Write the partial fraction decomposition of the rational expression.
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Graph the solution set of the system of inequalities or indicate that the system has no solution.
x ≥ 0


A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x^{2} – y^{2} = 20. The process is repeated and the ship is found to lie on a hyperbolic path described by y^{2} – 2x^{2}= 7. If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location.


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


Solve the system by the substitution method.
xy = 12


Graph the inequality.
(x1)^{2} + (y5)^{2}> 9


Graph the solution set of the system of inequalities or indicate that the system has no solution.
y > x^{2}


Solve by the method of your choice.
x^{3} + y = 0


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:
Find the quadratic function y = ax^{2}+bx + c whose graph passes through the given points.


In a 1mile race, the winner crosses the finish line 10 feet ahead of the secondplace runner and 23 feet ahead of the thirdplace runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the secondplace runner beat the thirdplace runner? (5280 feet in 1 mile.)


Graph the solution set of the system of inequalities or indicate that the system has no solution.
y ≥ 2x – 4


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?


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?


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 Constraints


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


Graph the solution set of the system of inequalities or indicate that the system has no solution.
x^{2} + y^{2} ≤ 49


Solve the system by the addition method.
x^{2} – 3y^{2} = 1


Solve the system by the substitution method.
x^{2} + y^{2} = 113


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 slopeintercept equation of the line that models the percentage, y, of women who smoke x years after 1990 and the slopeintercept equation of the line that models the percentage, y, of men who smoke x years after 1990]


A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width.

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