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1. + = 1p - 3q = 1
Based on the system of equations above, what is the value of p ?
2. y = x(y - 2)2 - 4 = -x
The system of equations above intersects at two points. What is the sum of the coordinates of the point of intersection in quadrant I?
3. 1 < (c - 1)2 < 36
What is the greatest integer solution to the inequality above?
4. 2y - x ≤ 4-2x + y ≥ -4
If s is the sum of the x- and y-coordinates of any point in the solution to the system of inequalities above as graphed in the xy-plane, what is the greatest possible value of s ?
5. Squares ABCD and WXYZ define two parallel planes such that AW = BX = CY = DZ = 5. Additionally, AB = WX = 4. Point Q lies between the two parallel planes such that it is equidistant from points A, B, C, and D and also equidistant from points W, X, Y, and Z. Lines AQY, BQZ, CQW, and DQX are drawn to create two pyramids. What is the total volume of the two pyramids?
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