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Practice for Quiz

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Lesson Quiz: Part I Variation 1. The volume V of a pyramid varies jointly as the area of the base B and the height h, and V = 24 ft 3 when B = 12 ft 2 and h = 6 ft. Find B when V = 54 ft 3 and h = 9 ft. 18 ft 2 2. The cost per person c of chartering a tour bus varies inversely as the number of passengers n. If it costs $22.50 per person to charter a bus for 20 passengers, how much will it cost per person to charter a bus for 36 passengers? $12.50

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Example 3 Given: y varies inversely as x, and y = 4 when x = 10. Write and graph the inverse variation function. Substitute 4 for y and 10 for x. Solve for k. 4 =4 = k = 40 y = k 10 y varies inversely as x. k x Write the variation formula. y =y = 40 x

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Example 3 Continued To graph, make a table of values for both positive and negative values of x. Plot the points, and connect them with two smooth curves. Because division by 0 is undefined, the function is undefined when x = 0. xy –2–20 –4–10 –6– 20/3 –8–5 xy /3 85

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5.2 Simplifying Rational Expressions Example 1 Simplify. Identify any x-values for which the expression is undefined. 6x 2 + 7x + 2 6x 2 – 5x – 5 (2x + 1)(3x + 2) (3x + 2)(2x – 3) Factor; then divide out common factors. = (2x + 1) (2x – 3) The expression is undefined at ????

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Multiply. Assume that all expressions are defined. Example 2: Multiplying Rational Expressions A. 3x 5 y 3 2x3y72x3y7 10x 3 y 4 9x2y59x2y5 3x 5 y 3 2x3y72x3y7 10x 3 y 4 9x2y59x2y x 3 3y 5 B. x – 3 4x + 20 x + 5 x 2 – 9 x – 3 4(x + 5) x + 5 (x – 3)(x + 3) 1 4(x + 3)

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Dividing: Example 2x 2 – 7x – 4 x 2 – 9 ÷ 4x 2 – 1 8x 2 – 28x +12 Divide. Assume that all expressions are defined. (2x + 1)(x – 4) (x + 3)(x – 3) 4(2x 2 – 7x + 3) (2x + 1)(2x – 1) (2x + 1)(x – 4) (x + 3)(x – 3) 4(2x – 1)(x – 3) (2x + 1)(2x – 1) 4(x – 4) (x +3) 2x 2 – 7x – 4 x 2 – 9 8x 2 – 28x +12 4x 2 – 1

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Example 5: Solving Simple Rational Equations Solve. Check your solution. Note that x 2. x 2 – 3x – 10 x – 2 = 7 (x + 5)(x – 2) (x – 2) = 7 x + 5 = 7 x = 2 Because the left side of the original equation is undefined when x = 2, there is no solution.

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