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1. If , what is the value of x + 2y?
If (a, b) is a point in the solution region for the system of inequalities shown above and a = 6, what is the minimum possible value for b?
3. If xn is the simplified form of the expression above, what is the value of n?
4. Note: Figure not drawn to scale.
In the figure above, the area of the shaded region is 52 square units. What is the height of the larger triangle?
5. If y = ax2 + bx + c passes through the points (-3, 10), (0, 1), and (2, 15), what is the value of a + b + c?
The figure above shows the solution for the system of inequalities . Suppose (a, b) is a solution to the system. If a = 0, what is the greatest possible integer value of b?
7. Given the function , what input value corresponds to an output of 3?
If the area of the shaded sector in circle C shown above is 6π square units, what is the diameter of the circle?
9. If a circle is given by the equation x2 + y2 + 10x - 4y = 20, what is its diameter?
10. In economics, the law of demand states that as the price of a commodity rises, the demand for that commodity goes down. A company determines that the monthly demand for a certain item that it sells can be modeled by the function q(p) = -2p + 34, where q represents the quantity sold in hundreds and p represents the selling price in dollars. It costs $7 to produce this item. How much more per month in profits can the company expect to earn by selling the item at $12 instead of $10? (Profit = sales – costs)
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