8-2 Adding and Subtracting Rational Expressions. Find the LCM of each set of polynomials x, 8x 2 y 3, 5x 3 y.
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1 Find the LCM of each set of polynomials x, 8x 2 y 3, 5x 3 y 80x 3 y y 2 9y, y 2 8y GEOMETRY Find the perimeter of the rectangle. 3y(y 3)(y 5) esolutions Manual - Powered by Cognero Page 1
2 Find the LCM of each set of polynomials x 2 y 3, 18xy 4, 10xz x 2 y 4 z x x 12, 4x x (x + 4)(2x 1) (2x + 3) CCSS PERSEVERANCE Simplify each expression GEOMETRY Both triangles in the figure at the right are equilateral. If the area of the smaller triangle is 200 square centimeters and the area of the larger triangle is 300 square centimeters, find the minimum distance from A to B in terms of x and y and simplify. 27. esolutions Manual - Powered by Cognero Page 2
3 Find the LCM of each set of polynomials xy 4, 14x 4 y 2, 5xyz 3, 15x 5 y x 2 3x 28, 2x 2 + 9x + 4, x 2 16 (x + 4)(x 4) (2x + 1)(x 7) esolutions Manual - Powered by Cognero Page 3
4 53. GEOMETRY An expression for the length of one 55. rectangle is is expressed as The length of a similar rectangle What is the scale factor of the two rectangles? Write in simplest form. (x 3)(x + 2) to 1 Find the slope of the line that passes through each pair of points. 59. PHOTOGRAPHY The focal length of a lens establishes the field of view of the camera. The shorter the focal length is, the larger the field of view. For a camera with a fixed focal length of 70 mm to focus on an object x mm from the lens, the film must be placed a distance y from the lens. This is represented by a. Express y as a function of x. b. What happens to the focusing distance when the object is 70 mm away? a. b. Sample answer: When the object is 70 mm away, y needs to be 0, which is impossible DOPPLER EFFECT Refer to the application at the beginning of the lesson. George is equidistant from two fire engines traveling toward him from opposite directions. a. Let x be the speed of the faster fire engine and y be the speed of the slower fire engine. Write and simplify a rational expression representing the difference in pitch between the two sirens according to George. b. If one is traveling at 45 meters per second and the other is traveling at 70 meters per second, what is the difference in their pitches according to George? The speed of sound in air is 332 meters per second, and both engines have a siren with a pitch of 500 Hz. a. b. about 55.2 Hz esolutions Manual - Powered by Cognero Page 4
5 63. CHALLENGE Simplify 69. SAT/ACT If Mauricio receives b books in addition to the number of books he had, he will have t times as many as he had originally. In terms of b and t, how many books did Mauricio have at the beginning? F G 65. OPEN ENDED Write three monomials with an LCM of 180a 4 b 6 c. Sample answer: 20a 4 b 2 c, 15ab 6, 9abc H J K 67. PROBABILITY A drawing is to be held to select the winner of a new bike. There are 100 seniors, 150 juniors, and 200 sophomores who had correct entries. The drawing will contain 3 tickets for each senior name, 2 for each junior, and 1 for each sophomore. What is the probability that a senior s ticket will be chosen? A 71. F B C 73. D D (n + 3)(n 6) esolutions Manual - Powered by Cognero Page 5
6 Graph each function. State the domain and range of each function Solve each equation. State the number and type of roots x + 8 = 0 ; 1 real 83. x 3 + 9x = 0 0, 3i, 3i; 1 real, 2 imaginary esolutions Manual - Powered by Cognero Page 6
7 Graph each function. 85. y = 4(x + 3) y = x 2 + 6x + 2 esolutions Manual - Powered by Cognero Page 7
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