Chapter 11 Review1. −3, 1_3 2. 3 ± 3i√—

√√2 _______2 3. −3, 9 4. −6, 3

5. 4_5, 2 ± 2i√—

√√3 _______5 6. 1 ± i√—

√√5 7. r = 4 ± √—

√√A√√___6 8. 4 ± √

—√√3

9. 6 cm, 6√—

√√3 cm 10. 1_2 second, _ 5_2 seconds_ 11. 2 or 300 watches

12. 27 13. Two rational solutions 14. 5x2 − 12x − 9 = 015. x 3x − 3x 2x − 16x + 48 = 0 16. ± 3i__

2 , ± √—√√5 17. −1, 10__

9 18. 9 19. t = 7 ± 2 √—√√18 − 8h ___________

8 20. (2, −10) 21. (−1, 5)

22. y = 3(x − 4)2 − 3 23. $102.50 24. −5 ≤ x ≤ 2

25. x < − 1_3 or _ x > 3

26. a. x < −3 or −1 < x <2 b. −3 < x < −1 or x > 2c. x = −3 or x = −1 or x = 2

Chapter 11 Cumulative Review1. 4 2. 78 3. −125___

8 4. 9__16 5. −13x + 13 6. 2x + 137. xy7 8. a21__

b3 9. 3 3√ 3 —√√2 10. 4x2√

—√√2x 11. − 3__

16 12. 4__25

13. − 3__11 14. −25__

4 15. x − 7y 7 16. x − 5 17. 1 + 4i

18. 9__13 + 7__13i i 19. 4 20. 51__

4 21. −3, 3 22. ∅ 23.∅ −3, −5

24. a = 4 25. 3 ± 2√—

√√2 _______2 26. 0, 9 ± √—√√65 _______

8 27. 1, 4 28. −1 ± i√—√√35 ________

9 29. −4, −3 30. 9 31. 9 32. −125, 21633. −36 ≤ x ≤ −18 34. x ≤ − 1, x ≥ −1_

3

35. −3 < x < 6 36. x < −2 or x ≥ 4

37. Lines parallel ∅∅ 38. Lines parallel ∅

39. 40.

41. y 2x + 2 42. y 4x − 2 43. (x 3 y)(x − 3 + y) 44. (x + 3)(x − 4) 45. 3 3

√ 3 —√√2 46. −3 + √

—√√15 _______2 47. {1, 4}

48. {2, 8} 49. 30°, 50°, 100° 50. $3,500 at 2%; $2,500 at 3% 51. −25__

9 52. 4 53. 328,290 people 54. 38,372 people

Chapter 11 Test

1. 9_2

, − 3_2 2. −1 ± 2i √—

√√3 ________4 3. −4 ± 5i 4. −5 ± i√—

√√2

5. 3_4 , −3 ± 3i√—√√3 ________

8 6. 1 ± i√—√√7 ______

2 7. r = 7 ± √—

√√A √√___7 8. 3 ± i √—

√√2

9. 4 m, 4√—

√√3 m 10. 1_4

second, 7_4 seconds

11. 5 or 100 letter openers 12. 8 13. Two complex solutions 14. 2x2 + 9x − 35 = 0 15. x3 − 5x2 − 9x + 45 16. ± 3_

4i, ±√

—√√3

17. 2, 1_4

18. 1_9

, 4 19. t = 5 ± √—√√16h + 25 ___________16

20. (1, 0) 21. (2, 2)

22. y = −(x − 2)2 + 4 23. $645 24. −1 ≤ x ≤ 4

25. x < −2 or x > 1_2

26. a. −2 < x < −1 or x > 1 b. x < −2 or −1 < x < 1c. x = −2 or x = −1 or x = 1

y

x

y

4

−5 2

−13 3

−36 −18 −13

−1

−3 6 22 4

x

y

x

y

x

y

−1 4

−2 12