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Week 5 Assignment

# Week 5 Assignment - Week 5 Assignment Section 3.5 5 9x2...

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Week 5 Assignment Section 3.5 5. 9x 2 - 25y 2 (3x) 2 - (5y) 2 = square roots of 9x 2 - 25y 2 (3x + 5y)(3x - 5y) 14. (3x + 5) 2 - y 2 ( 3x + 5 + y)(3x + 5 - y) 15. 4x 2 - (y + 1) 2 (2x) 2 - (y + 1) 2 [2x + (y + 1)][2x - (y + 1)] (2x + y + 1)(2x - y - 1) 18. 16s 2 - (3t + 1) 2 (4s) 2 - (3t + 1) 2 [4s + (3t + 1)][4s - (3t + 1)] (4s + 3t + 1)(4s - 3t - 1) 19. (x + 2) 2 - (x + 7) 2 [(x + 2) + (x + 7)][(x + 2) - (x + 7)] (x + 2 + x + 7)(x + 2 - x - 7) (2x + 9)(-5) -5(2x + 9) 21. 9x 2 - 36 9(x 2 - 4) 9(x 2 + 2)(x - 2) 27. a 3 b - 9ab ab(a 2 - 9) ab(a + 3)(a - 3) 31. n 4 - 81 (n 2 + 9)(n 2 - 9) (n 2 + 9)(n + 3)(n - 3) 32. 4x 2 + 9 This equation is not factorable because 4 and 9 do not have common square roots. 46. a 3 - 27 (a) 3 - (3) 3 (a - 3)(a 2 + 3a + 9) 49. 27x 3 + 64y 3

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(3x) 3 + (4y) 3 (3x + 4y)(9x 2 - 12xy + 16y 2 ) 51. 1 - 27a 3 (1) 3 - (3a) 3 (1 - 3a)(1 + 3a + 9a 2 ) 57. x 2 - 25 = 0 (x + 5)(x - 5) = 0 x + 5 = 0 or x - 5 = 0 x = -5 or x = 5 {-5, 5} 59. 9x 2 - 49 = 0 (3x + 7)(3x - 7) = 0 3x + 7 = 0 or 3x - 7 = 0 3x = -7 or 3x = 7 x = - 7 or x = 7 3 3 {-7 , 7 } 3 3 64. 4x 3 - 64x 4x 3 - 4x = 0 4x(x 3 + 4)(x - 4) = 0 x + 4 = 0 or x - 4 = 0 x = -4 or x = 4 {-4, 0, 4} 67. x 4 - 81 = 0 (x 2 + 9)(x 2 - 9) = 0 (x 2 + 9)(x + 3)(x - 3) = 0 x 2 + 9 = 0 or x + 3 = 0 or x - 3 = 0 x 2 = -9 or x = -3 or x = 3 Not a real number x = -3 or x = 3 {-3, 3} 69. 6x 3 + 24x = 0
6x(x 2 + 4) = 0 6x = 0 or x 2 + 4 = 0 x = 0 or x 2 = -4 x = 0 Not a real number {0} 71. The cube of a number equals nine times the same number. Find the number. Let x = number x 3 = 9x x 3 - 9x = 0 x(x 2 - 9) = 0 x(x + 3)(x - 3) = 0 x = 0 or x + 3 = 0 or x - 3 = 0 x = 0 or x = -3 or x = 3 The numbers are -3, 0, or 3. 74. The combined area of two squares is 26 square meters. The side of the larger square are five times as long as the sides of the smaller square. Find the dimensions of each of the squares. Let x = area of first (smaller) square Let 5x = area of second (larger) square A + a = 26 S = 5s A = S 2 and a = s 2 S 2 + s 2 = 26 (5s) 2 + s 2 = 26 25s 2 + s 2 = 26 26s 2 = 26 s 2 = 1 s = 1 The small square = 1m x 1m, the large square = 5m x 5m. 76. Suppose that the length of a rectangle is one and one-third times as long as its width. The area of the rectangle is 48 square centimeters. Find the length and width of the rectangle. Lw = 48 (6)4 = 48

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Let x = width Let 4 x = length 3 x 2 = 36 x = 6 4 (6) 2 = 4 (2) = 8 3 1 1 The length of the rectangle is 8 cm, and the width is 6 cm. 78. The total surface area of a right circular cone is 108π square feet. If the slant height of the cone is twice the length of the base, find the length of a radius. Let x = radius Let 2x = altitude S A = 339.12 sq. ft. S A = 2πr
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Week 5 Assignment - Week 5 Assignment Section 3.5 5 9x2...

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