Section 2.5 Formulas and Applications from Geometry 141 3c. F = 9 5 C + 32 Highlight the variable to isolate. 5(F ) = 5a9 5 C + 32b Multiply each side by the LCD, 5. 5F = 5a9 5 Cb + 5(32) Apply the distributive property. 5F = 9C + 160 Simplify. 5F - 160 = 9C + 160 - 160 Subtract 160 from each side. 5F - 160 = 9C Simplify. 5F - 160 9 = 9C 9 Divide each side by 9. 5F - 160 9 = C Simplify. So, C = 5F - 160 9 . 3d. 3x - y =6 Highlight the variable to isolate. Subtract 3x from each side. Note the term containing y has a coefficient of -1, so multiply each side by -1. Apply the distributive property. 3x - y - 3x = 6 - 3x -y=-3x + 6 1(-y) = -1(-3x + 6) - y = 3x - 6 So, y = 3x - 6. 3e. 2x + 3y = 12 Highlight the variable to isolate. 2x + 3y - 2x = 12 - 2x Subtract 2x from each side. 3y=-2x + 12 Simplify. 3y 3 = -2x + 12 3 Divide each side by 3. y = -2x 3 + 12 3 Divide each term by 3. y=- 2 3 x + 4 Simplify. So, y=- 2 3 x + 4. ������������ Parts (d ) and (e) will be presented more fully in Chapter 3 when we discuss linear equations in two variables. Student Check 3 Solve each formula for the specified variable. a. The formula d = rt calculates distance for a given rate and time. Solve for t. b. The formula V = 1 3 bh calculates the volume of a regular pyramid, given the length of its base and height. Solve for h. c. The formula A = h 2 (b1 + b2) calculates the area of a trapezoid. Solve for b1. d. Solve 4x - y = 8 for y. e. Solve 4x + 5y = -20 for y.
hendricks_beginning_algebra_1e_ch1_3
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