Alg 2 Practice Answers

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Practice — Chapter 1 Lesson 1.1

1.yes 2.yes 3.no 4.yes 5.no 6.yes 7.yes 8.no 9.yes 10.no 11.no 12.yes 13. 14. 15. 16.(6, 19) 17.(4, 20) 18.not linear 19.(ⴚ4, 23) 20.(8, ⴚ29) 21.(5, ⴚ14) Lesson 1.2 1. 2. 3. 4. 5. 6. 7. 8. 9.1 10.3 11. 12. 13. 14. 15. 16. Lesson 1.3 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. 29. 30. 31. 32.yⴝ ⴚ1 4xⴚ154 yⴝ ⴚ1 3x yⴝ4 3xⴙ83 yⴝ ⴚ4 3xⴙ2 yⴝxⴙ2 yⴝ ⴚ1 4xⴙ72 yⴝ ⴚ1 2xⴚ4 yⴝ1 2xⴚ10 yⴝ ⴚ1 3xⴚ2 yⴝ ⴚ2xⴙ8 yⴝ ⴚ3xⴙ3 yⴝ1 2xⴚ3 yⴝ3xⴚ4 yⴝ ⴚ1 2xⴚ1 yⴝ4xⴚ16 yⴝ ⴚ3xⴙ5 yⴝ2xⴙ15 yⴝ3 4xⴚ5 yⴝ ⴚ4xⴚ5 yⴝ ⴚ3xⴙ7 yⴝ ⴚ1 4xⴙ8 yⴝ ⴚ2xⴚ1 yⴝ4xⴚ13 yⴝ3 4xⴚ5 yⴝ ⴚ1 2xⴙ1 yⴝx yⴝ4 5xⴙ1110 yⴝ ⴚ9xⴚ13 yⴝ ⴚ1 2xⴙ1 yⴝ ⴚ1 5xⴙ85 yⴝ ⴚxⴙ2 yⴝxⴙ2 yⴝ ⴚ3 4xⴙ3 yⴝ5 6xⴙ3 mⴝ ⴚ3,bⴝ ⴚ7 mⴝ ⴚ2,bⴝ ⴚ4 mⴝ ⴚ3 8,bⴝ ⴚ32 mⴝ ⴚ3 4,bⴝ32 57 100 ⴚ2 3 yⴝ1 4xⴙ4 yⴝ1 6xⴙ3 yⴝ4 5xⴚ25 yⴝ ⴚ4xⴙ3 yⴝ3xⴙ1 yⴝ2xⴚ5 x y 2 2 4 6 8 4 6 8 2 2 4 6 8 4 6 8 x y x y 2 2 4 6 8 4 6 8 O Copyright © by Holt, Rinehart and Winston. All rights reserved.

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Lesson 1.4 1. 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 that 19.yes; Lesson 1.5 1. ; positive 2. ; negative 3. ; negative 4. 5. 6.0.360 Lesson 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 1.7 1. 2. 3. 4. 5. x 0 1 2 3 –1 –2 –3 x ⱕ 1 –2 –1 0 1 –3 –4 –5 x x ⱕ ⴚ4 x ⱕ 2 x ⬎ 2 x ⱖ ⴚ3 h ⴝ_{a ⴙ b}A a ⴝT0ⴚT z ⴚ z₀ q_pⴝ q D ⴛ Q P₁ⴝV2P2 V₁ r ⴝ_2πC W ⴝ_LDV x ⴝ1₂ x ⴝ ⴚ6₇ x ⴝ ⴚ6 x ⴝ ⴚ4 x ⴝ ⴚ₂₂5 x ⴝ 18 x ⴝ ⴚ6₅ x ⴝ ⴚ1₃ x ⴝ 7 x ⴝ ⴚ1₃ x ⴝ ⴚ21 x ⴝ 16 x ⴝ 2 x ⴝ1₂ x ⴝ ⴚ3 x ⴝ ⴚ2 x ⴝ7₈ x ⴝ 8 x ⴝ 6 x ⴝ 9 x ⴝ 5 x ⴝ 2 r 艐 0.96 y ⴝ 0.01x ⴙ 0.24 x y 4 2 6 8 10 10 –10 –20 –30 –40 (1, –2) O (2, –18) (7, –26) (9, –34) y 艐 ⴚ3.26x ⴚ 4.5 x y 2 4 6 8 10 10 –10 –20 –30 (2, 10) O (8, –27.45) (6, –20.15) (0, 1.9) y 艐 ⴚ4.44x ⴙ 8.85 x y 10 O 9 18 27 20 (0, 4) (2, 10) (6, 22) (8, 28) y ⴝ 3x ⴙ 4 y ⴝ 2x y ⴝ kx y ⴝ 3x z ⴝ1₃ x ⴝ ⴚ1 y ⴝ ⴚ5₄ z ⴝ5₂ x ⴝ 10 y ⴝ9₂ x ⴝ 4 x ⴝ 3 k ⴝ ⴚ3; y ⴝ ⴚ3x k ⴝ 2; y ⴝ 2x k ⴝ5₆; y ⴝ5₆x k ⴝ2₇; y ⴝ2₇x k ⴝ1₄; y ⴝ1₄x k ⴝ ⴚ4₃; y ⴝ ⴚ4₃x k ⴝ7₃; y ⴝ7₃x k ⴝ ⴚ5; y ⴝ ⴚ5x Copyright © by Holt, Rinehart and Winston. All rights reserved.

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6.no solution 7. 8. 9. Lesson 1.8 1.x ⴝ2and x ⴝ ⴚ8 2.x ⴝ10and x ⴝ ⴚ2 3.x ⴝ ⴚ6and x ⴝ1 4. and x ⴝ ⴚ3 5. and x ⴝ2 6.x ⬍1and 7. and 8. and 9. or 10. or Practice — Chapter 2 Lesson 2.1 1.rational, real 2.irrational, real 3.irrational, real 4.rational, real

5.integer, rational, real 6.rational, real

7.Inverse Property of Addition 8.Identity Property of Multiplication 9.Associative Property of Addition 10.Inverse Property of Multiplication 11.Commutative Property of Multiplication 12.Distributive Property

13.Identity Property of Addition

14.ⴚ33 _15.4 _16.43 _17.43 _18.49 19.28 20.26 21.7.2 22.56 23.90 6 x 0 2 4 –2 –4 –6 x ⱖ5 x ⱕ ⴚ2.5 6 x 0 2 4 –2 –4 –8 –6 x ⬎ 3 x ⬍ ⴚ7 x 2 3 1 0 x ⬎1₅ x ⬍11₅ x 0 1 2 3 –1 –2 –3 x ⬎1₆ x ⬍7₆ x 2 4 6 8 0 –2 –4 x ⬎ ⴚ9₅ x 0 2 –10 –8 –6 –4 –2 x ⴝ ⴚ10 x –2 0 2 4 –4 –6 –8 x ⴝ9₅ x –2 0 2 4 –4 –6 –8 x 4 6 8 10 2 0 –2 x –2 0 2 4 –4 –6 –8 x 190 180 170 160 150 200 162⬍ t ⬍192 x 0 2 4 6 –2 –4 –6 x ⬍5 x –1 0 1 2 –2 –3 –4 x ⱖ ⴚ2 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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Lesson 2.2 1.1 2. 3.36 4.1 5.ⴚ217 6. 7.25 8.32 9.2 10.16 11.32 12.9 13. 14.w4y2z2 15. 16.x14 17.z17 18. 19.y5z 20.1 21.81x12y20 22.16a12b4c24 23.125a6b9 24. 25. 26. 27.16m12p4 28. 29. 30.81x26y2 Lesson 2.3

1.yes 2.yes 3.no 4.yes 5.yes 6.no 7.yes 8.no 9.domain: ; range: {ⴚ3, 1, 3, 7} 10.domain:xⱖ ⴚ5; range:y ⱖ ⴚ2 11.domain: {ⴚ4.5, 3, 6.5, 12}; range: {6,ⴚ1.5,ⴚ5,ⴚ10.5} 12.domain: {ⴚ2, 0, 1, 5}; range: {12, 8, 9, 33} 13. 14. 15. 16. 17. Lesson 2.4 1.(f ⴙ g)(x)ⴝ8x2ⴙ5x ⴚ13; (f ⴚ g)(x)ⴝ6x2ⴙ5x ⴙ13 2.(f ⴙ g)(x)ⴝ13x2ⴚ5x ⴙ41; (f ⴚ g)(x)ⴝ ⴚ13x2ⴚ5x ⴙ41 3.(f ⴙ g)(x)ⴝx2ⴚ x ⴙ2; (f ⴚ g)(x)ⴝx2ⴙ x ⴙ16 4.(f ⴙ g)(x)ⴝ3x2ⴙ6; (f ⴚ g)(x)ⴝ ⴚ21x2ⴙ6 5.(f ⴢ g)(x)ⴝ175x ⴙ25; (x)ⴝ7x ⴙ1 6.(f ⴢ g)(x)ⴝ3x3ⴙ17x2ⴙ75x ⴙ425; (x)ⴝ ,x ⴝ ⴚ5 7.(f ⴢ g)(x)ⴝx4ⴚ256; (x)ⴝ ,x ⴝ ⴚ4 and x ⴝ4 8.(f ⴙ g)(x)ⴝ ⴚx ⴙ8 9.(f ⴚ g)(x)ⴝ ⴚ3x ⴚ12 10.(g ⴚ f)(x)ⴝ3x ⴙ12 11.(f ⴢ g)(x)ⴝ ⴚ2x2ⴚ22x ⴚ20 12. (x)ⴝ 13. (x)ⴝ 14. 15. 16. 17.ⴚ44 _18.ⴚ52 _19.ⴚ10 _20.ⴚ5 21.ⴚ5 _22.22 _23.ⴚ55 _24.ⴚ28 _25.44 Lesson 2.5 1.{(ⴚ16,ⴚ1), (ⴚ6, 0), (14, 2)}; yes; yes 2.{(2, 7), (3, 6), (4, 7), (5, 6)}; no; yes 3.{(16,ⴚ2), (1,ⴚ1), (1, 1), (16, 2)}; yes; no 4.{(7,ⴚ5), (7,ⴚ3), (7,ⴚ1), (7, 1)}; yes; no 5.{(4,ⴚ5), (9,ⴚ3), (12, 1), (13, 7)}; yes; yes 6.fⴚ1(x)ⴝ3x ⴚ1 7.hⴚ1(x)ⴝ3x ⴚ₂ 1 (fⴰg)(x)_{ⴝ ⴚ}x2_ⴙ1; (gⴰf)(x)_{ⴝ ⴚ}x2_ⴙ1 (fⴰg)(x)_ⴝ4x2_ⴚ4; (gⴰf)(x)_ⴝ16x2_ⴚ1 (fⴰg)(x)_ⴝx; (gⴰf)(x)_ⴝx ⴚx ⴙ₂ 10 x ⴙ2,x ⴝ ⴚ1

(

g f

)

ⴚ2x ⴙ2 x ⴙ10,x ⴝ ⴚ10

(

f g

)

x2ⴙ16 x2ⴚ16

(

f g

)

2 3 x2ⴙ25 3x ⴙ17

(

f g

)

(

f g

)

22 3 20 3 f(0.5)ⴝ1.25;f(0)ⴝ0 f(11)ⴝ361;f(ⴚ4)ⴝ46 f(7)ⴝ ⴚ9;f(ⴚ5)ⴝ27 f(ⴚ3)ⴝ45;f(5)ⴝ125 f(ⴚ2)ⴝ ⴚ44;f(8)ⴝ156

再

ⴚ1, 0, 1₂,3₂

冎

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8. 9.fⴚ1(x) ⴝ 2x ⴙ 2.5 10. 11.hⴚ1(x) ⴝ 4x ⴙ 32 12. not a function 13. function 14. function Lesson 2.6 1. 2. 3. 4. if if 5.f(x) ⴝ x ⴙ 3 if x ⱕ ⴚ3, f(x) ⴝ 0 if ⴚ3 ⬍ x ⬍ 0, f(x) ⴝ x if x ⱖ 0 6.f(x) ⴝ x ⴚ 2 if x ⬍ 0, f(x) ⴝ 0 if x ⴝ 0, f(x) ⴝ x ⴙ 2 if x ⬎ 0 7.ⴚ10 _8.32 _9.13.13 _10.0 _11.7 12.ⴚ7.5 _13.1.5 _14.1 _15.ⴚ19 _16.ⴚ7 x ⱖ 2 f(x) ⴝ 1 ⴚ4 ⬍ x ⬍ 2, f(x) ⴝ1₂x f(x) ⴝ ⴚ2 if x ⱕ ⴚ4, x O y 2 –2 –4 4 2 –2 –4 4 x O y –2 –4 2 4 2 –2 –4 4 x O y 2 –2 –4 4 2 –2 –4 4 x O y 1 –2 2 4 –4 –8 8 x O y 1 –1 –2 2 4 –4 –8 8 x O y 2 –2 –4 4 4 8 12 16 gⴚ1_{(x) ⴝ}x 8ⴚ2 gⴚ1(x) ⴝx ⴙ 4 11 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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Lesson 2.7

1.a horizontal translation 7.5 units to the left

2.a vertical translation 7.5 units up

3.a horizontal compression by a factor of 52 4.a vertical stretch by a factor of 2 and a

reflection across the x-axis

5.a vertical stretch by a factor of 14 and a vertical translation 6 units up

6.a vertical stretch by a factor of 12 and a horizontal translation 7 units to the right 7.a translation 21 units to the left

8.a vertical stretch by a factor of 17 9.a horizontal stretch by a factor of 2 10.a vertical translation 13.7 units up 11.a vertical stretch by a factor of 3 and a

reflection across the x-axis

12.a vertical stretch by a factor of 41 and a horizontal translation 8 units to the right

13. 14. 15. 16. 17. 18. Practice — Chapter 3 Lesson 3.1 1.independent; (0, 4)

2.dependent; infinitely many solutions 3.independent; (ⴚ1,ⴚ1) 4.inconsistent; no solution 5.independent; (1, 3) 6.independent; (1, 6) 7.(6,ⴚ1) _8.(12, 1) _9. 10.(ⴚ4, 8) _11.(ⴚ8, 5) _12. Lesson 3.2 1.(2,ⴚ1) _2.no solution _3.(6, 2) 4.(3, 0) 5.(4,ⴚ3) _6.no solution 7.(ⴚ9,ⴚ4) _8.infinitely many solutions 9.(8, 8) 10.(ⴚ4, 1) _11.(2,ⴚ1)

12.(ⴚ3, 3) _13.(1,ⴚ2) _14.(5,ⴚ8) 15. 16.(1, 7) 17.

18.infinitely many solutions

19. 20.(3, 10) 21.no solution 22. 23. 24.(11,ⴚ3) Lesson 3.3 1. 2. 2 2 4 –4 –2 4 –4 –2 x y 2 O 2 4 –4 –2 4 –4 –2 x y

(

2 3, 2

)

(

1 4, 1

)

(

1 3,23

)

(

1 2, 3

)

(

1 2,12

)

(

3,1₂

)

(

1 2, 4

)

g(x)ⴝx3ⴚ33 g(x)ⴝ ⴚ2₃x ⴙ9 g(x)ⴝ

ⱍ

₁₂x

ⱍ

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3. 4. 5. 6. 7a.8x ⴙ 12y ⱕ 400 b. c.50 hours; 33 hours Lesson 3.4 1. 2. 2 2 4 –4 4 –4 –2 x y 2 2 4 –4 –2 4 –4 –2 O x y 1 3 30 20 10 24 32 8 16 40 O x y 2 2 4 –4 –2 4 –4 –2 O x y 2 O 2 4 –4 –2 4 –4 –2 x y 2 O 2 4 –4 4 –4 –2 x y 2 O 2 4 –4 –2 4 –4 –2 x y Copyright © by Holt, Rinehart and Winston. All rights reserved.

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3. 4. 5. 6. 7. Lesson 3.5 1. 2. 3. 4.maximum: 41; minimum: 4 5.maximum: 17; minimum:ⴚ12 6.maximum: 12; minimum:ⴚ7 7.maximum ⴝ50 _8. maximum ⴝ68 minimum ⴝ0 minimum ⴝ0 9.maximum ⴝ200 _10. maximum ⴝ62 minimum ⴝ20 minimum ⴝ ⴚ25 2 2 4 6 8 4 6 8 O x y 2 2 4 6 8 4 6 8 O x y 2 2 4 6 8 4 6 8 O x y x O y 15 30 15 30

再

x ⴙ y ⱕ30 6x ⴙ7y ⱖ126

再

y ⱖ1 y ⬍1₂ⴙ2 y ⱕ ⴚx ⴙ5

再

x ⱕ4 y ⱖ ⴚ x y ⬍1₂x ⴙ3

再

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Lesson 3.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10a. b. 11a.25 seconds b.3750 feet Practice — Chapter 4 Lesson 4.1 1.2ⴛ2 _2.2ⴛ2 _3.3ⴛ3 _4.3ⴛ3 5.

6.not possible; the matrices do not have the same dimensions.

7. 8. 9. 10. 11.

冤

ⴚ6 0 ⴚ12 6 ⴚ2 4 8 ⴚ4 ⴚ4

冥

冤

76 20 5 7 ⴚ2 0 14 ⴚ8

冥

冤

ⴚ7 ⴚ4 ⴚ4 3

冥

冤

7₄ ⴚ43

冥

冤

ⴚ03 ⴚ6 12

冥

冤

ⴚ2 ⴚ3 ⴚ7 ⴚ4 ⴚ3 0 ⴚ2 ⴚ6 5

冥

x O y 100 200 300 400 2000 4000

再

x(t)ⴝ150t y(t)ⴝ12t y ⴝx₉2ⴙ1 y ⴝ1₃x ⴚ2 y ⴝ ⴚ1₂x ⴙ16 y ⴝ ⴚ1₂x ⴙ8 y ⴝ6x ⴙ2 y ⴝ1₂x ⴚ14 x O y 2 –2 –4 4 6 2 –2 –4 –6 x O y 2 –2 –4 4 2 4 6 8 x O y 2 –2 –4 –6 4 4 2 –2 –4 Copyright © by Holt, Rinehart and Winston. All rights reserved.

(11)

12.

13.

14.3ⴛ3 _15.101 medals 16.90 gold medals

17.the number of bronze medals, 27, won by Germany

18. Gold Silver Bronze

Lesson 4.2

1. 2.

3.does not exist 4.

5.

6.

7.

8.does not exist

9.

10.Xⴕ(ⴚ3, 0),Yⴕ(6, 6),Zⴕ(3,ⴚ6) 11.

12.an enlargement by a factor of

Lesson 4.3

1.yes 2.yes 3.no 4.yes 5.yes 6.yes 7. 8. 9. 10. 11.Dⴝ0; no inverse 12. 13. 14. 15.no inverse

冤

ⴚ3.5 2.5 ⴚ32

冥

冤

ⴚ1 3 ⴚ12

冥

D ⴝ4; inverse:

冤

_ⴚ1₄ ⴚ0.75_3.25

冥

D ⴝ2; inverse:

冤

_ⴚ_3.52 ⴚ_5.53

冥

D ⴝ5; inverse:

冤

_ⴚ_1.41 ⴚ_1.61

冥

D ⴝ1; inverse:

冤

_ⴚ4₅ ⴚ7₉

冥

D ⴝ1; inverse:

冤

_ⴚ3₄ ⴚ5₇

冥

3 2 Z' Y' X' _x y 2 –4 –6 6 2 –4 –6 4 6 Z X Y

冤

11₃₄ ⴚ328

冥

冤

23 ⴚ5 0

冥

32

冤

12.5 18 13 4 3

冥

冤

102 6 ⴚ10 ⴚ2 ⴚ6 5 1 3

冥

冤

4₇ ⴚ6 4

冥

[ⴚ20 4]

冤

ⴚ1 ⴚ9 45 44

冥

冤

4420 26 16 32 18 21 22 25 27 16 12

冥

United States Germany Russia China

冤

14₃ ⴚ2 14

冥

冤

ⴚ1 3 1 7 2 2 6 4 ⴚ7

冥

(12)

16. 17.no inverse 18. Lesson 4.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ; (4, ⴚ2, ⴚ1) 11. (3, 9, ⴚ6) 12. no solution 13. (ⴚ3, 5, ⴚ4) 14. (ⴚ1, 10, 2) Lesson 4.5 1. 2. 3. 4. 5. 6. 7.

冤

1 0 0 0 1 0 0 0 1 M M M 2 ⴚ1 4

冥

冤

1 0 0 0 1 0 0 0 1 M M M 1 3 2

冥

冤

1 0 0 0 1 0 0 0 1 M M M ⴚ2 1 ⴚ1

冥

冤

1 0 0 0 1 0 0 0 1 M M M 1 ⴚ2 ⴚ1

冥

冤

1 2 6 1 3 7 1 3 3 M M M ⴚ1 4 8

冥

冤

2 5 7 1 6 8 ⴚ3 1 ⴚ3 M M M 4 6 2

冥

冤

4 7 1 5 9 1 1 2 1 M M M 2 7 2

冥

冤

8 5 12 1 2 1 ⴚ1 ⴚ9 5

冥冤

x y z

冥

ⴝ

冤

0 ⴚ3 8

冥

;

冤

12 3 5 7 4 3 1 2 ⴚ3

冥冤

x y z

冥

ⴝ

冤

ⴚ5 3 12

冥

;

冤

1 3 5 ⴚ2 1 ⴚ10 1 ⴚ2 5

冥冤

x y z

冥

ⴝ

冤

15 8 21

冥

;

冤

1 3 3 ⴚ2 1 ⴚ2 ⴚ3 1 ⴚ4

冥冤

x y z

冥

ⴝ

冤

3 12 15

冥

;

冤

3 5 7 ⴚ3 6 5 5 ⴚ2 0

冥冤

x y z

冥

ⴝ

冤

13 10 18

冥

冤

4 8 0 1 ⴚ4 5 1 ⴚ7 9

冥冤

x y z

冥

ⴝ

冤

1 2 3

冥

; (0.5, ⴚ3, 2)

冤

3 5 ⴚ7 ⴚ8

冥冤

x y

冥

ⴝ

冤

2527

冥

; (ⴚ1, ⴚ4)

冤

7 4 53

冥冤

xy

冥

ⴝ

冤

149

冥

; (ⴚ3, 7)

冤

8 4 ⴚ79

冥冤

x y

冥

ⴝ

冤

655

冥

; (5, ⴚ5)

再

3x ⴙ 2y ⴚ z ⴝ ⴚ6 2x ⴙ 3y ⴙ z ⴝ 1 4x ⴙ 4y ⴙ 3z ⴝ 20

再

2x ⴙ 3y ⴚ z ⴝ 1 3x ⴙ 4y ⴙ z ⴝ 6 ⴚx ⴚ y ⴙ 2z ⴝ 7

冤

9 3 4 ⴚ5 1 ⴚ3 1 ⴚ1 ⴚ2

冥冤

x y z

冥

ⴝ

冤

6 2 ⴚ1

冥

冤

5 ⴚ1 4 ⴚ2 4 ⴚ8 1 ⴚ1 3

冥冤

x y z

冥

ⴝ

冤

13 ⴚ1 6

冥

冤

3 ⴚ1 2 1 ⴚ1 2 ⴚ1 3 1

冥冤

x y z

冥

ⴝ

冤

ⴚ19 21 ⴚ7

冥

冤

4 2 53

冥

冤

ⴚ1 2 ⴚ35

冥

(13)

8. 9. 10.(ⴚ3, 8) _11.(7,ⴚ1) _12.(ⴚ5, 4) 13.(1,ⴚ4, 6) _14.(ⴚ3, 2, 5) _15.(2,ⴚ4, 6) 16.(3, 4,ⴚ1) _17.(4,ⴚ1, 2) _18.(1, 4, 2) Practice — Chapter 5 Lesson 5.1 1. ;a ⴝ1,b ⴝ ⴚ8,c ⴝ15 2. ;a ⴝ1,b ⴝ ⴚ16, c ⴝ63 3. ;a ⴝ ⴚ3, b ⴝ30,c ⴝ33 4. ;a ⴝ6,b ⴝ13, c ⴝ ⴚ5 5. ;a ⴝ1,b ⴝ ⴚ6,c ⴝ5 6.yes 7.no 8.no 9.no 10.yes 11.yes

12.up; minimum value 13.up; minimum value 14.up; minimum value 15.down; maximum value

16. (0,ⴚ3) 17. (ⴚ0.5, 6.25) 18. (ⴚ1.75, 5.0625) Lesson 5.2 1.ⴚ10 or 10 2. 3.ⴚ12 or 6 4.ⴚ2兹5_{艐 ⴚ}4.47 or 2兹5_艐 4.47 ⴚ兹3_{艐 ⴚ}1.73 or 兹3_艐 1.73 x O y 2 –2 –6 4 2 –2 –4 6 x O y –2 –4 4 2 –2 4 x y 2 –2 –4 4 2 4 6 d(x)ⴝx2ⴚ6x ⴙ5 h(x)ⴝ6x2ⴙ13x ⴚ5 k(x)ⴝ ⴚ3x2ⴙ30x ⴙ33 g(x)ⴝx2ⴚ16x ⴙ63 f(x)ⴝx2ⴚ8x ⴙ15

冤

10 0 0 1 0 0 0 1 M M M 0 5 ⴚ4

冥

冤

10 0 0 1 0 0 0 1 M M M 3 ⴚ2 1

冥

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5.ⴚ4 or 4 6. or 7. or 8. or 9. or 10. or 11.c ⬇ 9.4 12.j ⬇ 5.8 13.r ⬇ 5.0 14.c ⬇ 16.6 15.b ⬇ 6.9 16.a ⬇ 2.4 17.c ⬇ 11.5 Lesson 5.3 1.12(x ⴚ 5) 2.ⴚ4x(6 ⴚ x) 3.(2 ⴚ 7x)(1 ⴚ 3x) 4.(4x ⴚ 3)(x ⴚ 12) 5.3x(x ⴙ 7) 6.ⴚ3x(x ⴚ 35) 7.(x ⴙ 4)(x ⴙ 13) 8.(x ⴚ 5)(x ⴙ 4) 9.(x ⴚ 9)(x ⴙ 2) 10.(x ⴙ 4)(x ⴙ 7) 11.(x ⴚ 10)(x ⴙ 9) 12.(x ⴙ 13)(x ⴚ 2) 13.(2x ⴙ 1)2 14.(3x ⴚ 1)(x ⴙ 2) 15.(2x ⴙ 1)(x ⴚ 2) 16.ⴚ16 or 16 17.ⴚ5 or 5 _18.ⴚ7 or ⴚ2 19.x ⴝ 1 20.1.5 21. 22. 23. 24. 25.ⴚ3, 4 _26.ⴚ2.5, 1 _27.ⴚ15, 3 28.6, 7 29.ⴚ2, 0.5 _30.ⴚ1.5 Lesson 5.4 1.x2ⴙ24x ⴙ 144; (x ⴙ 12)2 2.x2ⴚ40x ⴙ 400; (x ⴚ 20)2 3.x2ⴚ20x ⴙ 100; (x ⴚ 10)2 4.x2ⴙ5x ⴙ 6.25; (x ⴙ 2.5)2 5.x2ⴙ9x ⴙ 20.25; (x ⴙ 4.5)2 6.x2ⴚ19x ⴙ 90.25; (x ⴚ 9.5)2 7.ⴚ1.8 or 3.8 _8.2.3 or 5.7 9.ⴚ0.1 or 14.1 _10.ⴚ20.1 or 0.1 11.0.2 or 4.8 12.ⴚ0.6 or 6.6 13.ⴚ2.1 or 3.1 _14.ⴚ6.7 or ⴚ0.3 15.ⴚ8.2 or 0.2 16. 17.f(x) ⴝ ⴚ3x2ⴙ7; (0, 7); x ⴝ 0 18.f(x) ⴝ (x ⴚ 6)2ⴚ39; (6, ⴚ39); x ⴝ 6 19.f(x) ⴝ (x ⴚ 1)2ⴚ11; (1, ⴚ11); x ⴝ 1 20.f(x) ⴝ (x ⴚ 5)2ⴚ35; (5, ⴚ35); x ⴝ 5 21.f(x) ⴝ 3(x ⴙ 2.5)2ⴚ20.75; (ⴚ2.5, ⴚ20.75); x ⴝ ⴚ2.5 Lesson 5.5 1.0.3 or 9.7 2.0.3 or 3.7 3.ⴚ3.3 or 3.3 _4.ⴚ5.7 or 2.7 5.ⴚ5.6 or 1.6 _6.ⴚ6.9 or 1.9 7.ⴚ2.9 or 2.4 _8.1.4 or 5.6 9.ⴚ1.1 or 4.1 _10.ⴚ0.9 or 2.2 11.ⴚ2.2 or 3.7 _12.ⴚ0.6 or 0.4 13.x ⴝ ⴚ1; (ⴚ1, ⴚ5) 14.x ⴝ 1.5; (1.5, 11.75) 15.x ⴝ 1; (1, ⴚ1) 16.x ⴝ ; 17.x ⴝ 1; (1, ⴚ3) 18.x ⴝ ;

(

ⴚ2 5, ⴚ145

)

ⴚ2 5

(

ⴚ2 3, ⴚ1013

)

ⴚ2 3 f(x) ⴝ ⴚ1₂x2_{; (0, 0); x ⴝ 0} ⴚ2 7 or 1 1 or 1₅ ⴚ2 3 or 23 ⴚ1 3 or 12 ⴚ1 ⴙ 兹23 艐 3.80 ⴚ1 ⴚ 兹23 艐 ⴚ5.80 3兹2 艐 4.24 ⴚ3兹2 艐 ⴚ4.24 2 ⴙ 兹5 艐 4.24 2 ⴚ 兹5 艐 ⴚ0.24 兹6.5 艐 2.55 ⴚ兹6.5 艐 ⴚ2.55 2兹3 3 艐 1.15 ⴚ2兹3 3 艐 ⴚ1.15 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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Lesson 5.6 1.1; two; x ⴝ 1.5 or x ⴝ 1 2.ⴚ27; none; x ⴝ or 3.ⴚ68; none; or 4.ⴚ63; none; or 5.ⴚ87; none; or 6.ⴚ96; none; or 7.ⴚ2 ⴙ 11i _8.7 ⴚ 10i _9.13 ⴙ 9i 10.ⴚ1 ⴙ 3i _11.ⴚ15 ⴙ 5i _12.5i 13.ⴚ4 ⴙ i _14.4 ⴚ 5i _15.ⴚ8 ⴙ 7i 16.ⴚ15i _17.27 ⴙ 4i _18.ⴚ12 ⴚ 19i 19.ⴚ4 ⴚ 28i _20. _21.30 22.4 ⴚ 2i 23.ⴚ21 ⴙ 20i _24.18 ⴙ 6i 25.ⴚ4 ⴚ 5i _26.ⴚi Lesson 5.7 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14.9.25 feet 15.about 0.6 second 16.3 feet 17.about 1.4 seconds

Lesson 5.8 1. 2. 3. 4.no solution 5. 6. 7. x O y 2 –2 –4 4 2 –2 4 6 –5 –4 –3 –2 –1 0 1 2 ⴚ3.79 ⬍ x ⬍ 0.79 –2 –1 0 1 2 3 4 5 x ⬍ ⴚ0.30 or x ⬎ 3.30 –6 –8 –4 –2 0 2 4 ⴚ5 ⱕ x ⱕ ⴚ2 –6 –4 –2 0 2 4 6 ⴚ4 ⱕ x ⱕ 2 –6 –4 –2 0 2 4 6 x ⱕ ⴚ4 or x ⱖ 4 f(x) ⴝ ⴚ16x2_ⴙ_{20x ⴙ 3} f(x) ⴝ 5x2_ⴙ_{x ⴚ 7} f(x) ⴝ x2_ⴙ1 2x ⴙ 3 f(x) ⴝ x2_ⴚ_{9x ⴙ 2} f(x) ⴝ3₂x2_ⴚ_{x ⴙ 4} f(x) ⴝ 2x2_ⴙ_{4x ⴚ 5} f(x) ⴝ ⴚ3x2_ⴙ_{3x ⴚ 2} f(x) ⴝ ⴚ2x2_ⴙ_{7x ⴚ 3} f(x) ⴝ 6x2_ⴚ_{3x ⴚ 1} f(x) ⴝ 5x2_ⴙ_{2x ⴚ 3} f(x) ⴝ 0.5x2_ⴙ_{x ⴚ 3} f(x) ⴝ 3x2_ⴚ_{2x ⴙ 5} f(x) ⴝ ⴚ4x2_ⴙ_{3x ⴙ 2} 12 13ⴚ135i x ⴝ1₂ⴚi兹6 2 x ⴝ1₂ⴙi兹6 2 x ⴝ1₄ⴙi兹87 12 x ⴝ1₄ⴚi兹87 12 x ⴝ1₈ⴙ3i兹7 8 x ⴝ1₈ⴚ3i兹7 8 x ⴝ1₃ⴙi兹17 3 x ⴝ1₃ⴚi兹17 3 x ⴝ ⴚ3₂ⴙ3i兹3 2 ⴚ3 2ⴚ3i兹32 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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8. 9. 10. 11. 12. Practice — Chapter 6 Lesson 6.1 1.1.01 2.0.9 3.0.93 4.1.12 5.1.1 6.0.97 7.0.948 8.1.075 9.1.004 10.0.941 11.1.414 12.15.874 13.0.016 14.28 15.35.318 16.226.274 17.1.875 18.8.25 19.630.346 20.271.529 21a.1,275,868 b.1,307,375 22a.6400 b.25,600 Lesson 6.2

1.quadratic 2.linear 3.linear 4.exponential 5.quadratic 6.exponential 7.linear 8.exponential 9.exponential 10.exponential growth 11.exponential decay 12.exponential decay 13.exponential growth 14.exponential growth 15.exponential decay x y 4 2 –2 –4 4 2 6 –2 x O y 6 4 2 –2 –2 2 4 –4 –6 x y 6 4 2 –2 –6 –8 x y 2 4 6 –2 2 –4 –6 x O y 2 –6 2 –2 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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16.exponential decay 17.exponential growth 18.exponential growth 19.$2117.56 20.$1075.52 21.$977.06 22.$1226.08 23.$343.10 24.$1294.22 25.$5325.11 26.$2358.76 Lesson 6.3 1.log₁₉361 ⴝ 2 2.log₂₀8000 ⴝ 3 3.log₃₃₇₅15 ⴝ 4. 5. 6. 7.122ⴝ144 _8.56ⴝ15,625 9.213ⴝ9261 _10. 11. 12. 13.x⬇ 1.54 14.x⬇ 1.96 15.x⬇ ⴚ0.70 16.x⬇ 0.26 17.x⬇ ⴚ1.10 18.x⬇ 3.02 19.vⴝ3 _20.vⴝ2 _21.vⴝ2 22.vⴝ256 _23. _24. 25.vⴝ10 _26.vⴝ3 _27.vⴝ4 Lesson 6.4

1.log₁₀4 ⴙ log₁₀100 ⴝ log₁₀4 ⴙ 2 2.log₅72 ⴚ log₅25 ⴝ log₅72 ⴚ 2 3.log₇5 ⴙ log₇3 ⴙ log₇4

4.log₃15 ⴙ log₃q

5.log₈64 ⴚ log₈4 ⴝ 2 ⴚ log₈4 6.log₉3 ⴙ log₉aⴚlog₉7 ⴝ

0.5 ⴙ log₉aⴚlog₉7 7.log₃30 8.log₅ 9.log₈64 ⴝ 2 10.log₉ 11.log₁₂144 ⴝ 2 12.log₃135 13.log_b 14.log_b ⴝlog_b 15.log_b ⴝlog_b 16.12 17.73 18. 2.5 19.4.7 20.ⴚ1 21.10 22.2 23.2 24. 25.ⴚ3, 3 26.ⴚ1, 6 _27.3 _28.4 _29.2 Lesson 6.5 1.x⬇ 1.72 2.x⬇ 0.95 3.x⬇ 6.64 4.x⬇ 1.19 5.x⬇ 2.81 6.x⬇ ⴚ0.48 7.x⬇ 1.05 8.x⬇ ⴚ0.11 9.x⬇ 1.46 10.x⬇ 1.16 11.x⬇ 1.43 12.x⬇ 0.90 13.x⬇ 4.09 14.x⬇ 1.33 15.x⬇ 0.42 16.xⴝ1.76 _17.xⴝ2.18 _18.xⴝ3.70 19.xⴝ ⴚ0.57 _20.xⴝ3.19 _21.xⴝ0.40 22.xⴝ1.16 _23.xⴝ3.09 _24.xⴝ1.30 25.xⴝ ⴚ0.46 _26.xⴝ ⴚ0.55 _27.xⴝ1.43 28.xⴝ7.32 _29.xⴝ3.42 _30.xⴝ ⴚ0.65 4 3 z2y 4 z3y 4z x2 4 x3 4x 2m x 5y 4 x 2 vⴝ 1 343 vⴝ 1 625

(

1 5

)

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Lesson 6.6 1.2980.958 2.12.182 3.181.272 4.109.196 5.3.555 6.2.534 7.not defined 8.1.242 9.4.718 10.ln 55 ⬇ x 11.e3.78⬇44 12.ln 0.05 ⬇ ⴚ3 13.e2.30⬇10 14.ln 54.6 ⬇4 15.e4.83⬇125 16.ln 148 ⬇5 17.e0ⴝ1 18.ln 0.45 ⬇ ⴚ0.8 19.x ⬇1.23 20.x ⬇1.10 21.x ⬇2.17 22.x ⬇ ⴚ8.67 23.x ⬇10.48 24.x ⬇ ⴚ0.75 25.x ⬇ ⴚ1.17 26.x ⬇ ⴚ1.34 27.x ⬇0.78 28.$1215.31 Lesson 6.7 1.x ⴝ4 2. 3.x ⴝ2 4.x ⴝ1000 5. 6. 7. 8.x ⴝ5 9.x ⴝlog 28 ⬇1.45 10.x ⴝ4 11.x ⴝ4 12.x ⴝ6 13.x ⴝ3 14. 15. 16.x ⴝ3 ln 0.64 ⬇ ⴚ1.34 17.5.0ⴛ1021ergs 18.7.2 Practice — Chapter 7 Lesson 7.1

1.yes; quintic trinomial 2.yes; quadratic trinomial 3.no 4.yes; cubic polynomial 5.no 6.no 7.ⴚ36 _8.ⴚ2 9.61 10.410 11.80 12.ⴚ152 13.8x4ⴙ11x3ⴙ5x2 14.22x5ⴚ13x4ⴚ3x2ⴚx ⴙ8 15.ⴚx4ⴚ5x3ⴙ10x2ⴚ1.2x ⴙ2 16.5.1x3ⴙ12.2x2ⴚ7x ⴙ26 17. upside-down W-shape 18. W-shape x y 2 –4 –2 4 2 x O y 2 –2 –4 4 2 4 –4 –2 6 x ⴝe₂3艐10.0 x ⴝ4₃ x ⴝ1₃ ln 15 艐 0.90 x ⴝln 6_{ln 9}艐 0.82 x ⴝ1₂ x ⴝ2₃艐 0.67 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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19.

S-shape

Lesson 7.2

1.local minimum at (ⴚ1.5, 1.75) 2.local maximum at (0.2, 6)

3.local maximum at (0, 1); local minimum at (0.7, 0.7)

4.local maximum at (ⴚ0.2, 2.2); local minima at (ⴚ1.7, 2.7) and (1.3,ⴚ2.3) 5.local maximum at (0, 2); local minimum

at (0.5, 1.8); increasing for ⴚ6_ⱕx ⱕ0 and 0.5 ⬍ x ⱕ6; decreasing for 0 ⬍ x ⱕ

0.5

6.local maximum at (ⴚ0.7, 0.4); local minima at (ⴚ2.3,ⴚ1.5) and (0.5,ⴚ0.4); increasing for ⴚ2.3_ⱕx ⱕ ⴚ0.7 and 0.5ⱕ x ⱕ4; decreasing for

ⴚ4_ⱕx ⱕ ⴚ2.3 and ⴚ0.7_{ⱕ x ⱕ}0.5 7.local maximum at (ⴚ0.8,ⴚ1.7); local

minimum at (0,ⴚ2); increasing for ⴚ5_{ⱕ x ⱕ ⴚ}0.8 and 0 _{ⱕ x ⱕ}4; decreasing for ⴚ0.8_{ⱕ x ⱕ}0

8.local maxima at (0, 1) and (1.6, 2.1); local minimum at (0.3, 1.0); increasing for ⴚ4_ⱕx ⱕ0 and 0.3 _{ⱕ x ⱕ}1.6; decreasing for 0ⱕ x ⱕ0.3 and 1.6 ⱕ x ⱕ4

9.rises on the left, falls on the right

10.falls on the left, rises on the right 11.falls on the left and on the right 12.rises on the left and on the right

13.f(x)ⴝ ⴚ4.17x4ⴚ30.83x3ⴙ473.42x2ⴚ 1019.27x ⴙ6039.64 Lesson 7.3 1.8x5ⴚ5x4ⴙ3x2 2.2x2ⴚ17x ⴚ30 3.5x3ⴚ17x2ⴚ5x ⴚ28 4.x3ⴚ7x2ⴚ10x ⴙ16 5.2x3ⴚx2ⴚ8x ⴚ5 6.27x3ⴚ27x2ⴙ9x ⴚ1 7.no 8.yes 9.no 10.yes 11.yes 12.no 13.2x ⴚ5 14.2x ⴚ1ⴚ 15.4x2ⴙ4x ⴙ1ⴙ 16.5x2ⴚ4x ⴙ3 _17.x ⴚ3 18.x2ⴙ3x ⴙ4 _19.x ⴙ3 20.x3ⴙ2x ⴙ 21.11 22.25 23.10 24.83 Lesson 7.4 1.ⴚ9, 0, and 9 _2.0, 1, and 10 3. , 0, and 1 4.ⴚ5, 0, and 3 5.ⴚ3, 0, and 4 _6.0, , and 1 7.ⴚ2, 2, and 3 _8.ⴚ3,ⴚ2, and 1 9.3,ⴚ4, and _10.ⴚ1, 6, and 7 11.ⴚ1 and 6 (multiplicity 2) 1 3 1 3 ⴚ1₂ 6x ⴚ3 x2ⴚ3 4 2x ⴙ1 5x 3x ⴙ5 x O y 2 –2 –4 4 2 –2 –4 4 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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12.ⴚ4 and 4 (multiplicity 2) 13. , and 14. , and 15. , and 3 16. , and 17.ⴚ4, 4,ⴚ1, 1 18. , and 19.1.3, 0.3, and ⴚ1.5 20.ⴚ1.2,ⴚ0.4, and 0.3 21.ⴚ0.9, 0 (multiplicity 2), and 0.9 22.ⴚ0.2, 0.4, and 1.1 23.ⴚ0.4, 0.3, and 0.9 24.ⴚ2.9,ⴚ2.4,ⴚ0.2, and 1.4 Lesson 7.5 1. and 1 2.ⴚ2, , and 2 3.ⴚ1, , and 4. , 1, and 2 5.ⴚ1 (multiplicity 2), , and 4 6. , and 1 7.ⴚ5, , and 8.ⴚ3, 2i, andⴚ2i 9.3, , and 10.5, 3i, andⴚ3i 11.2,ⴚ2ⴙ2i, andⴚ2ⴚ2i 12.1, 4,i, andⴚi 13.ⴚ1.46 and 1.66 14.ⴚ2.24, 0, and 2.24 15.ⴚ1.41, 0, and 1.41 16.ⴚ1.85 and 1.16 17.P(x)ⴝ5x3ⴚ15x2ⴚ50x ⴙ120 18.P(x)ⴝ ⴚ2x3ⴚ6x2ⴚ32x ⴚ96 Practice — Chapter 8 Lesson 8.1 1. ; 16.8, 8.4, 5.25, 4.2 2. ; 8, 0.16, 0.1, 0.04 3. ; 25, 10, 7.5, 2.5 4. ; 9.6, 0.8, 0.48, 0.3 5.y ⴝ8xz; 4 6.y ⴝ24xz; 144 7.y ⴝ0.6xz; 10.8 8.y ⴝ32xz; 96 9. ; 75 10. ; 9 11. ; 10 12. ; 17.5 13.0.5;A ⴝ0.5ap; 13.8 in.2 Lesson 8.2

1.yes; all real numbers except and 2.no; |x|ⴚ2 is not a polynomial. 3.yes; all real numbers except ⴚ1 and 1 4.vertical:x ⴝ9; horizontal:y ⴝ2 兹3 ⴚ兹3 z ⴝ12_wxy z ⴝ5₂xy_w z ⴝ8_wxy z ⴝ20_wxy y ⴝ4.8_x y ⴝ150_x y ⴝ0.8_x y ⴝ84_x ⴚ2i兹3 2i兹3 ⴚi兹2 i兹2 ⴚ2₃,ⴚ1₂,2₃ 1 2 ⴚ1₄ 1 2 1 3 1 3 1 5 兹10 ⴚ兹2,兹2,ⴚ兹10 兹5 ⴚ兹2,兹2,ⴚ兹5 ⴚ兹6,兹6,ⴚ3 兹7 ⴚ兹3,兹3,ⴚ兹7 兹6 ⴚ2, 2, ⴚ兹6 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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5.vertical:x ⴝ1.5; horizontal:y ⴝ0

6.vertical: and ;

horizontal:y ⴝ0

7.all real numbers except 0 and 6;

vertical:x ⴝ0,x ⴝ6; horizontal:y ⴝ0 8.all real numbers except 1 and ⴚ5;

vertical:x ⴝ ⴚ5; horizontal:y ⴝ0; hole at x ⴝ1

9.all real numbers except ⴚ3 and ⴚ4; vertical:x ⴝ ⴚ3, horizontal:y ⴝ3; hole at x ⴝ ⴚ4 10. 11. 12. Lesson 8.3 1. 2. 3. 4. 5. 6.3x6 7.3x ⴚ9 8.1 9. 10.x 11.x2ⴚx ⴚ12 12. 13. 14. 15. 16. 17. 18. Lesson 8.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.0 16. 17. 18. 19. 20. 21. 22. 23. Lesson 8.5 1.3.5 2.11 3.7.5 4.15 5. ,ⴚ3 6.ⴚ2,ⴚ4 _7.ⴚ2.5 _8.2 _9.7, 1 10.0, 11.6 12.1 13.x ⬍2or x ⬎4 14.x ⬍6or x ⬎12 15.ⴚ1_{⬍ x ⬍}0or x ⬎1 _16.x ⬍2or x ⬎3 17.1⬍ x ⬍3 18.x ⬍ ⴚ3or ⴚ2⬍ x ⬍2 19.x ⬍ⴚ1or ⬍ x ⬍1 ⴚ3 4or x ⬎15 ⴚ1₃ ⴚ3₄ 1 2 3ⴙ4y ⴙ2x (x ⴙ3)(y ⴚ2) ⴚ2(3x2ⴙ2x ⴙ5) (3x ⴙ2)(x ⴚ5) x ⴚ3 x ⴚx ⴙ6 (x ⴙ3)(x ⴚ3) 2(x ⴚ2) x ⴚ4 2x x ⴚ5 1 x ⴙ3 3 x ⴙ7 x ⴚ1 2x(x ⴙ1) x2ⴙ3 x x ⴚ3 2x ⴚ1 4x ⴚ1 x ⴚ2 2x ⴙ28 x ⴚ3 ⴚ 1 x ⴚ5 x ⴚ3 x ⴙ8 ⴚ2 x 16 x2ⴚ16 2x2ⴙ2x ⴙ13 x2ⴙx ⴚ6 5x ⴚ2 3x2ⴚ12 5 6x 3x ⴚ7 x3ⴙ1 7x ⴚ22 12 3y3 (x ⴚ y) 4x x ⴙ5 3x ⴙ21 x x ⴚ3 2x ⴚ1 x ⴚ2 x2ⴚ3x 3x ⴚ12 x ⴚ1 x ⴙ1 1 x2ⴚ5x ⴚ50 4 x ⴙ2 x ⴙ4 x ⴚ2 1 2x2 3x ⴙ2 3x ⴚ2 x ⴚ7 x ⴙ7 3 x2 x O y 2 –2 –4 4 y = 1 x = 1 hole 2 –2 –4 4 x O y 1 2 y = 0 x = 1₂ hole x O y –4 8 4 –4 –8 8 x = 4 y = 3 x ⴝ 兹7 x ⴝ ⴚ兹7 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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21.x ⬍ ⴚ1 or x ⬎ 1 22.ⴚ2.2 ⱕ x ⬍ 3 or x ⬎ 3 23.ⴚ4 ⬍ x ⬍ 0.5 or x ⬍ ⴚ4.5 24.x ⬍ 0.7 or 4 ⬍ x ⬍ 4.3 25.0 ⬍ x ⬍ 2 26.x ⬍ ⴚ6.5 or 0 ⬍ x ⬍ 2.5 or x ⬎ 4 27.ⴚ1.4 ⬍ x ⬍ 0 or 1.4 ⬍ x ⬍ 2 Lesson 8.6 1.x ⱖ 2.5 2.x ⱖ 4 3.x ⱕ ⴚ6 or x ⱖ 6 4.x ⱕ ⴚ2.5 or x ⱖ 2.5 5.x ⱖ 5 6.x ⱕ ⴚ3 or x ⱖ ⴚ1 7. 8. 9. 10.4 11.7.5 12.ⴚ6 _13.ⴚ24 14.4 15.ⴚ2 _16. ; 12.4 feet Lesson 8.7 1.2 2.3 3.12|x|y2 4.7xy3 5. 6. 7.2x2 8.4xy2 9.10x4y2 10. 11. 12. 13. 14. 15. 16. 17. 18.432 19. 20. 21. 22. 23. 24. Lesson 8.8 1.95 2.10 3.ⴚ4, 4 4.no solution 5. 6.2, 6 7.no solution 8.2, 3 9.5 10.3 ⱕ x ⱕ 12 11.x ⬎ 14 12.0 ⱕ x ⬍ 13.x ⬍ ⴚ0.5 or x ⬎ 2.5 14.x ⬎ 1 15.8 ⬍ x ⬍ 13 16.no solution 81₃ ⴚ兹2, 兹2 9兹7 ⴙ 9兹2 5 5兹3 ⴚ 5兹2 16 ⴙ 8兹3 7兹2 ⴚ 7 4兹2 兹2 ⴚ58 ⴚ 13兹5 ⴚ24 ⴚ 15兹2 5 ⴚ 兹2 3 ⴙ 13兹3 25 ⴙ 2兹2 2x2_y2 4_兹2xy2 2yz兹3xyz3 2y兹x5 2_yz3 兹y 3 兹x ⴚ2xy(2y) 1 3 4x2_(5x)12 3 兹x2_z 兹2 3

兹

6V π d ⴝ x O y 2 2 y = x2_{– 2x – 5} y = 1 – √x + 6 y = 1 + √x + 6 y ⴝ 1 ⴚ 兹x ⴙ 6, y ⴝ 1 ⴙ 兹x ⴙ 6 x y –4 6 4 2 –2 4 y = 2 – x2 O y = √2 – x y = –√2 – x y ⴝ ⴚ兹2 ⴚ x, y ⴝ 兹2 ⴚ x x O y 2 4 6 6 8 y = x2_{– 6x + 8} y = 3 + √x + 1 y = 3 – √x + 1 y ⴝ 3 ⴚ 兹x ⴙ 1, y ⴝ 3 ⴙ 兹x ⴙ 1 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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17.x ⬍ ⴚ6.5 18. ⱕ x ⱕ 13 19.x ⬎ 5.6 20.ⴚ1.8 ⱕ x ⱕ 1.5 _21.ⴚ4 ⱕ x ⱕ 1.3 22.x ⱖ 5.8 23.x ⬎ 0.4 24.0.4 ⱕ x ⱕ 0.8 or x ⱖ 6.2 25.ⴚ9 ⱕ x ⱕ ⴚ0.8 or x ⱖ 3.9 26.x ⬎ 3.4 27.x ⱖ 10.5 Practice — Chapter 9 Lesson 9.1 1. parabola 2. circle 3. hyperbola 4.13; (2.5, 6) 5.10; (8, ⴚ2) 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 ⴙ 1 ⴝ (x ⴚ 3)2 x ⴙ 1 ⴝ1₄y2 y ⴝ₁₂1(x ⴚ 3)2 562π 4 π_兹562 101π 4 π_兹101 145π 4 π_兹145 289π 4 1681π 4 兹13 艐 3.61; (0, 0.5) 12兹2 艐 16.97; (ⴚ2, ⴚ2) 兹85 艐 9.22; (3, 4) 2兹101 艐 20.10; (2, 3) 2 4 –4 4 –4 –2 O x y y ⴝ ⴚ3兹x2_ⴚ_{1, y ⴝ 3兹x}2_ⴚ₁ 10 10 –10 –10 O x y y ⴝ ⴚ兹400 ⴚ x2_{, y ⴝ 兹400 ⴚ x}2 2 2 4 6 8 4 –4 –2 O x y y ⴝ1₃x2 3 4 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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4. 5. 6. 7. 8. 9. 10. 11. 12. Lesson 9.3 1.(x ⴙ 5)2ⴙ(y ⴚ 2)2ⴝ16 2.(x ⴚ 6)2ⴙ(y ⴚ 3)2ⴝ 3.x2ⴙ(y ⴙ 4)2ⴝ25 4.x2ⴙy2ⴝ 5.(x ⴙ 2)2ⴙ(y ⴚ 1)2ⴝ6.25 6.(x ⴙ 3)2ⴙ(y ⴙ 3)2ⴝ576 7. 8. 9. 10.(x ⴚ 5)2ⴙ(y ⴚ 8)2ⴝ1; C(5, 8); r ⴝ 1 11.(x ⴙ 11)2ⴙ(y ⴚ 1)2ⴝ2; C(ⴚ11, 1); Lesson 9.4 1. 2.(x ⴙ 3) 2 4 ⴙ(y ⴙ 2) 2 16 ⴝ1 x2 64ⴙy 2 36ⴝ1 r ⴝ 兹2 x O y 2 –2 –4 –6 2 6 (3, 3) r = 3 x O y 2 4 6 8 2 4 –2 –4 r = 4 _{(0, 5)} x O y –8 8 (0, 0) r = 16 8 –8 9 16 25 4 y ⴝ₂₀1(x ⴚ 9)2 x ⴚ 6 ⴝ ⴚ1₈(y ⴙ 7)2 y ⴚ 2 ⴝ1₄(x ⴚ 5)2 x ⴝ₁₂1 y2 x ⴚ 10 ⴝ1₈y2 y ⴝ₂₄1x2 2 2 4 6 4 F(3, 2) V(1, 2) x = –1 6 directrix O y x 2 2 4 6 8 4 F(1, 5) V(1, 4) y = 3 –2 –4 directrix O y x 2 2 4 –2 4 F(1, 0) x = –1 6 directrix O y x V(0, 0) Copyright © by Holt, Rinehart and Winston. All rights reserved.

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3. 4. 5. 6. 7. 8. 9. 10. ; center: (ⴚ3, 0) foci: (ⴚ3 ⴚ , 0) and (ⴚ3 ⴙ , 0); vertices: (ⴚ9, 0) and (3, 0); co-vertices: (ⴚ3, ⴚ3), and (ⴚ3, 3) Lesson 9.5 1. 2. 3. 4. 5. 6. 7. 8. ; center: (14, ⴚ3); vertices: (12, ⴚ3) and (16, ⴚ3); co-vertices: (14, ⴚ4) and (14, ⴚ2); foci: and Lesson 9.6 1.(1, 6) and (4, 21) 2.none 3.(ⴚ2.83, ⴚ2.83) and (2.83, 2.83) 4.(ⴚ3, 0) and (3, 0) (14 ⴙ 兹5, ⴚ3) (14 ⴚ 兹5, ⴚ3) (x ⴚ 14)2 4 ⴚ(y ⴙ 3)2ⴝ1 (y ⴚ 1)2 25 ⴚ(x ⴚ 1) 2 144 ⴝ1 x2 9 ⴚ(y ⴙ 2) 2 16 ⴝ1 x2 10ⴚy 2 15ⴝ1 x O y –2 –4 –6 2 4 6 C (1, 1) y = – x –3₄ 1₄ y = x +3₄ 1₄ (1, 4) (5, 1) (6, 1) (–4, 1) (–3, 1) (1, –2) x y –2 –4 2 4 C (0, 0) y = – x5₃ 2 4 –2 y = x5₃ (0, –√34) (0, 3) (0, –3) (–5, 0) (5, 0) (0, √34) y2 16ⴚx 2 25ⴝ1 x2 9 ⴚy 2 16ⴝ1 3兹3 3兹3 (x ⴙ 3)2 36 ⴙy 2 9 ⴝ1 x2 400ⴙ y 2 464ⴝ1 x2 109ⴙy 2 9 ⴝ1 x2 625ⴙ y 2 225ⴝ1 x O y 1 –2 –4 –6 2 4 6 8 (1, –3) (7, –3) (4, 2) (4, 1) (4, –3) (4, –7) (4, –8) x O y 4 –8 4 –4 –8 8 (7, 0) (0, 3) (0, 1) (1, –3) (–7, 0) (0, –5) (0, 7) x y 4 4 –4 –8 8 (0, √77) (0, –√77) (0, 9) (0, 0) (–2, 0) (2, 0) (0, –9) (x ⴚ 3)2 25 ⴙ(y ⴚ 2) 2 9 ⴝ1 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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5.(ⴚ2.24,ⴚ1.73), (ⴚ2.24, 1.73), (2.24, –1.73), and (2.24, 1.73) 6.(ⴚ4.24,ⴚ2.45), (ⴚ4.24, 2.45), (4.24,ⴚ2.45), and (4.24, 2.45) 7.none 8.(ⴚ2.08,ⴚ1.44), (ⴚ2.08, 1.44), (2.08,ⴚ1.44), and (2.08, 1.44) 9.none 10.parabola; 11.hyperbola; Practice — Chapter 10 Lesson 10.1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.1,000,000 15.676,000 16.456,976,000 17.67,600,000 18.6,760,000 Lesson 10.2 1.5040 2.2520 3.840 4.840 5.479,001,600 6.about 4.36 ⴛ1010 7.about 2.18 ⴛ1011 8.about 6.03 ⴛ1013 9.20,160 10.2520 11.10,080 12.5040 13.4,989,600 14.907,200 15.43,758 16.720 17.5040 18.3,628,800 Lesson 10.3 1.56 2.120 3.35 4.6435 5.84 6.60 7.40 8.5 9.40 10.about 33% 11.about 39% 12.about 16% 13.combination 14.combination 15.permutation 16.permutation Lesson 10.4 1.inclusive; 2.mutually exclusive; 3.inclusive; 4.inclusive;39₅₂ⴝ75% 19 26艐73% 6 13艐46% 4 13艐31% 85 150艐57% 107 150艐71% 43 150艐29% 65 150艐43% 42 150ⴝ28% 1 6艐17% 21 26艐81% 1 3艐33% 11 13艐85% 1 2ⴝ50% 5 11艐45% 4 5ⴝ80% 7 10ⴝ70% x O y 2 4 6 4 2 6 8 (x ⴚ5)2 9 ⴚ(y ⴚ4) 2 4 ⴝ1 x O y 2 4 6 8 –2 4 2 6 8 y ⴚ3ⴝ1₄(x ⴚ7)2 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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5.mutually exclusive; 6.inclusive; 7. 8. 9. 10. 11. 12. 13. 14. 15. Lesson 10.5 1.0.02ⴝ2% _2.0.08ⴝ8% 3.0.04ⴝ4% _4.0.05ⴝ5% 5.0.008ⴝ0.8% _6.0.01ⴝ1% 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Lesson 10.6 1. 2. 3. 4. 5. 6. 7. 8. 9.1ⴝ100% 10. 11. 12. 13. 14. 15. 16. 17.0.625ⴝ62.5% 18. 19. 20.0.064ⴝ6.4% _21.0.4ⴝ40% 22.0.5625ⴝ56.25% Lesson 10.7

1–6.Simulation results will vary.

Practice — Chapter 11 Lesson 11.1 1.2.5, 5, 7.5, 10, 12.5, 15 2.0, , 1, 1 , 2, 2 3.13, 16, 21, 28, 37, 48 4.20, 70, 220, 670, 2020, 6070 5.1, 101, 201, 301, 401, 501 6.ⴚ5,ⴚ15,ⴚ45,ⴚ135,ⴚ405,ⴚ1215 7.a₁ⴝ1;a_nⴝ11a_{n ⴚ}₁; 14,641; 161,051; 1,771,561 8.a₁ⴝ81;a_nⴝa_{n ⴚ}₁ⴚ3; 69, 66, 63 9.a₁ⴝ2;a_nⴝ ⴚ3a_{n ⴚ}₁; 162,ⴚ486, 1458 10.a₁ⴝ ;a_nⴝ ⴚ4a_{n ⴚ}₁; 64,ⴚ256, 1024 11.a₁ⴝ2;a_nⴝ3a_{n ⴚ}₁ⴙ5; 362, 1091, 3278 12.a₁ⴝ ⴚ2;a_nⴝ5a_{n ⴚ}₁ⴚ4;ⴚ1874;ⴚ9374; ⴚ46,874 13.4.5ⴙ9ⴙ13.5ⴙ18ⴙ22.5ⴙ27ⴙ31.5; 126 14.11ⴙ22ⴙ35ⴙ50ⴙ67; 185 15.210 16.ⴚ24 _17.10 18.1432.5 19.397 20.1911.4 1 4 1 2 1 2 1 2 1 2ⴝ50% 9 10ⴝ90% 1 3艐33% 1 2 ⴝ50% 4 5ⴝ80% 1 5ⴝ20% 2 5 ⴝ40% 3 5ⴝ60% 1 4ⴝ25% 1 2ⴝ50% 1 8ⴝ12.5% 1 8 ⴝ12.5% 1 2 ⴝ50% 1 3艐33% 2 3 艐67% 1 2 ⴝ50% 1 6艐17% 1 3艐33% 1 12艐8% 1 8ⴝ12.5% 1 24艐4% 4 9艐44% 1 36艐3% 1 4ⴝ25% 1 9艐11% 1 18艐6% 7 72艐10% 25 36艐69% 3 16ⴝ18.75% 1 24艐4% 49 144艐34% 5 18艐28% 22 36艐61% 5 9艐56% 13 36艐36% 19 36艐53% 3 4ⴝ75% 3 8ⴝ37.5% 5 8ⴝ62.5% 5 8ⴝ62.5% 41 52艐79% 27 52艐52% Copyright © by Holt, Rinehart and Winston. All rights reserved.

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Lesson 11.2 1.yes;d ⴝ3 2.no 3.yes;d ⴝ2.5 4.no 5.yes;d ⴝ 6.yes;d ⴝ ⴚ2.3 7.t_nⴝ25ⴚ9n _8.t_nⴝ8n ⴚ23 9.t_nⴝ3n ⴙ10 _10.t_nⴝ12n ⴚ37 11.t_nⴝ11n ⴚ2 _12.t_nⴝ9.9ⴚ1.3n 13.50, 150, 250, 350 14.7.5, 10, 12.5, 15 15.ⴚ20,ⴚ12,ⴚ4, 4 _16.25, 65, 105, 145 17.8.5, 9, 9.5, 10 18.ⴚ15,ⴚ27,ⴚ39,ⴚ51 19.ⴚ5, 2, and 9 _20.52, 64, 76, and 88 21.62 and 74 22.10.5, 14, and 17.5 23.34, 28, and 22 24.ⴚ2, 4, 10, and 16 Lesson 11.3 1.350 2. 3.ⴚ165 _4.2905 5.711 6.1482 7.25,425 8.360 9.1300 10.9555 11.9555 12.330 13.990 14.165 15.239.25 16.ⴚ1914 17. 18.84 19.ⴚ132 20.590 21.228 22.795 23.ⴚ351 Lesson 11.4 1.no 2.yes;r ⴝ0.4 3.yes;r ⴝ 4.yes;r ⴝ1.5 5.yes;r ⴝ 6.no 7.18,ⴚ36, 72,ⴚ144 8.ⴚ4,ⴚ10,ⴚ25,ⴚ62.5,ⴚ156.25 9.10, 5, 2.5, 1.25 10.0.625 or ⴚ0.625 11. or 12. or 13. 14.t_nⴝ ⴚ30(ⴚ0.2)n ⴚ1 15.t_nⴝ40(0.8)n ⴚ1 16.t_nⴝ _17.t_nⴝ 18.t_nⴝ 19.35 and 175 20.ⴚ14 and ⴚ7 21.48, 192, and 768 or ⴚ48, 192, and ⴚ768 22.15, 18, and 21.6 or ⴚ15, 18, and ⴚ21.6 23.60, 300, and 1500 or ⴚ63, 300, and ⴚ1500 24.12, 36, 108, and 324 Lesson 11.5 1.6,973,568,800 2.86.4 3.ⴚ147 4. 5.ⴚ1064.7 6.6144 7.1,572,864 8.12,285 9.3,145,725 10.378 11.1,708,554.00 12.1.67 13.14,348,906

14.Show the statement is true for n ⴝ1:

13ⴝ1 and .Assume that the

statement is true for a natural number k. Then

13ⴙ23ⴙ33ⴙ…ⴙk3ⴝ and 13ⴙ23ⴙ33ⴙ…ⴙk3ⴙ(k ⴙ1)3ⴝ

. Thus, the statement is true for k ⴙ1.

(k ⴙ1)2[(k ⴙ1)ⴙ1]2 4 (k ⴙ1)2(k ⴙ2)2 4 ⴝ (k ⴙ1)2(k2ⴙ4k ⴙ4) 4 ⴝ (k ⴙ1)2[k2ⴙ4(k ⴙ1)] 4 ⴝ k2(k ⴙ1)2ⴙ4(k ⴙ1)3 4 ⴝ k2(k ⴙ1)2 4 ⴙ(k ⴙ1)3ⴝ k2(k ⴙ1)2 4 12₍₁ⴙ1)2 4 ⴝ1 5467 3125⬇1.7 ⴚ1₄(ⴚ6)n 80

(

1₄

)

n 2

(

5₂

)

nⴚ1 t_nⴝ250

(

2₅

)

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Lesson 11.6

1.does not exist 2.1.2 3.2.625 4.25 5.4 6.does not exist 7.12.375 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 11.7

1.sixth entry, row 7; 21 2.fourth entry, row 6; 20 3.seventh entry, row 8; 28 4.sixth entry, row 10; 252 5.eleventh entry, row 13; 286 6.sixth entry, row 12; 792

7.120 8.1716 9.6435 10.153 11.0.3125 12.about 0.66 13.about 0.01 14.about 0.64 15.0.5 16.0.4375 17.about 0.23 18.about 0.89 19.about 0.34 20. about 0.09 21.about 0.66 22. about 0.34 Lesson 11.8 1.s5ⴙ5s4tⴙ10s3t2ⴙ10s2t3ⴙ5st4ⴙt5 2.b6ⴙ6b5wⴙ15b4w2ⴙ20b3w3ⴙ 15b2_w4ⴙ6bw5ⴙw6 3.16 terms 4.3 5.3003r5s10 6.3125x5ⴙ3125x4yⴙ1250x3y2ⴙ 250x2_y3ⴙ25xy4ⴙy5 7. w4ⴙw3zⴙ6w2z2ⴙ16wz3ⴙ16z4 8. a5ⴚ a4dⴙ a3d2ⴚ a2d3ⴙ ad4ⴚd5 9.64m6ⴚ576m5qⴙ2160m4q2ⴚ 4320m3_q3ⴙ4860m2q4ⴚ2916mq5ⴙ 729q6 10.about 0.20 11.about 0.26 12.about 0.74 13.about 0.11 14.about 0.61 Practice — Chapter 12 Lesson 12.1 1.66; 62; 62 2.24.571; 28; 28 3.3.617; 3.6; 3.6 4.622.833; 725; 725 5.2593.333; 1714; 1600

6.24.05; 24.25; 25; all are reasonable measures because they are so close, but the mean and median are better than the mode because 6 of the 8 numbers are less than the mode.

15 4 45 8 135 32 405 256 243 1024 1 16 445ⴢ

(

₁₀₀₀1

)

k

兺

⬁ kⴝ1 11ⴢ

(

₁₀₀₀1

)

k

兺

⬁ kⴝ1 358ⴢ

(

₁₀₀₀1

)

k

兺

⬁ kⴝ1 15ⴢ

(

₁₀₀1

)

k

兺

⬁ kⴝ1 93ⴢ

(

₁₀₀1

)

k

兺

⬁ kⴝ1 7ⴢ

(

₁₀₀1

)

k

兺

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7. mean: 8. estimated mean: 10.75 Lesson 12.2 1. 45; 64; flat 2. 3.75; 2.3 and 4.8; mound-shaped 3. 4. 5. 33.2% Passenger cars 50% Trucks 15.9% Buses 0.9% Motor-cycles Motor Vehicle Registration by Type, 1994 Number 10 11 12 13 14 0 0.1 0.2 0.3 Pr ob ab ilit y Number 0 1.0 1.1 1.2 1.3 1.4 1 2 3 4 5 6 Fre qu en cy Stem Leaf 3|₁ⴝ3.1 1 7 2 3, 3 3 1, 6, 9 4 0, 3, 8, 8 Stem Leaf 3|₈ⴝ38 3 3, 7, 8 4 0, 2, 5 5 4, 6, 8 6 4, 4 16.05 Copyright © by Holt, Rinehart and Winston. All rights reserved.

Age (years) Tally Frequency

14 3

15 3

16 4

17 6

18 2

No. of books Class mean Freq. Product

1–5 3 8 24 6–10 8 4 32 11–15 13 3 39 16–20 18 1 18 21–25 23 2 46 25–30 28 2 56 Number Frequency 1.0 5 1.1 2 1.2 3 1.3 6 1.4 4

Number Frequency Rel. Freq.

10 8 16%

11 12 24%

12 7 14%

13 11 22%

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Lesson 12.3 1.Q₁ⴝ2,Q₂ⴝ7,Q₃ⴝ8; range ⴝ8; IQR ⴝ6 2.Q₁ⴝ10,Q₂ⴝ14.5,Q₃ⴝ17; rangeⴝ14;IQR ⴝ7 3.Q₁ⴝ12.1,Q₂ⴝ23.9,Q₃ⴝ38.5; rangeⴝ33.8;IQR ⴝ26.4 4.minimum ⴝ3, maximum ⴝ17; Q₁ⴝ5,Q₂ⴝ10,Q₃ⴝ15; rangeⴝ14;IQR ⴝ10 5.minimum ⴝ10, maximum ⴝ39; Q₁ⴝ16,Q₂ⴝ23,Q₃ⴝ35; range ⴝ29; IQR ⴝ19

6.the data for 1992

7.The quartiles and the extremes all decreased, so it appears that the birth rates decreased in general.

8.about 75% Lesson 12.4 1.32; 9.6 2.19; 3.55; 4.80; 22 5.7.1; 2 6.62; about 18.9 7.16; 4 8.721.6; about 26.9 9.74,064; about 272.1 10.5; about 2.2 11.83.7856; about 9.2 12. ; about 0.3 13.20 14.4.3 15.26.24 16.about 5.1 Lesson 12.5 1.9.375% 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 3.0.9641 4.0.1554 5.0.4772 6.0.0793 7.0.1359 8.0.1586 9.0.5403 10.16% 11.2% 12.82% 13.16% 14.about 420 customers 15.about 820 customers Practice — Chapter 13 Lesson 13.1 1. ; 0.9756 2. ; 0.2195 3. ; 4.4444 4. ; 0.2195 5. ; 0.9756 6. ; 0.225 7. ; 4.5556 8. ; 4.5556 9. ; 4.4444 10.8.3; 57ⴗ; 33ⴗ _11.11.6; 61ⴗ; 29ⴗ 12.21.6; 34ⴗ; 56ⴗ _13.59ⴗ; 4.9; 4.2 14.36ⴗ; 4.9; 3.5 _15.56ⴗ; 5.2; 4.3 Lesson 13.2 1.–313ⴗ; 47ⴗ _2.237ⴗ; 57ⴗ _3.ⴚ142ⴗ; 38ⴗ 4.152ⴗ; 28ⴗ _5.138ⴗ; 42ⴗ _6.ⴚ53ⴗ; 53ⴗ 7.42ⴗ; 42ⴗ _8.175ⴗ; 5ⴗ _9.285ⴗ; 75ⴗ 10.75ⴗ _11.33ⴗ _12.5ⴗ 40 9 41 9 41 9 9 40 40 41 9 41 40 9 9 41 40 41 0.08 16.3 5.3 8 12 16 20 24 28 32 36 40 2 4 6 8 10 12 14 16 18 Copyright © by Holt, Rinehart and Winston. All rights reserved.

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13.36ⴗ 14.40ⴗ 15.72ⴗ 16.2ⴗ 17.80ⴗ 18.60ⴗ 19. 20. 21. 22. 23. 24. 25. 26. 27. Lesson 13.3 1. 2. 3. 4. 5. 6. 7.(0.743, 0.669) 8.(ⴚ0.629, 0.777) 9.(ⴚ0.438, ⴚ0.899) 10.(0.574, ⴚ0.819) 11.(0.755, ⴚ0.656) 12.(ⴚ0.259, ⴚ0.966) 13.0; 1; 0 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.ⴚ1 _25.ⴚ2 Lesson 13.4

1. radians 2. radians 3. radian 4. radians 5. radians

6. radians 7. radians 8. radians 9.450ⴗ 10.165ⴗ 11.140ⴗ 12.195ⴗ 13.472.69ⴗ

14.103.13ⴗ 15.171.89ⴗ 16.28.65ⴗ 17.47.1 feet 18.5.2 feet 19.41.9 feet 20.10.5 feet 21.50 feet 22.80 feet 23.146 feet 24.200 feet 25.0 26. 27. 28.ⴚ1 _29. 30. 31.0 32.2 Lesson 13.5 1.1; 0.5; 0; ⴚ0.5; ⴚ1; ⴚ0.5; 0; 0.5; 1 2.4.5; π radians

3.does not exist; π radians 4.1.2; 2π radians 5.shift of 45ⴗ right; translation of 1.5 units up ␪ 90° 180° 270° 1 –1 y = cos ␪ y = cos 2␪ ⴚ兹2 2 兹3 3 ⴚ兹3 ⴚ1 2 5π 12 7π 18 ⴚ17π 36 7π 12 5π 6 π 5 5π 3 3π 4 兹3 3 1 2 兹2 2 ⴚ兹3 ⴚ2兹3 3 ⴚ兹3 2 兹3 2 ⴚ1 2;兹32 ; ⴚ兹33 兹3 2 ; ⴚ12; ⴚ兹3 ⴚ兹2 2 ;兹22 ; ⴚ1 (2兹3, 2) (ⴚ5兹2, 5兹2) (20兹3, ⴚ20)

(

ⴚ15 2 , ⴚ15兹32

)

(6, 6兹3)

(

5兹2 2 ,5兹22

)

3兹7 7 5 13 4 3 兹39 8 兹89 5 ⴚ3 4 9兹97 97 ;4兹9797 ; 2.25; 兹979 ;兹974 ;49 2兹5 5 ; ⴚ兹55 ; ⴚ2;兹55 ; ⴚ兹5; ⴚ12 2兹13 13 ;3兹1313 ;23;兹132 ;兹133 ;32 Copyright © by Holt, Rinehart and Winston. All rights reserved. ␪ 90° 180° 270° 360° –1 0 1 2 3 y

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6.shift ofπunits left;

translation of 1 unit down

Lesson 13.6 1.ⴚ60ⴗ _2.120ⴗ _3.0ⴗ _4.0ⴗ _5.ⴚ45ⴗ 6.ⴚ60ⴗ _7.0 _8.ⴚ1 _9. 10. radians 11.ⴚ45ⴗ _12. radians 13.1.5459 radians 14.0.0345 radians 15.2.5173 radians 16.0.6831 radians 17.ⴚ1.5446 radians _18.ⴚ0.5769 radians 19.9.6ⴗ _20.35.5ⴗ _21.48.1ⴗ Practice — Chapter 14

Note: Throughout Chapter 14, answers may vary slightly due to rounding, method of calculation, 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 6.28.9 7.m⬔C ⴝ38ⴗ,b ⴝ4.4,c ⴝ3.1 8.m⬔A ⴝ35ⴗ,c ⴝ21.7,a ⴝ12.7 9.m⬔C ⴝ45ⴗ,a ⴝ25.8,c ⴝ18.5 10.m⬔B ⴝ44ⴗ,a ⴝ5.5,b ⴝ4.0 11.m⬔C ⴝ82ⴗ,a ⴝ15.5,c ⴝ21.4 12.m⬔A ⴝ75ⴗ,a ⴝ82.9,c ⴝ78.4 13.one; m⬔B ⴝ46.0ⴗ,m⬔C ⴝ70.0ⴗ,c ⴝ20.9 14.none 15.two; (1) m⬔A ⴝ46.2ⴗ, m⬔C ⴝ105.8ⴗ, c ⴝ53.3; (2) m⬔A ⴝ133.8ⴗ, m⬔C ⴝ18.2ⴗ,c ⴝ17.3 16.1532.7 feet Lesson 14.2 1.SAS;a ⴝ17.3 2.SAS;c ⴝ28.2 3.SAS;a ⴝ5.3 4.SSA;b ⴝ9.8 5.SAS;c ⴝ31.3 6.SAS;a ⴝ13.9 7.m⬔A ⴝ44.7ⴗ, m⬔B ⴝ38.3ⴗ, m⬔C ⴝ97.0ⴗ 8.m⬔A ⴝ78.3ⴗ, m⬔B ⴝ37.4ⴗ, m⬔C ⴝ64.3ⴗ 9.m⬔A ⴝ73.0ⴗ, m⬔B ⴝ61.2ⴗ, m⬔C ⴝ45.8ⴗ 10.m⬔A ⴝ45.8ⴗ, m⬔B ⴝ30.7ⴗ, m⬔C ⴝ103.5ⴗ 11.m⬔A ⴝ41.1ⴗ, m⬔B ⴝ80.3ⴗ, m⬔C ⴝ58.6ⴗ 12.SAS;b ⴝ131.2, m⬔A ⴝ32.5ⴗ, m⬔C ⴝ37.5ⴗ 13.SSS; m⬔A ⴝ50.0ⴗ, m⬔B ⴝ98.7ⴗ, m⬔C ⴝ31.3ⴗ 14.SSS; m⬔A ⴝ104.5ⴗ, m⬔B ⴝ29.0ⴗ, m⬔C ⴝ46.5ⴗ 15.SAS;a ⴝ6.5, m⬔B ⴝ20.7ⴗ, m⬔C ⴝ109.3ⴗ

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Lesson 14.3 1. 2. 3. cos2␪ 4.

5.sin␪ _6.tan2␪ _7.ⴚ1 _8.tan␪

9.sin␪ _10.sec␪ 11. 12. (1ⴙcos␪)ⴝsin␪ 13. ⴝ Lesson 14.4 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.(ⴚ5.66,ⴚ1.41), (ⴚ9.19,ⴚ4.95), (ⴚ12.02,ⴚ2.12), (ⴚ8.49, 1.41) Lesson 14.5

1–4.Check students’ work.

5–11.Answers may vary. Sample answers:

5. 6. 7.2 cos2␪

8.tan2␪ _9.tan␪ _10.cot␪

11.1ⴙsin␪ _12.27 feet Lesson 14.6 1.30ⴗ ⴙn(360ⴗ), 150ⴗ ⴙn(360ⴗ), 210ⴗ ⴙn(360ⴗ), and 330ⴗ ⴙn(360ⴗ) 2.45ⴗ ⴙn(360ⴗ) _3.120ⴗ ⴙn(360ⴗ) 4.120ⴗ ⴙn(360ⴗ) _5.120ⴗand 240ⴗ 6.210ⴗ, 270ⴗ, and 330ⴗ 7.45ⴗ, 135ⴗ, 225ⴗ, and 315ⴗ 8.30ⴗ, 150ⴗ, 210ⴗ, and 330ⴗ 9.π₃ and 5₃π 10.π₄ and 5₄π 1ⴙcos␪ 2 1ⴚcos␪ 2

冤

ⴚ0.37 0.93 ⴚⴚ0.930.37

冥

冤

ⴚ0.770.64 0.64 0.77

冥

冤

0.42_0.91 ⴚ0.91 0.42

冥

冤

ⴚ0.71 ⴚ0.71 0.71 ⴚ0.71

冥

冤

ⴚ0.71 0.71 ⴚⴚ0.710.71

冥

冤

ⴚ0.5 0.87 ⴚⴚ0.870.5

冥

ⴚ兹₄2 ⴚ兹₄6 ⴚ兹₂3 兹2 4 ⴙ兹₄6 兹2 4 ⴚ兹₄6 ⴚ兹₄2ⴙ兹₄6 ⴚ兹₂3 兹2 2 ⴚ兹₄2ⴙ兹₄6 兹2 4 ⴙ兹₄6 兹6 4 ⴚ兹₄2 兹2 4 ⴚ兹₄6 兹2 4 ⴙ兹₄6 兹2 4 ⴚ兹₄6 ⴚ兹₄2ⴚ兹₄6 ⴚ兹₄2ⴙ兹₄6 ⴚ兹₄2ⴚ兹₄6 兹2 4 ⴙ兹₄6 兹2 4 ⴚ兹₄6 1 sin␪ sin␪ⴙ(cos␪)

(

cos_sin␪

␪

)

ⴝcsc␪

(

1 sin␪ⴚcos ␪ sin␪

)

ⴝsin␪ 1 sin␪ⴚsin␪ cos2␪ sin2␪ 1ⴙtan2␪ⴝ1ⴙy2 x2ⴝx 2ⴙy2 x2 ⴝr 2 x2ⴝsec2␪ x2ⴙy2 y2 ⴝr 2 y2ⴝ 1ⴙcot2␪ⴝ1ⴙx2 y2ⴝ ⴚx2 r2ⴝ ⴚcos2␪ y2ⴚr2 r2 ⴝ y2 r2 ⴚ1ⴝ

(

y rⴚ1

)(

yrⴙ1

)

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