CHAPTER 6 Test 409 6.1, 6.2, 6.10 99. Gas Mileage The gas mileage, m, of a specific car can be estimated by the equation (or function) m n n 30 0.002 , 20 80 2 = − ≤ ≤ where n is the speed of the car in miles per hour. Estimate the gas mileage when the car travels at 60 mph. 22.8 mpg 100. Filtered Light The percent of light filtering through Swan Lake, P, can be approximated by the function P x( ) 100(0.92) , x = where x is the depth in feet. Determine the percent of light filtering through at a depth of 4.5 ft. ≈ 68.7% 95. y x x4 21 2 = − − + * 96. f x x x ( ) 2 8 6 2 = + + * In Exercises 97 and 98, graph the function and state the domain and range. 97. y 4x = * 98. y 1 2 x = ⎛ ⎝⎜ ⎞ ⎠⎟ * Test CHAPTER 6 1. Evaluate x x 3 6 1, 2 + − when x 2. = − −1 In Exercises 2 and 3, solve the equation. 2. x x 4 6 2(3 7) + = − 10 3. x x x x 2( 3) 6 2 3( 4) − − + = + − 18 In Exercise 4, write an equation to represent the problem. Then solve the equation. 4. Salary Mary’s salary is $350 per week plus a 6% commission of sales. How much in sales must Mary make to earn a total of $710 per week? + = x 350 0.06 710; $6000 5. Evaluate L ah bh ch = + + when a b c 2, 5, 4, = = = and h 7. = 77 6. Solve x y 3 5 11 + = for y. = − + = − + y x y x 3 11 5 or 3 5 11 5 7. For a constant area, the length, l, of a rectangle varies inversely as the width, w. If l 15 ft = when w 9 ft, = determine the length of a rectangle with the same area if the width is 20 ft. 6.75 ft 8. Graph the solution set of x x 5 14 2 35 − + ≤ + on the real number line. * 9. Determine the slope of the line through the points ( 2, 8) − and (1, 14). 2 10. Graph the equation x y 2 3 15 − = * 11. Solve the system of equations graphically. y x2 12 = − x y 2 2 6 + = − * In Exercises 12 and 13, solve the system of equations by the method indicated. 12. x y 1 + = − x y 2 3 5 + = − (substitution) − (2, 3) 13. x y 4 3 5 + = x y 2 4 10 + = (addition) −( 1, 3) 14. MODELING—Truck Rental U-Haul charges a daily fee plus a mileage charge to rent a truck. Dorothy rented $ a truck from U-Haul and was charged $132 for 3 days’ rental and 150 miles driven. Elena rented the same truck and was charged $142 for 2 days’ rental and 400 miles driven. Determine the daily fee and the mileage charge for renting this truck. Daily fee: $35; mileage charge: $0.18 15. Graph the inequality y x 3 5 12. ≥ − * 16. The set of constraints and profit formula for a linear programming problem are + ≤ + ≤ ≥ ≥ = + x y x y x y P x y 3 6 4 3 15 0 0 6 4 a) Graph the constraints and determine the vertices of the feasible region. * b) Use the vertices to determine the maximum and minimum profit. Maximum is 22.5 at (3.75, 0); minimum is 0 at (0, 0). 17. Solve the equation x x7 6 2 + = − by factoring. − − 1, 6 18. Solve the equation x x 3 2 8 2 + = by using the quadratic formula. − 4 3 , 2 19. Evaluate f x x x ( ) 2 8 7 2 = − − + when x 2. = − 15 20. For the graph of the equation y x x2 4, 2 = − + a) determine whether the parabola will open upward or downward. Upward b) determine the equation of the axis of symmetry. = x 1 c) determine the vertex. (1, 3) d) determine the y-intercept. (0, 4) e) determine the x-intercepts if they exist. No x-intercepts f) graph the function. * g) determine the domain and range of the function. Domain: ;R range: ≥ y 3 *See Instructor Answer Appendix *See Instructor Answer Appendix $
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