196 CHAPTER 1 Equations and Inequalities Perform each operation. Write answers in standard form. 19. 16 - i2 + 17 - 2i2 20. 1-11 + 2i2 - 18 - 7i2 21. 15i - 13 + 2i2 - 11 22. -6 + 4i - 18i - 22 23. 15 - i213 + 4i2 24. 1-8 + 2i21-1 + i2 25. 15 - 11i215 + 11i2 26. 14 - 3i22 27. -5i13 - i22 28. 4i12 + 5i212 - i2 29. -12 - i -2 - 5i 30. -7 + i -1 - i Simplify each power of i. 31. i11 32. i60 33. i1001 34. i110 35. i -27 36. 1 i17 Solve each equation. 37. 1x + 722 = 5 38. 12 - 3x22 = 8 39. 2x2 + x - 15 = 0 40. 12x2 = 8x - 1 41. -2x2 + 11x = -21 42. -x13x + 22 = 5 43. 12x + 121x - 42 = x 44. 22 x2 - 4x + 22 = 0 45. x2 - 25 x - 1 = 0 46. 1x + 421x + 22 = 2x 47. Concept Check Which equation has two real, distinct solutions? Do not actually solve. A. 13x - 422 = -9 B. 14 - 7x22 = 0 C. 15x - 9215x - 92 = 0 D. 17x + 422 = 11 48. Concept Check See Exercise 47. (a) Which equations have only one distinct real solution? (b) Which equation has two nonreal complex solutions? Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 49. -6x2 + 2x = -3 50. 8x2 = -2x - 6 51. -8x2 + 10x = 7 52. 16x2 + 3 = -26x 53. x19x + 62 = -1 54. 25x2 + 110x + 121 = 0 Solve each problem. 55. (Modeling) Height of a Projectile A projectile is fired straight up from ground level. After t seconds its height s, in feet above the ground, is given by s = -16t2 + 220t. At what times is the projectile exactly 750 ft above the ground? 56. Dimensions of a Picture Frame Zach went into a frame-it-yourself shop. He wanted a frame 3 in. longer than it was wide. The frame he chose extended 1.5 in. beyond the picture on each side. Find the outside dimensions of the frame if the area of the unframed picture is 70 in.2. 57. Kitchen Flooring Ciara plans to replace the vinyl floor covering in her 10-ft by 12-ft kitchen. She wants to have a border of even width of a special material. She can afford only 21 ft2 of this material. How wide a border can she have? 10 ft x 12 ft 1
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