Question 1 of 20 0.0/ 5.0 Points Write the partial fraction decomposition of the rational expression. A. + + B. + C. + + D. + + Question 2 of 20 0.0/ 5.0 Points Graph the solution set of the system of inequalities or indicate that the system has no solution. x ? 0 y ? 0 3x + 2y ? 6 3x + y ? 5 A. B. C. D. Question 3 of 20 0.0/ 5.0 Points A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x2 - y2 = 20. The process is repeated and the ship is found to lie on a hyperbolic path described by y2 - 2x2= 7. If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location. A. ( -3, -5) B. ( 5, 3) C. ( 3, 5) D. ( -5, -3) Question 4 of 20 5.0/ 5.0 Points Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + y = -8 x - y = 14 A. {( 3, -11)} B. {( 3, 11)} C. {(x, y) | x + y = -8} D. ? Question 5 of 20 5.0/ 5.0 Points Solve the system by the substitution method. xy = 12 x2 + y2= 40 A. {( 2, 6), ( 6, 2), ( 2, -6), ( 6, -2)} B. {( 2, 6), ( -2, -6), ( 2, -6), ( -2, 6)} C. {( 2, 6), ( -2, -6), ( 6, 2), ( -6, -2)} D. {( -2, -6), ( -6, -2), ( -2, 6), ( -6, 2)} Question 6 of 20 0.0/ 5.0 Points Graph the inequality. (x-1)2 + (y-5)2> 9 A. B. C. D. Question 7 of 20 0.0/ 5.0 Points Graph the solution set of the system of inequalities or indicate that the system has no solution. y > x2 10x + 6y ? 60 A. B. C. D. Question 8 of 20 0.0/ 5.0 Points Solve by the method of your choice. x3 + y = 0 11x2- y = 0 A. {(-1, 1), (-11, 1331)} B. {(0, 0), (-11, 1331)} C. {(0, 0), (-11, 121)} D. {(0, 0), ( 11, -1331)} Question 9 of 20 0.0/ 5.0 Points You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds. Consider the following data: x, seconds after ball is thrown y, ball's height, in feet, above the ground 1 114 2 146 4 114 Find the quadratic function y = ax2+bx + c whose graph passes through the given points. A. y = -12x2 + 80x + 46 B. y = -10x2 + 60x + 64 C. y = -16x2 + 100x + 30 D. y = -16x2 + 80x + 50 Question 10 of 20 0.0/ 5.0 Points In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 23 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.) A. -13.06 ft B. 13.02 ft C. 3.01 ft D. -10.04 ft Question 11 of 20 5.0/ 5.0 Points Graph the solution set of the system of inequalities or indicate that the system has no solution. y ? 2x – 4 x + 2y ? 7 y ? -2 x ? 1 A. B. C. D. Question 12 of 20 0.0/ 5.0 Points A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 15 hours to paint, and 7 hours to fire. If the workshop has 116 hours for prep time, 64 hours for painting, and 110 hours for firing, How many of each can be made? A. 8 wreaths, 6 trees, 2 sleighs B. 6 wreaths, 2 trees, 8 sleighs C. 9 wreaths, 7 trees, 3 sleighs D. 2 wreaths, 8 trees, 6 sleighs Question 13 of 20 5.0/ 5.0 Points Ms. Adams received a bonus check for $12,000. She decided to divide the money among three different investments. With some of the money, she purchased a municipal bond paying 5.8% simple interest. She invested twice the amount she paid for the municipal bond in a certificate of deposit paying 4.9% simple interest. Ms. Adams placed the balance of the money in a money market account paying 3.7% simple interest. If Ms. Adams' total interest for one year was $534, how much was placed in each account? A. municipal bond: $ 1500 certificate of deposit: $ 3000 money market: $ 7500 B. municipal bond: $ 2500 certificate of deposit: $ 5000 money market: $ 4500 C. municipal bond: $ 2000 certificate of deposit: $ 4000 money market: $ 6000 D. municipal bond: $ 1750 certificate of deposit: $ 3500 money market: $ 6750 Question 14 of 20 5.0/ 5.0 Points An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. Objective Function z = 21x - 25y Constraints 0 ? x ? 5 0 ? y ? 8 4x + 5y ? 30 4x + 3y ? 20 A. Maximum: 105; at (5, 0) B. Maximum: -150; at (0, 6) C. Maximum: 0; at (0, 0) D. Maximum: -98.75; at (1.25, 5) Question 15 of 20 0.0/ 5.0 Points Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 4x - 3y = 6 -12x + 9y = -24 A. {( 3, 4)} B. C. {(x, y) | 4x - 3y = 6 } D. ? Question 16 of 20 0.0/ 5.0 Points Graph the solution set of the system of inequalities or indicate that the system has no solution. x2 + y2 ? 49 5x + 4y ? 20 A. B. C. D. Question 17 of 20 0.0/ 5.0 Points Solve the system by the addition method. x2 - 3y2 = 1 3x2 + 3y2= 15 A. {( 1, 2), ( -1, 2), ( 1, -2), ( -1, -2)} B. {( 1, 2), ( -1, -2)} C. {( 2, 1), ( -2, 1), ( 2, -1), ( -2, -1)} D. {( 2, 1), ( -2, -1)} Question 18 of 20 5.0/ 5.0 Points Solve the system by the substitution method. x2 + y2 = 113 x + y = 15 A. {( -8, 7), ( -7, 8)} B. {( 8, -7), ( 7, -8)} C. {( 8, 7), ( 7, 8)} D. {( -8, -7), ( -7, -8)} Question 19 of 20 5.0/ 5.0 Points In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. Let x represent the number of years since 1990 and y represent the percentage of women in Milton Lake who smoke. The graph of y against x includes the data points (0, 15.9) and ( 13, 19.67). Let x represent the number of years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph of y against x includes the data points (0, 29.7) and ( 15, 26.85). Determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time? [Hint: first find the slope-intercept equation of the line that models the percentage, y, of women who smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, y, of men who smoke x years after 1990] A. 2019; 24% B. 2021; 24% C. 2023; 23% D. 2017; 25% Question 20 of 20 0.0/ 5.0 Points A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width. A. 34 inches B. 35 inches C. 23 inches D. 12 inches
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