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p - 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 ?
A cube with side length 6 is shown in the figure above. If point Q lies on square ABCD and is equidistant from points A , B , C , and D , what is the volume of pyramid EFGHQ?
As a space probe descends to the surface of Mars, its distance in meters above the surface can be modeled by the equation above. If t is the time in seconds it will take the probe to reach the surface, and it takes the probe 8 seconds to descend the final 120 meters to the surface, what is the value of the deceleration constant a ?
7. 3h - j = 7
2h + 3j = 1
Based on the system of equations above, what is the value of h ?
8. A rectangular box has a volume of 24. If the length is halved and the height is tripled, what will be the new volume of the box?
9. If 6 e ( e + 3) = 3 e (2 e + 4) + 5, what is the value of e ?
10. Abeena is making punch for a winter party in a punch bowl that can hold at most 9 quarts. She wants to get as much vitamin C in her punch as possible, so she is using only orange juice and grape juice. She has 6 quarts of orange juice, which has 2 grams of vitamin C per quart, and 7 quarts of grape juice, which has 1 gram of vitamin C per quart. If there are 4 cups in a quart, what is the greatest possible amount of vitamin C, in grams, that Abeena can have in one cup of her punch?
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