2, b� �4

m� �38 , b� �

32m� �34 , b�

3257100

�23y�

14x� 4y�16x� 3

y�45x�

25y� �4x� 3y� 3x� 1y� 2x� 5

x

y

22468

4 6 8

22468

4 6 8 x

y

x

y

22468

4 6 8O

Algebra 2 1

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Lesson 1.41. 2.3. 4.5. 6.7. 8.9. 10. 11.

12. 13. 14.15. 16. 17. yes;18. no; there is no constant, k, such that19. yes;Lesson 1.5

1. ; positive

2. ; negative

3. ; negative

4. 5. 6. 0.360Lesson 1.6

1. 2. 3. 4.5. 6. 7.8. 9. 10.

11. 12. 13.14. 15. 16.17. 18. 19.20. 21. 22.23. 24. 25.26. 27.28.

Lesson 1.71. 2. 3.4.

5.x0 1 2 3–1–2–3

x � 1–2 –1 0 1–3–4–5 x

x � �4x � 2x � 2x � �3

h �Aa � b

a �T0 � Tz � z0qp �

qD � QP1 �

V2P2V1r �C2π

W �VLD

x �12x � �

67x � �6x � �4x � �

522x � 18x � �

65x � �13x � 7

x � �13x � �21x � 16

x � 2x �12x � �3

x � �2x �78x � 8

x � 6x � 9x � 5x � 2

r � 0.96y � 0.01x � 0.24

x

y

42 6 8 1010

–10–20–30–40

(1, –2)O(2, –18) (7, –26)

(9, –34)

y � �3.26x � 4.5

x

y

2 4 6 8 1010

–10–20–30

(2, 10)O

(8, –27.45)(6, –20.15)

(0, 1.9)

y � �4.44x � 8.85x

y

10O

91827

20(0, 4)

(2, 10)

(6, 22)(8, 28)

y � 3x � 4

y � 2xy � kx

y � 3xz �13x � �1

y � �54z �

52x � 10y �

92x � 4x � 3k � �3; y � �3xk � 2; y � 2xk �

56 ; y �56xk �

27 ; y �27x

k �14 ; y �

14xk � �43 ; y � �

43xk �

73 ; y �73xk � �5; y � �5x

2 Algebra 2

AnswersCopyright © by Holt, Rinehart and Winston. All rights reserved.

6. no solution7.

8.

9.

Lesson 1.81. x � 2 and x � �8

2. x � 10 and x � �2

3. x � �6 and x � 1

4. and x � �3

5. and x � 2

6. x � 1 and

7. and

8. and

9. or

10. or


1. rational, real2. irrational, real3. irrational, real4. rational, real5. integer, rational, real6. rational, real7. Inverse Property of Addition8. Identity Property of Multiplication9. Associative Property of Addition

10. Inverse Property of Multiplication11. Commutative Property of Multiplication12. Distributive Property13. Identity Property of Addition14. �33 15. 4 16. 43 17. 43 18. 4919. 28 20. 26 21. 7.2 22. 56 23. 90

6 x0 2 4–2–4–6x � 5x � �2.5

6 x0 2 4–2–4–8 –6x � 3x � � 7

x2 310x �

15x �115

x0 1 2 3–1–2–3x �

16x �76

x2 4 6 80–2–4x � �

95

x0 2–10 –8 –6 –4 –2x � �10

x–2 0 2 4–4–6–8x �

95x–2 0 2 4–4–6–8

x4 6 8 1020–2

x–2 0 2 4–4–6–8

x190180170160150 200162 � t � 192

x0 2 4 6–2–4–6x � 5

x–1 0 1 2–2–3–4x � �2

Algebra 2 3

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Lesson 2.21. 1 2. 3. 36 4. 1 5. �2176. 7. 25 8. 32 9. 2 10. 16

11. 32 12. 9 13. 14. w4y2z2 15.16. x14 17. z17 18. 19. y5z 20. 121. 81x12y20 22. 16a12b4c24 23. 125a6b924. 25. 26. 27. 16m12p428. 29. 30. 81x26y2

Lesson 2.31. yes 2. yes 3. no 4. yes 5. yes6. no 7. yes 8. no9. domain: ; range: {�3, 1, 3, 7}

10. domain: x � �5; range: y � �211. domain: {�4.5, 3, 6.5, 12};range: {6, �1.5, �5, �10.5}12. domain: {�2, 0, 1, 5}; range: {12, 8, 9, 33}13.14.15.16.17.

Lesson 2.41. ( f � g)(x) � 8x2 � 5x � 13;( f � g)(x) � 6x2 � 5x � 132. ( f � g)(x) � 13x2 � 5x � 41;( f � g)(x) � �13x2 � 5x � 413. ( f � g)(x) � x2 � x � 2;

( f � g)(x) � x2 � x � 16

4. ( f � g)(x) � 3x2 � 6;( f � g)(x) � �21x2 � 65. ( f � g)(x) � 175x � 25;

(x) � 7x � 16. ( f � g)(x) � 3x3 � 17x2 � 75x � 425;

(x) � , x � �57. ( f � g)(x) � x4 � 256;

(x) � , x � �4 and x � 48. ( f � g)(x) � �x � 8 9. ( f � g)(x) � �3x � 12

10. (g � f )(x) � 3x � 1211. ( f � g)(x) � �2x2 � 22x � 2012. (x) �

13. (x) �

14.15.16.17. �44 18. �52 19. �10 20. �521. �5 22. 22 23. �55 24. �28 25. 44Lesson 2.5

1. {(�16, �1), (�6, 0), (14, 2)}; yes; yes2. {(2, 7), (3, 6), (4, 7), (5, 6)}; no; yes3. {(16, �2), (1, �1), (1, 1), (16, 2)}; yes; no4. {(7, �5), (7, �3), (7, �1), (7, 1)}; yes; no5. {(4, �5), (9, �3), (12, 1), (13, 7)}; yes; yes6. f �1(x) � 3x � 17. h�1(x) �

3x � 12

( f � g)(x) � �x2 � 1; (g � f )(x) � �x2 � 1( f � g)(x) � 4x2 � 4; (g � f )(x) � 16x2 � 1( f � g)(x) � x ; (g � f )(x) � x

�x � 102x � 2 , x � �1(gf ) �2x � 2x � 10 , x � �10( fg)

x2 � 16x2 � 16( fg)23x 2 � 253x � 17( fg)

( fg)

223203

f(0.5) � 1.25; f(0) � 0f(11) � 361; f(�4) � 46f(7) � �9; f(�5) � 27f(�3) � 45; f(5) � 125f(�2) � �44; f(8) � 156

��1, 0, 12 , 32�

1xy61xy3z4

w18k3a4b6x4w2z8

1x 35

1k81d925

�115

4 Algebra 2


8.9. f �1(x) � 2x � 2.5

10.11. h�1(x) � 4x � 3212.

not a function13.

function14.

function

Lesson 2.61.

2.

3.

4. ifif5. f(x) � x � 3 if x � �3, f(x) � 0 if

�3 � x � 0, f(x) � x if x � 06. f(x) � x � 2 if x � 0, f(x) � 0 if x � 0,f(x) � x � 2 if x � 0

7. �10 8. 32 9. 13.13 10. 0 11. 712. �7.5 13. 1.5 14. 1 15. �19 16. �7

x � 2f(x) � 1�4 � x � 2, f(x) �12xf(x) � �2 if x � �4,

xO

y

2–2–4 42

–2–4

4

xO

y

–2–4 422

–2–4

4

xO

y

2–2–4 42

–2–4

4

xO

y

1–2 24

–4–8

8

xO

y

1–1–2 24

–4–8

8

xO

y

2–2–4 448

1216

g�1(x) �x8 � 2

g�1(x) �x � 411

Algebra 2 5

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Lesson 2.71. a horizontal translation 7.5 units to the left2. a vertical translation 7.5 units up3. a horizontal compression by a factor of 524. a vertical stretch by a factor of 2 and areflection across the x-axis5. a vertical stretch by a factor of 14 and avertical translation 6 units up6. a vertical stretch by a factor of 12 and ahorizontal translation 7 units to the right7. a translation 21 units to the left8. a vertical stretch by a factor of 179. a horizontal stretch by a factor of 2

10. a vertical translation 13.7 units up11. a vertical stretch by a factor of 3 and areflection across the x-axis12. a vertical stretch by a factor of 41 and ahorizontal translation 8 units to the right13. 14.15. 16.17. 18.


1. independent; (0, 4)2. dependent; infinitely many solutions3. independent; (�1, �1)4. inconsistent; no solution5. independent; (1, 3)

6. independent; (1, 6)7. (6, �1) 8. (12, 1) 9.

10. (�4, 8) 11. (�8, 5) 12.

Lesson 3.21. (2, �1) 2. no solution 3. (6, 2)4. (3, 0) 5. (4, �3) 6. no solution7. (�9, �4) 8. infinitely many solutions9. (8, 8) 10. (�4, 1) 11. (2, �1)

12. (�3, 3) 13. (1, �2) 14. (5, �8)15. 16. (1, 7) 17.18. infinitely many solutions19. 20. (3, 10) 21. no solution22. 23. 24. (11, �3)Lesson 3.3

1.

2.

224

–4–2 4–4 –2 x

y

2O24

–4–2 4–4 –2 x

y

(23 , 2)(14 , 1)(13 , 23 )(12 , 3)(12 , 12 )

(3, 12 )(12 , 4)

g(x) � x3 � 33g(x) � �23x � 9

g(x) � �x12�g(x) � (26x)4

g(x) � (x � 7)5g(x) � �x 3

6 Algebra 2


3.

4.

5.

6.

7a. 8x � 12y � 400b.

c. 50 hours; 33 hoursLesson 3.4

1.

2.

224

–44–4 –2 x

y

224

–4–2 4–4 –2 O x

y

13302010

2432

816

40O x

y

224

–4–2 4–4 –2 O x

y

2O24

–4–2 4–4 –2 x

y

2O24

–44–4 –2 x

y

2O24

–4–2 4–4 –2 x

y

Algebra 2 7

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3.

4.

5.

6.

7.

Lesson 3.51.

2.

3.

4. maximum: 41; minimum: 45. maximum: 17; minimum: �126. maximum: 12; minimum: �77. maximum � 50 8. maximum � 68minimum � 0 minimum � 09. maximum � 200 10. maximum � 62minimum � 20 minimum � �25

22468

4 6 8O x

y2

2468

4 6 8O x

y2

2468

4 6 8O x

y

xO

y

1530

15 30

� x � y � 306x � 7y � 126

� y � 1y �12 � 2

y � �x � 5

� x � 4y � � xy �

12x � 3

� y � 4y � 2x � 4y � �2x � 4

224

–24–4 –2 O x

y

8 Algebra 2


Lesson 3.61.

2.

3.

4.5.6.7.8.9.

10a.b.

11a. 25 secondsb. 3750 feet


1. 2 � 2 2. 2 � 2 3. 3 � 3 4. 3 � 35.

6. not possible; the matrices do not havethe same dimensions.7.

8.

9.

10.

11. ��60

�126

�248

�4�4 �

� 762057

�2014

�8 ��7

�4 �43 �� 74 4

�3 �� 0

�3 �612 �

��2�3�7

�4�30

�2�65 �

xO

y

100200300400

2000 4000

� x(t) � 150ty(t) � 12t

y �x29 � 1

y �13x � 2

y � �12x � 16

y � �12x � 8

y � 6x � 2y �

12x � 14

xO

y

2

–2–4

46

2–2–4–6

xO

y

2

–2–4

4

2 4 6 8

xO

y

2

–2–4–6

4

42–2–4

Algebra 2 9

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12.

13.14. 3 � 3 15. 101 medals16. 90 gold medals17. the number of bronze medals, 27, won byGermany18. Gold Silver Bronze

Lesson 4.21.2.3. does not exist4.

5.

6.

7.

8. does not exist

9.10. X�(�3, 0), Y�(6, 6), Z�(3, �6)11.

12. an enlargement by a factor ofLesson 4.3

1. yes 2. yes 3. no 4. yes5. yes 6. yes7.

8.

9.

10.11. D � 0; no inverse12.

13.

14.15. no inverse

��3.52.5 3�2 �

��13 1�2 �

D� 4; inverse: � 1�4 �0.753.25 �

D� 2; inverse: � 2�3.5 �35.5 �

D� 5; inverse: � 1�1.4 �11.6 �

D� 1; inverse: � 4�5 �79 �

D� 1; inverse: � 3�4 �57 �

32Z'

Y'

X' x

y

2–4–6 62

–4–6

46

Z

XY

�1134 32�8 �

�23

�50 �

32�12.518

1343 ��1026

�10�2�6

513 ��47 �64 �

[�20 4]��1

�9 4544 �

�44202616

32182122

25271612 �United StatesGermanyRussiaChina

� 143 �214 ��

�131722

64�7 �

10 Algebra 2


16.17. no inverse18.

Lesson 4.41.

2.

3.

4.

5.

6.

7.

8.

9.

10. ; (4, �2, �1)

11. (3, 9, �6)

12. no solution

13. (�3, 5, �4)

14. (�1, 10, 2)

Lesson 4.51.

2.

3.

4.

5.

6.

7. � 100010

001M

M

M

2�14 �

�100

010001

M

M

M

132 ��

100010

001M

M

M

�21�1 �

�100

010001

M

M

M

1�2�1 �

�126

137133

M

M

M

�148 ��

257168

�31�3

M

M

M

462 ��

471591

121M

M

M

272 �

�8512

121�1�95 ��

xyz �� 0

�38 �;�

1235743

12�3 ��

xyz �� 5312 �;

�135

�21�10

1�25 ��

xyz �� 15821 �;

�133

�21�2

�31�4 ��

xyz �� 31215 �;

� 357�365

5�20 ��

xyz �� 131018 �

�480

1�45

1�79 ��

xyz �� 123 �; (0.5, �3, 2)

� 35 �7�8 �� xy �� 2527 �; (�1, �4)

� 74 53 �� xy �� 149 �; (�3, 7)� 84 7

�9 �� xy �� 565 �; (5, �5)� 3x � 2y � z � �62x � 3y � z � 14x � 4y � 3z � 20

� 2x � 3y � z � 13x � 4y � z � 6�x � y � 2z � 7

� 934�51�3

1�1�2 ��

xyz �� 62�1 �

� 5�14

�24�8

1�13 ��

xyz �� 13�16 �

�3

�121

�12�131 ��

xyz �� 1921�7 �

�42 53 �

��12 3�5 �

Algebra 2 11

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8.

9.

10. (�3, 8) 11. (7, �1) 12. (�5, 4)13. (1, �4, 6) 14. (�3, 2, 5) 15. (2, �4, 6)16. (3, 4, �1) 17. (4, �1, 2) 18. (1, 4, 2)Practice — Chapter 5Lesson 5.1

1. ; a � 1, b � �8, c � 152. ; a � 1, b � �16,c � 633. ; a � �3,b � 30, c � 334. ; a � 6, b � 13,c � �55. ; a � 1, b � �6, c � 56. yes 7. no 8. no 9. no

10. yes 11. yes12. up; minimum value13. up; minimum value14. up; minimum value15. down; maximum value

16.

(0, �3)17.

(�0.5, 6.25)18.

(�1.75, 5.0625)Lesson 5.2

1. �10 or 102.3. �12 or 64. �2�5 � �4.47 or 2�5 � 4.47

��3 � �1.73 or �3 � 1.73

xO

y

2–2–6 42

–2–4

6

xO

y

–2–4 42

–2

4

x

y

2–2–4 4246

d(x) � x2 � 6x � 5h(x) � 6x2 � 13x � 5k(x) � �3x2 � 30x � 33g(x) � x2 � 16x � 63f(x) � x2 � 8x � 15

�100

010001

M

M

M

05�4 �

�100

010001

M

M

M

3�21 �

12 Algebra 2


5. �4 or 46. or7. or8. or9. or

10. or11. c � 9.4 12. j � 5.8 13. r � 5.014. c � 16.6 15. b � 6.9 16. a � 2.417. c � 11.5Lesson 5.3

1. 12(x � 5) 2. �4x(6 � x)3. (2 � 7x)(1 � 3x) 4. (4x � 3)(x � 12)5. 3x(x � 7) 6. �3x(x � 35)7. (x � 4)(x � 13) 8. (x � 5)(x � 4)9. (x � 9)(x � 2) 10. (x � 4)(x � 7)

11. (x � 10)(x � 9) 12. (x � 13)(x � 2)13. (2x � 1)2 14. (3x � 1)(x � 2)15. (2x � 1)(x � 2) 16. �16 or 1617. �5 or 5 18. �7 or �219. x � 1 20. 1.5 21.22. 23. 24.25. �3, 4 26. �2.5, 1 27. �15, 328. 6, 7 29. �2, 0.5 30. �1.5Lesson 5.4

1. x2 � 24x � 144; (x � 12)22. x2 � 40x � 400; (x � 20)23. x2 � 20x � 100; (x � 10)24. x2 � 5x � 6.25; (x � 2.5)2

5. x2 � 9x � 20.25; (x � 4.5)26. x2 � 19x � 90.25; (x � 9.5)27. �1.8 or 3.8 8. 2.3 or 5.79. �0.1 or 14.1 10. �20.1 or 0.1

11. 0.2 or 4.8 12. �0.6 or 6.613. �2.1 or 3.1 14. �6.7 or �0.315. �8.2 or 0.216.17. f(x) � �3x2 � 7; (0, 7); x � 018. f(x) � (x � 6)2 � 39; (6, �39); x � 619. f(x) � (x � 1)2 � 11; (1, �11); x � 120. f(x) � (x � 5)2 � 35; (5, �35); x � 521. f(x) � 3(x � 2.5)2 � 20.75;(�2.5, �20.75); x � �2.5Lesson 5.5

1. 0.3 or 9.7 2. 0.3 or 3.73. �3.3 or 3.3 4. �5.7 or 2.75. �5.6 or 1.6 6. �6.9 or 1.97. �2.9 or 2.4 8. 1.4 or 5.69. �1.1 or 4.1 10. �0.9 or 2.2

11. �2.2 or 3.7 12. �0.6 or 0.413. x � �1; (�1, �5)14. x � 1.5; (1.5, 11.75)15. x � 1; (1, �1)16. x � ;17. x � 1; (1, �3)18. x � ; (�

25 , �145 )�25

(�23 , �1013 )�

23

f(x) � �12x2; (0, 0); x � 0

�27 or 11 or 15�

23 or 23�

13 or 12

�1 � �23 � 3.80�1 � �23 � �5.803�2 � 4.24�3�2 � �4.242 � �5 � 4.242 � �5 � �0.24�6.5 � 2.55��6.5 � �2.55

2�33 � 1.15�2�33 � �1.15

Algebra 2 13

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Lesson 5.61. 1; two; x � 1.5 or x � 12. �27; none; x � or

3. �68; none; or

4. �63; none; or

5. �87; none; or

6. �96; none; or

7. �2 � 11i 8. 7 � 10i 9. 13 � 9i10. �1 � 3i 11. �15 � 5i 12. 5i13. �4 � i 14. 4 � 5i 15. �8 � 7i16. �15i 17. 27 � 4i 18. �12 � 19i19. �4 � 28i 20. 21. 3022. 4 � 2i 23. �21 � 20i 24. 18 � 6i25. �4 � 5i 26. �iLesson 5.7

1.2.3.4.5.6.7.

8.9.

10.11.12.13.14. 9.25 feet 15. about 0.6 second16. 3 feet 17. about 1.4 secondsLesson 5.8

1.

2.

3.

4. no solution5.

6.

7.

xO

y

2–2–4 42

–2

46

–5 –4 –3 –2 –1 0 1 2�3.79 � x � 0.79

–2 –1 210 3 4 5x � �0.30 or x � 3.30

–6–8 –4 –2 0 2 4�5 � x � �2

–6 –4 –2 0 2 4 6�4 � x � 2

–6 –4 –2 0 2 4 6x � �4 or x � 4

f(x) � �16x2 � 20x � 3f(x) � 5x2 � x � 7f(x) � x2 �

12x � 3f(x) � x2 � 9x � 2f(x) �

32x2 � x � 4f(x) � 2x2 � 4x � 5

f(x) � �3x2 � 3x � 2f(x) � �2x2 � 7x � 3f(x) � 6x2 � 3x � 1f(x) � 5x2 � 2x � 3f(x) � 0.5x2 � x � 3f(x) � 3x2 � 2x � 5f(x) � �4x2 � 3x � 2

1213 �5i13

x �12 �

i�62x �

12 �i�62

x �14 �

i�8712x �

14 �i�8712

x �18 �

3i�78x �

18 �3i�78

x �13 �

i�173x �

13 �i�173

x � �32 �

3i�32�

32 �3i�32

14 Algebra 2


8.

9.

10.

11.

12.


1. 1.01 2. 0.9 3. 0.93 4. 1.12 5. 1.16. 0.97 7. 0.948 8. 1.075 9. 1.004

10. 0.941 11. 1.414 12. 15.874 13. 0.01614. 28 15. 35.318 16. 226.274 17. 1.87518. 8.25 19. 630.346 20. 271.529

21a. 1,275,868b. 1,307,375

22a. 6400b. 25,600

Lesson 6.21. quadratic 2. linear 3. linear4. exponential 5. quadratic6. exponential 7. linear8. exponential 9. exponential

10. exponential growth11. exponential decay12. exponential decay13. exponential growth14. exponential growth15. exponential decay

x

y

42–2–4

42

6

–2

xO

y

642–2–2

24

–4–6

xy

642–2

–6–8

x

y

2 4 6–22

–4–6

xO

y

2–62

–2

Algebra 2 15

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16. exponential decay17. exponential growth18. exponential growth19. $2117.56 20. $1075.52 21. $977.0622. $1226.08 23. $343.10 24. $1294.2225. $5325.11 26. $2358.76Lesson 6.3

1. log19 361 � 22. log20 8000 � 33. log3375 15 �

4.5.6.7. 122 � 144 8. 56 � 15,6259. 213 � 9261 10.

11.12.13. x � 1.54 14. x � 1.96 15. x � �0.7016. x � 0.26 17. x � �1.10 18. x � 3.0219. v � 3 20. v � 2 21. v � 222. v � 256 23. 24.25. v � 10 26. v � 3 27. v � 4Lesson 6.4

1. log10 4 � log10 100 � log10 4 � 22. log5 72 � log5 25 � log5 72 � 23. log7 5 � log7 3 � log7 44. log3 15 � log3 q

5. log8 64 � log8 4 � 2 � log8 46. log9 3 � log9 a � log9 7 �0.5 � log9 a � log9 77. log3 308. log59. log8 64 � 2

10. log911. log12 144 � 212. log3 13513. logb14. logb � logb15. logb � logb16. 12 17. 73 18. 2.5 19. 4.7 20. �121. 10 22. 2 23. 2 24. 25. �3, 326. �1, 6 27. 3 28. 4 29. 2Lesson 6.5

1. x � 1.72 2. x � 0.95 3. x � 6.644. x � 1.19 5. x � 2.81 6. x � �0.487. x � 1.05 8. x � �0.11 9. x � 1.46

10. x � 1.16 11. x � 1.43 12. x � 0.9013. x � 4.09 14. x � 1.33 15. x � 0.4216. x � 1.76 17. x � 2.18 18. x � 3.7019. x � �0.57 20. x � 3.19 21. x � 0.4022. x � 1.16 23. x � 3.09 24. x � 1.3025. x � �0.46 26. x � �0.55 27. x � 1.4328. x � 7.32 29. x � 3.42 30. x � �0.65

43

z2y4z3y4z

x24x34x2mx

5y4

x2

v �1343v �

1625

(15 )�4� 625

11�4 �114,641

360012 � 60log11 11331 � �3log37

27343 � 3log34

64 � �313

16 Algebra 2


Lesson 6.61. 2980.958 2. 12.182 3. 181.2724. 109.196 5. 3.555 6. 2.5347. not defined 8. 1.242 9. 4.718

10. ln 55 � x 11. e3.78� 44

12. ln 0.05 � �3 13. e2.30� 10

14. ln 54.6 � 4 15. e4.83� 125

16. ln 148 � 5 17. e0 � 118. ln 0.45 � �0.8 19. x � 1.2320. x � 1.10 21. x � 2.17 22. x � �8.6723. x � 10.48 24. x � �0.7525. x � �1.17 26. x � �1.3427. x � 0.78 28. $1215.31Lesson 6.7

1. x � 4 2. 3. x � 24. x � 1000 5.6.7.8. x � 59. x � log 28 � 1.45

10. x � 4 11. x � 4 12. x � 613. x � 3 14. 15.16. x � 3 ln 0.64 � �1.34 17. 5.0 � 1021 ergs18. 7.2


1. yes; quintic trinomial2. yes; quadratic trinomial3. no 4. yes; cubic polynomial5. no 6. no 7. �36 8. �29. 61 10. 410 11. 80 12. �152

13. 8x4 � 11x3 � 5x214. 22x5 � 13x4 � 3x2 � x � 815. �x4 � 5x3 � 10x2 � 1.2x � 216. 5.1x3 � 12.2x2 � 7x � 2617.

upside-down W-shape18.

W-shape

x

y

2–4 –2 42

xO

y

2–2–4 424

–4–2

6

x �e32 � 10.0x �

43

x �13 ln 15 � 0.90

x �ln 6ln 9 � 0.82

x �12

x �23 � 0.67

Algebra 2 17

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19.

S-shapeLesson 7.2

1. local minimum at (�1.5, 1.75)2. local maximum at (0.2, 6)3. local maximum at (0, 1); local minimumat (0.7, 0.7)4. local maximum at (�0.2, 2.2); localminima at (�1.7, 2.7) and (1.3, �2.3)5. local maximum at (0, 2); local minimumat (0.5, 1.8); increasing for �6 � x � 0and 0.5 � x � 6; decreasing for 0 � x �0.56. local maximum at (�0.7, 0.4); localminima at (�2.3, �1.5) and (0.5, �0.4);increasing for �2.3 � x � �0.7 and 0.5 � x � 4; decreasing for

�4 � x � �2.3 and �0.7 � x � 0.57. local maximum at (�0.8, �1.7); localminimum at (0, �2); increasing for

�5 � x � �0.8 and 0 � x � 4;decreasing for �0.8 � x � 08. local maxima at (0, 1) and (1.6, 2.1); localminimum at (0.3, 1.0); increasing for

�4 � x � 0 and 0.3 � x � 1.6; decreasing for 0 � x � 0.3 and 1.6 � x � 49. rises on the left, falls on the right

10. falls on the left, rises on the right11. falls on the left and on the right12. rises on the left and on the right13. f(x) � �4.17x4 � 30.83x3 � 473.42x2 �1019.27x � 6039.64Lesson 7.3

1. 8x5 � 5x4 � 3x22. 2x2 � 17x � 303. 5x3 � 17x2 � 5x � 284. x3 � 7x2 � 10x � 165. 2x3 � x2 � 8x � 56. 27x3 � 27x2 � 9x � 17. no 8. yes 9. no 10. yes

11. yes 12. no13. 2x � 514. 2x � 1 �

15. 4x2 � 4x � 1 �

16. 5x2 � 4x � 3 17. x � 318. x2 � 3x � 4 19. x � 320. x3 � 2x �

21. 11 22. 25 23. 10 24. 83Lesson 7.4

1. �9, 0, and 9 2. 0, 1, and 103. , 0, and 1 4. �5, 0, and 35. �3, 0, and 4 6. 0, , and 17. �2, 2, and 3 8. �3, �2, and 19. 3, �4, and 10. �1, 6, and 7

11. �1 and 6 (multiplicity 2)13

13�

12

6x � 3x2 � 3

42x � 15x3x � 5

xO

y

2–2–4 42

–2–4

4

18 Algebra 2


12. �4 and 4 (multiplicity 2)13. , and14. , and15. , and 316. , and17. �4, 4, �1, 118. , and19. 1.3, 0.3, and �1.520. �1.2, �0.4, and 0.321. �0.9, 0 (multiplicity 2), and 0.922. �0.2, 0.4, and 1.123. �0.4, 0.3, and 0.924. �2.9, �2.4, �0.2, and 1.4Lesson 7.5

1. and 12. �2, , and 23. �1, , and 4. , 1, and 25. �1 (multiplicity 2), , and 46. , and 17. �5, , and 8. �3, 2i, and �2i9. 3, , and

10. 5, 3i, and �3i11. 2, �2 � 2i, and �2 � 2i12. 1, 4, i, and �i13. �1.46 and 1.66

14. �2.24, 0, and 2.2415. �1.41, 0, and 1.4116. �1.85 and 1.1617. P(x) � 5x3 � 15x2 � 50x � 12018. P(x) � �2x3 � 6x2 � 32x � 96Practice — Chapter 8Lesson 8.1

1. ; 16.8, 8.4, 5.25, 4.22. ; 8, 0.16, 0.1, 0.043. ; 25, 10, 7.5, 2.54. ; 9.6, 0.8, 0.48, 0.35. y � 8xz; 46. y � 24xz; 1447. y � 0.6xz; 10.88. y � 32xz; 969. ; 75

10. ; 911. ; 1012. ; 17.513. 0.5; A � 0.5ap; 13.8 in.2Lesson 8.2

1. yes; all real numbers except and 2. no; |x| � 2 is not a polynomial.3. yes; all real numbers except �1 and 14. vertical: x � 9; horizontal: y � 2

�3��3

z �12xyw

z �5xy2w

z �8xyw

z �20xyw

y �4.8x

y �150x

y �0.8x

y �84x

� 2i�32i�3�i�2i�2

�23 , �

12 , 2312

�14

121313

15

�10��2, �2, ��10�5��2, �2, ��5

��6, �6, �3�7��3, �3, ��7

�6�2, 2, ��6

Algebra 2 19

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5. vertical: x � 1.5; horizontal: y � 06. vertical: and ;horizontal: y � 07. all real numbers except 0 and 6;vertical: x � 0, x � 6; horizontal: y � 08. all real numbers except 1 and �5;vertical: x � �5; horizontal: y � 0;hole at x � 19. all real numbers except �3 and �4;vertical: x � �3, horizontal: y � 3;hole at x � �4

10.

11.

12.

Lesson 8.31. 2. 3. 4.5. 6. 3x6 7. 3x � 9 8. 19. 10. x 11. x2 � x � 12

12. 13. 14.15. 16. 17.18.

Lesson 8.41. 2. 3. 4.5. 6. 7.8. 9. 10.

11. 12. 13.14. 15. 0 16. 17.18. 19. 20.21. 22.23.

Lesson 8.51. 3.5 2. 11 3. 7.5 4. 15 5. , �36. �2, �4 7. �2.5 8. 2 9. 7, 1

10. 0, 11. 6 12. 113. x � 2 or x � 4 14. x � 6 or x � 1215. �1 � x � 0 or x � 1 16. x � 2 or x � 317. 1 � x � 3 18. x � �3 or �2 � x � 219. x ��1 or � x � 120. �3 � x � 4 or x � 152

�13

�34

12

3 � 4y � 2x(x � 3)(y � 2)� 2(3x 2 � 2x � 5)(3x � 2)(x � 5)x � 3x

� x � 6(x � 3)(x � 3)2(x � 2)x � 42xx � 51x � 33x � 7x � 12x(x � 1)

x 2 � 3xx � 32x � 14x � 1x � 22x � 28x � 3�

1x � 5x � 3x � 8�

2x16x 2 � 162x 2 � 2x � 13x 2 � x � 65x � 23x 2 � 1256x3x � 7x 3 � 17x � 2212

3y3 (x � y)4xx � 53x � 21xx � 32x � 1x � 2

x 2 � 3x3x � 12x � 1x � 11x 2 � 5x � 504x � 2

x � 4x � 212x 23x � 23x � 2x � 7x � 73x 2

xO

y

2

–2–4

4

y = 1

x = 1

hole2–2–4 4

xO

y

12

y = 0x = 12

hole

xO

y

–4 84

–4–8

8

x = 4

y = 3

x � �7x � ��7

20 Algebra 2


21. x � �1 or x � 122. �2.2 � x � 3 or x � 323. �4 � x � 0.5 or x � �4.524. x � 0.7 or 4 � x � 4.325. 0 � x � 226. x � �6.5 or 0 � x � 2.5 or x � 427. �1.4 � x � 0 or 1.4 � x � 2Lesson 8.6

1. x � 2.5 2. x � 4 3. x � �6 or x � 64. x � �2.5 or x � 2.5 5. x � 56. x � �3 or x � �17.

8.

9.

10. 4 11. 7.5 12. �6 13. �24 14. 4 15. �2 16. ; 12.4 feetLesson 8.7

1. 2 2. 3 3. 12|x|y2 4. 7xy35. 6. 7. 2x28. 4xy2 9. 10x4y2 10.

11. 12.13. 14. 15.16. 17.18. 432 19. 20. 21.22. 23.24.

Lesson 8.81. 95 2. 10 3. �4, 44. no solution 5.6. 2, 6 7. no solution 8. 2, 39. 5 10. 3 � x � 12 11. x � 14

12. 0 � x � 13. x � �0.5 or x � 2.514. x � 1 15. 8 � x � 13 16. no solution

813

��2 , �2

9�7 � 9�255�3 � 5�216 � 8�3

7�2 � 74�2�2�58 � 13�5�24 � 15�2

5 � �23 � 13�325 � 2�22x2y2 4�2xy22yz 3�3xyz

2y 5�x2yz3�y3�x

�2xy(2y)134x2(5x)123

�x2z�2

3�6V

πd �

xO

y

22

y = x2 – 2x – 5

y = 1 – √x + 6

y = 1 + √x + 6

y � 1 � �x � 6, y � 1 � �x � 6

x

y

–46 4 2

–2

4

y = 2 – x2

Oy = √2 – x

y = –√2 – x

y � ��2 � x, y � �2 � xxO

y

2 4 6

68

y = x2 – 6x + 8y = 3 + √x + 1

y = 3 – √x + 1

y � 3 � �x � 1, y � 3 � �x � 1

Algebra 2 21

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17. x � �6.5 18. � x � 13 19. x � 5.620. �1.8 � x � 1.5 21. �4 � x � 1.322. x � 5.8 23. x � 0.4 24. 0.4 � x � 0.8 or x � 6.225. �9 � x � �0.8 or x � 3.926. x � 3.4 27. x � 10.5Practice — Chapter 9Lesson 9.1

1.

parabola2.

circle

3.

hyperbola4. 13; (2.5, 6) 5. 10; (8, �2) 6.7.8.9.

10. (9, 14); 10π; 25π

11. (4.5, 20); 41π;12. (0, 8.5); 17π;13. (3.5, 1); ;14. (15, 5.5); ;15. (2.5, 2.5); ;Lesson 9.2

1.2.3. y � 1 � (x � 3)2x � 1 �

14 y2y �

112(x � 3)2

562π4π�562101π4π�101

145π4π�145289π4

1681π4

�13 � 3.61; (0, 0.5)12�2 � 16.97; (�2, �2)�85 � 9.22; (3, 4)2�101 � 20.10; (2, 3)

2

4

–44–4 –2 O x

yy � �3�x2 � 1, y � 3�x2 � 1

1010

–10–10 O x

yy � ��400 � x2, y � �400 � x2

22468

4–4 –2 O x

yy �

13x2

34

22 Algebra 2


4.

5.

6.

7. 8.9. 10.

11. 12.

Lesson 9.31. (x � 5)2 � (y � 2)2 � 162. (x � 6)2 � (y � 3)2 �

3. x2 � (y � 4)2 � 254. x2 � y2 �

5. (x � 2)2 � (y � 1)2 � 6.256. (x � 3)2 � (y � 3)2 � 5767.

8.

9.

10. (x � 5)2 � (y � 8)2 � 1; C(5, 8); r � 111. (x � 11)2 � (y � 1)2 � 2; C(�11, 1);

Lesson 9.41.2. (x � 3)24 �

(y � 2)216 � 1x264 �

y236 � 1

r � �2

xO

y2

–2–4–6

2 6(3, 3) r = 3

xO

y

2468

2 4–2–4

r = 4 (0, 5)

xO

y

–8

8(0, 0) r = 168–8

916

254

y �120(x � 9)2x � 6 � �

18(y � 7)2y � 2 �

14(x � 5)2x �112 y2

x � 10 �18 y2y �

124x2

2246

4F(3, 2)

V(1, 2)x = –1 6

directrixO

y

x

22468

4

F(1, 5)V(1, 4)y = 3

–2–4directrix

O

y

x

224

–24F(1, 0)

x = –16

directrix

O

y

xV(0, 0)

Algebra 2 23

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3.4.

5.

6.

7.8.9.

10. ; center: (�3, 0)foci: (�3 � , 0) and (�3 � , 0);vertices: (�9, 0) and (3, 0); co-vertices:(�3, �3), and (�3, 3)

Lesson 9.51. 2.3.

4.

5. 6.7.8. ; center: (14, �3);vertices: (12, �3) and (16, �3);co-vertices: (14, �4) and (14, �2);foci: and

Lesson 9.61. (1, 6) and (4, 21) 2. none3. (�2.83, �2.83) and (2.83, 2.83)4. (�3, 0) and (3, 0)

(14 � �5, �3)(14 � �5, �3)

(x � 14)24 � (y � 3)2 � 1

(y � 1)225 �

(x � 1)2144 � 1

x29 �(y � 2)2

16 � 1x210 �y215 � 1

xO

y

–2–4–6 2 4 6

C (1, 1)

y = – x –34 14y = x +34 14

(1, 4)

(5, 1) (6, 1)(–4, 1) (–3, 1)

(1, –2)

x

y

–2–4 2 4C (0, 0)y = – x53 2

4

–2y = x53

(0, –√34)

(0, 3)

(0, –3)(–5, 0) (5, 0)

(0, √34)

y216 �

x225 � 1x29 �y216 � 1

3�33�3(x � 3)2

36 �y29 � 1

x2400 �y2

464 � 1x2109 �

y29 � 1

x2625 �y2

225 � 1

xO

y1

–2–4–6

2 4 6 8(1, –3) (7, –3)

(4, 2)(4, 1)

(4, –3)(4, –7)(4, –8)

xO

y

4

–8

4–4–8 8(7, 0)(0, 3)(0, 1)(1, –3)(–7, 0)

(0, –5)

(0, 7)

x

y

44–4–8 8

(0, √77)

(0, –√77)

(0, 9)

(0, 0)(–2, 0) (2, 0)

(0, –9)

(x � 3)225 �

(y � 2)29 � 1

24 Algebra 2


5. (�2.24, �1.73), (�2.24, 1.73),(2.24, –1.73), and (2.24, 1.73)6. (�4.24, �2.45), (�4.24, 2.45),(4.24, �2.45), and (4.24, 2.45)7. none8. (�2.08, �1.44), (�2.08, 1.44),(2.08, �1.44), and (2.08, 1.44)9. none

10. parabola;

11. hyperbola;


1. 2. 3.4. 5. 6.

7. 8. 9.10. 11.12. 13.14. 1,000,000 15. 676,00016. 456,976,000 17. 67,600,00018. 6,760,000Lesson 10.2

1. 5040 2. 2520 3. 840 4. 840 5. 479,001,6006. about 4.36 � 10107. about 2.18 � 10118. about 6.03 � 10139. 20,160 10. 2520 11. 10,080 12. 5040

13. 4,989,600 14. 907,200 15. 43,75816. 720 17. 5040 18. 3,628,800Lesson 10.3

1. 56 2. 120 3. 35 4. 6435 5. 846. 60 7. 40 8. 5 9. 40

10. about 33% 11. about 39%12. about 16% 13. combination14. combination 15. permutation16. permutationLesson 10.4

1. inclusive;2. mutually exclusive;3. inclusive;4. inclusive; 3952 � 75%

1926 � 73%613 � 46%

413 � 31%

85150 � 57%107150 � 71%43150 � 29%65150 � 43%

42150 � 28%16 � 17%2126 � 81%

13 � 33%1113 � 85%12 � 50%511 � 45%45 � 80%710 � 70%

xO

y

246

42 86

(x � 5)29 �

(y � 4)24 � 1

xO

y

2468

–242 86

y � 3 �14(x � 7)2

Algebra 2 25

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5. mutually exclusive;6. inclusive;7. 8.9. 10.

11. 12.13. 14.15.

Lesson 10.51. 0.02 � 2% 2. 0.08 � 8%3. 0.04 � 4% 4. 0.05 � 5%5. 0.008 � 0.8% 6. 0.01 � 1%7. 8.9. 10.

11. 12.13. 14.15. 16.17. 18.19. 20.

Lesson 10.61. 2. 3.4. 5. 6.7. 8. 9. 1 � 100%

10. 11. 12.13. 14. 15.

16. 17. 0.625 � 62.5%18. 19.20. 0.064 � 6.4% 21. 0.4 � 40%22. 0.5625 � 56.25%Lesson 10.71–6. Simulation results will vary.Practice — Chapter 11Lesson 11.1

1. 2.5, 5, 7.5, 10, 12.5, 152. 0, , 1, 1 , 2, 23. 13, 16, 21, 28, 37, 484. 20, 70, 220, 670, 2020, 60705. 1, 101, 201, 301, 401, 5016. �5, �15, �45, �135, �405, �12157. a1 � 1; an � 11an � 1; 14,641; 161,051;1,771,5618. a1 � 81; an � an � 1 � 3; 69, 66, 639. a1 � 2; an � �3an � 1; 162, �486, 1458

10. a1 � ; an � �4an � 1; 64, �256, 102411. a1 � 2; an � 3an � 1 � 5; 362, 1091, 327812. a1 � �2; an � 5an � 1 � 4; �1874; �9374;

�46,87413. 4.5 � 9 � 13.5 � 18 � 22.5 � 27 � 31.5;12614. 11 � 22 � 35 � 50 � 67; 18515. 210 16. �24 17. 1018. 1432.5 19. 397 20. 1911.4

14

121212

12 � 50%910 � 90%13 � 33%

12 � 50%45 � 80%15 � 20%25 � 40%35 � 60%14 � 25%

12 � 50%18 � 12.5%18 � 12.5%12 � 50%13 � 33%23 � 67%12 � 50%16 � 17%

13 � 33%112 � 8%18 � 12.5%124 � 4%49 � 44%136 � 3%14 � 25%19 � 11%

118 � 6%772 � 10%2536 � 69%316 � 18.75%

124 � 4%49144 � 34%

518 � 28%2236 � 61%59 � 56%

1336 � 36%1936 � 53%34 � 75%38 � 37.5%

58 � 62.5%58 � 62.5%4152 � 79%

2752 � 52%

26 Algebra 2


Lesson 11.21. yes; d � 3 2. no 3. yes; d � 2.54. no 5. yes; d � 6. yes; d � �2.37. tn � 25 � 9n 8. tn � 8n � 239. tn � 3n � 10 10. tn � 12n � 37

11. tn � 11n � 2 12. tn � 9.9 � 1.3n13. 50, 150, 250, 350 14. 7.5, 10, 12.5, 1515. �20, �12, �4, 4 16. 25, 65, 105, 14517. 8.5, 9, 9.5, 10 18. �15, �27, �39, �5119. �5, 2, and 9 20. 52, 64, 76, and 8821. 62 and 74 22. 10.5, 14, and 17.523. 34, 28, and 22 24. �2, 4, 10, and 16Lesson 11.3

1. 350 2. 3. �165 4. 29055. 711 6. 1482 7. 25,425 8. 3609. 1300 10. 9555 11. 9555 12. 330

13. 990 14. 165 15. 239.25 16. �191417. 18. 84 19. �13220. 590 21. 228 22. 795 23. �351Lesson 11.4

1. no 2. yes; r � 0.4 3. yes; r �

4. yes; r � 1.5 5. yes; r � 6. no7. 18, �36, 72, �144 8. �4, �10, �25, �62.5, �156.259. 10, 5, 2.5, 1.25 10. 0.625 or �0.625

11. or12. or13.14. tn � �30(�0.2)n � 1

15. tn � 40(0.8)n � 116. tn � 17. tn �

18. tn �

19. 35 and 175 20. �14 and �721. 48, 192, and 768 or �48, 192, and �76822. 15, 18, and 21.6 or �15, 18, and �21.623. 60, 300, and 1500 or �63, 300, and

�150024. 12, 36, 108, and 324Lesson 11.5

1. 6,973,568,800 2. 86.4 3. �1474. 5. �1064.76. 6144 7. 1,572,864 8. 12,2859. 3,145,725 10. 378 11. 1,708,554.00

12. 1.67 13. 14,348,90614. Show the statement is true for n � 1:

13 � 1 and . Assume that thestatement is true for a natural number k.Then13 � 23 � 33 � … � k3 � and13 � 23 � 33 � … � k3 � (k � 1)3 �

.Thus, the statement is true for k � 1.(k � 1)2[(k � 1) � 1]2

4(k � 1)2(k � 2)24 �

(k � 1)2(k2 � 4k � 4)4 �

(k � 1)2[k2 � 4(k � 1)]4 �

k2(k � 1)2 � 4(k � 1)34 �

k2(k � 1)24 � (k � 1)3 �

k2(k � 1)24

12(1 � 1)24 � 1

54673125 �1.7

�14(�6)n

80(14 )n2(52 )n�1

tn � 250(25 )n�1�164014164014�32�232�2

23�

35

528�5 � 1180.64

1612

35

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Lesson 11.61. does not exist 2. 1.2 3. 2.6254. 25 5. 4 6. does not exist7. 12.375 8. 3 9. 10. 11.5

11. does not exist 12. 50 13.14. 15. 16. 17. 18. 19.20. 21.

22. 23.

24. 25.

Lesson 11.71. sixth entry, row 7; 212. fourth entry, row 6; 203. seventh entry, row 8; 284. sixth entry, row 10; 2525. eleventh entry, row 13; 2866. sixth entry, row 12; 7927. 120 8. 1716 9. 6435 10. 153

11. 0.3125 12. about 0.66 13. about 0.0114. about 0.64 15. 0.5 16. 0.437517. about 0.23 18. about 0.8919. about 0.34 20. about 0.0921. about 0.66 22. about 0.34

Lesson 11.81. s5 � 5s4t � 10s3t 2 � 10s2t3 � 5st4 � t52. b6 � 6b5w � 15b4w2 � 20b3w3 �15b2w4 � 6bw5 � w63. 16 terms 4. 3 5. 3003r5s106. 3125x5 � 3125x4y � 1250x3y2 �250x2y3 � 25xy4 � y57. w4 � w3z � 6w2z2 � 16wz3 � 16z48. a5 � a4d � a3d2 � a2d3 �

ad4 � d59. 64m6 � 576m5q � 2160m4q2 �4320m3q3 � 4860m2q4 � 2916mq5 �729q6

10. about 0.20 11. about 0.26 12. about 0.74 13. about 0.11 14. about 0.61Practice — Chapter 12Lesson 12.1

1. 66; 62; 622. 24.571; 28; 283. 3.617; 3.6; 3.64. 622.833; 725; 7255. 2593.333; 1714; 16006. 24.05; 24.25; 25; all are reasonablemeasures because they are so close, butthe mean and median are better than themode because 6 of the 8 numbers are lessthan the mode.

154458135324052562431024

116

445 � ( 11000 )k��

k�111 � ( 11000 )k��

k�1

358 � ( 11000 )k��

k�115 � ( 1100 )k��

k�1

93 � ( 1100 )k��

k�17 � ( 1100 )k��

k�1

1027251112513334999379919

22291.81

28 Algebra 2


7.

mean:8.

estimated mean: 10.75Lesson 12.2

1.

45; 64; flat2.

3.75; 2.3 and 4.8; mound-shaped

3.

4.

5.33.2%Passengercars

50%Trucks

15.9%Buses0.9%Motor-cycles

Motor VehicleRegistration by Type, 1994Number10 11 12 13 140

0.10.20.3

Probabili

ty

Number0 1.0 1.1 1.2 1.3 1.4123456

Frequen

cy

Stem Leaf 3|1 � 3.11 72 3, 33 1, 6, 94 0, 3, 8, 8

Stem Leaf 3|8 � 383 3, 7, 84 0, 2, 55 4, 6, 86 4, 4

16.05

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Age (years) Tally Frequency14 315 316 417 618 2

No. of books Class mean Freq. Product1–5 3 8 24

6–10 8 4 3211–15 13 3 3916–20 18 1 1821–25 23 2 4625–30 28 2 56

Number Frequency1.0 51.1 21.2 31.3 61.4 4

Number Frequency Rel. Freq.10 8 16%11 12 24%12 7 14%13 11 22%14 12 24%

Lesson 12.31. Q1 � 2, Q2 � 7, Q3 � 8; range � 8;IQR � 62. Q1 � 10, Q2 � 14.5, Q3 � 17;range � 14; IQR � 73. Q1 � 12.1, Q2 � 23.9, Q3 � 38.5;range � 33.8; IQR � 26.44. minimum � 3, maximum � 17;Q1 � 5, Q2 � 10, Q3 � 15;range � 14; IQR � 10

5. minimum � 10, maximum � 39;Q1 � 16, Q2 � 23, Q3 � 35; range � 29;IQR � 19

6. the data for 19927. The quartiles and the extremes alldecreased, so it appears that the birthrates decreased in general.8. about 75%

Lesson 12.41. 32; 9.6 2. 19; 3. 55;4. 80; 22 5. 7.1; 2 6. 62; about 18.97. 16; 4 8. 721.6; about 26.99. 74,064; about 272.1 10. 5; about 2.2

11. 83.7856; about 9.2 12. ; about 0.313. 20 14. 4.3 15. 26.24 16. about 5.1

Lesson 12.51. 9.375% 2. 9.375% 3. 34.375%4. 10.9375% 5. 0.8% 6. 81.92%7. 6.4% 8. 94.208% 9. 0.672%

10. about 20.1% 11. 7.68% 12. 68.256%13. 31.104% 14. 17.92% 15. about 2.3%16. about 0.27% 17. about 99.7%18. about 1.1%Lesson 12.6

1. 0.5 2. 0.8849 3. 0.96414. 0.1554 5. 0.4772 6. 0.07937. 0.1359 8. 0.1586 9. 0.5403

10. 16% 11. 2% 12. 82% 13. 16%14. about 420 customers15. about 820 customersPractice — Chapter 13Lesson 13.1

1. ; 0.9756 2. ; 0.2195 3. ; 4.44444. ; 0.2195 5. ; 0.9756 6. ; 0.2257. ; 4.5556 8. ; 4.5556 9. ; 4.4444

10. 8.3; 57; 33 11. 11.6; 61; 29

12. 21.6; 34; 56 13. 59; 4.9; 4.214. 36; 4.9; 3.5 15. 56; 5.2; 4.3Lesson 13.2

1. –313; 47 2. 237; 57 3. �142; 38

4. 152; 28 5. 138; 42 6. �53; 53

7. 42; 42 8. 175; 5 9. 285; 75

10. 75 11. 33 12. 5

4094194199404041941

4099414041

0.08

16.35.3

8 12 16 20 24 28 32 36 40

2 4 6 8 10 12 14 16 18

30 Algebra 2


13. 36 14. 40 15. 72 16. 2

17. 80 18. 60

19.20.21.22. 23. 24. 25.26. 27.

Lesson 13.31. 2.3. 4.5. 6.7. (0.743, 0.669) 8. (�0.629, 0.777)9. (�0.438, �0.899) 10. (0.574, �0.819)

11. (0.755, �0.656) 12. (�0.259, �0.966)13. 0; 1; 0 14.15. 16.17. 18. 19. 20.21. 22. 23. 24. �1 25. �2Lesson 13.4

1. radians 2. radians 3. radian4. radians 5. radians 6. radians 7. radians8. radians 9. 450 10. 165

11. 140 12. 195 13. 472.69

14. 103.13 15. 171.89 16. 28.65

17. 47.1 feet 18. 5.2 feet 19. 41.9 feet20. 10.5 feet 21. 50 feet 22. 80 feet23. 146 feet 24. 200 feet 25. 026. 27. 28. �1 29.30. 31. 0 32. 2Lesson 13.5

1. 1; 0.5; 0; �0.5; �1; �0.5; 0; 0.5; 1

2. 4.5; π radians 3. does not exist; π radians4. 1.2; 2π radians5. shift of 45 right;translation of 1.5 units up

�90° 180° 270°

1

–1

y = cos �

y = cos 2�

��22

�33��3�12

5π127π18�

17π367π125π6

π55π33π4

�3312�22��3�

2�33��32�32

�12 ; �32 ; �

�33�32 ; �12 ; ��3

��22 ; �22 ; �1

(2�3, 2)(�5�2, 5�2)(20�3, �20)(�

152 , �15�32 ) (6, 6�3)(5�22 , 5�22 )

3�7751343�398�895�

349�9797 ; 4�9797 ; 2.25; �979 ; �974 ; 492�55 ; �

�55 ; �2; �55 ; ��5; �12

2�1313 ; 3�1313 ; 23 ; �132 ; �133 ; 32

Algebra 2 31

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�90° 180° 270° 360°

–10123

y

6. shift of π units left;translation of 1 unit down

Lesson 13.61. �60 2. 120 3. 0 4. 0 5. �45

6. �60 7. 0 8. �1 9.10. radians 11. �45 12. radians13. 1.5459 radians 14. 0.0345 radians15. 2.5173 radians 16. 0.6831 radians17. �1.5446 radians 18. �0.5769 radians19. 9.6 20. 35.5 21. 48.1

Practice — Chapter 14Note: Throughout Chapter 14, answers mayvary slightly due to rounding, method ofcalculation, or order in which solutions were found.Lesson 14.1

1. 25.5 2. 24.8 3. 16.7 4. 29.7 5. 5.6 6. 28.97. m�C � 38, b � 4.4, c � 3.18. m�A � 35, c � 21.7, a � 12.79. m�C � 45, a � 25.8, c � 18.5

10. m�B � 44, a � 5.5, b � 4.011. m�C � 82, a � 15.5, c � 21.412. m�A � 75, a � 82.9, c � 78.413. one; m�B� 46.0, m�C� 70.0, c � 20.914. none15. two; (1) m�A � 46.2, m�C � 105.8,c � 53.3; (2) m�A � 133.8,m�C � 18.2, c � 17.316. 1532.7 feetLesson 14.2

1. SAS; a � 17.3 2. SAS; c � 28.23. SAS; a � 5.3 4. SSA; b � 9.8 5. SAS; c � 31.3 6. SAS; a � 13.9 7. m�A � 44.7, m�B � 38.3,m�C � 97.0

8. m�A � 78.3, m�B � 37.4,m�C � 64.3

9. m�A � 73.0, m�B � 61.2,m�C � 45.8

10. m�A � 45.8, m�B � 30.7,m�C � 103.5

11. m�A � 41.1, m�B � 80.3,m�C � 58.6

12. SAS; b � 131.2, m�A � 32.5,m�C � 37.5

13. SSS; m�A � 50.0, m�B � 98.7,m�C � 31.3

14. SSS; m�A � 104.5, m�B � 29.0,m�C � 46.5

15. SAS; a � 6.5, m�B � 20.7,m�C � 109.3

16. SSA; not possible17. 29.0, 75.5, and 75.5

π2π6�32

32 Algebra 2


xπ 2π

–2–1012y

π2 3π2

Lesson 14.31.2.

3. cos2 �

4.5. sin � 6. tan2 � 7. �1 8. tan �

9. sin � 10. sec �

11.

12. (1 � cos �) � sin �

13. �

Lesson 14.41. 2.3. 4.5. 6.7. 8.9. 10.

11. 12. 13.14. 15.16. 17. 18.

19.

20.

21.

22.

23.

24.

25. (�5.66, �1.41), (�9.19, �4.95),(�12.02, �2.12), (�8.49, 1.41)Lesson 14.51–4. Check students’ work.5–11. Answers may vary. Sample answers:

5. 6. 7. 2 cos2 �

8. tan2 � 9. tan � 10. cot �

11. 1 � sin � 12. 27 feetLesson 14.6

1. 30 � n(360), 150 � n(360),210 � n(360), and 330 � n(360)2. 45 � n(360) 3. 120 � n(360) 4. 120 � n(360) 5. 120 and 240

6. 210, 270, and 330

7. 45, 135, 225, and 315

8. 30, 150, 210, and 330

9. 10. π4 and 5π4π3 and 5π3

1 � cos �21 � cos �2

��0.370.93 �0.93�0.37 �

� 0.77�0.64 0.640.77 �

� 0.420.91 �0.910.42 ��0.71

�0.71 0.71� 0.71 �

��0.710.71 �0.71� 0.71 �

��0.50.87 �0.87�0.5 �

��24 �

�64��32�24 �

�64�24 �

�64��24 �

�64�

�32�22��24 �

�64�24 �

�64�64 ��24

�24 ��64�24 �

�64�24 �

�64��24 �

�64�

�24 ��64�

�24 ��64

�24 ��64�24 �

�64

1sin �sin � � (cos �)( cos �sin � ) � csc �

( 1sin ��

cos �sin � )� sin �

1sin �� sin �

cos2 �sin2 �

1�tan2 � � 1�y2x2 �

x2 � y2x2 �

r2x2 � sec2 �

x2 � y2y2 �

r2y2 �1 � cot2 � � 1 �x2y2 �

�x2r2 � �cos2 �

y2 � r2r2 �

y2r2 � 1 �(yr � 1)(yr � 1) �

(sin � � 1)(sin � � 1) �

cot �cos ��

xy xr �

xy �rx �

ry � csc �

Algebra 2 33

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11.12.13. 1.23, 1.91, 4.37, and 5.0514. 0.34, 0.52, 2.62, and 2.8015. 25.2

π2 , 7π6 , and 11π6π9 , 5π9 , 7π9 , 11π9 , 13π9 , and 17π9

34 Algebra 2


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