x y = 5Quantity Ax2 y2Quantity B5
Answer(s): D
Since x2 2 = (x y)(x + ) 5(x + ), the value of Quantity A depends on x + y.If x + > 1, then x2 y2 > 5.If x + = 1, then x2 y2 = 5.If x + < 1, then x2 y2 < 5.Because all three cases are possible, the relationship cannot be determined from the information given.
Triangle PQR is inscribed in a circle, and side PR is a diameter of the circle.Quantity AThe area of triangle PQRQuantity B1/3 of the area of the circle
Answer(s): B
Since PR is a diameter, triangle PQR is a right triangle with right angle at Q.Let the diameter be d. The legs PQ and QR satisfy.PQ2 + QR2 = d2The area of the triangle is(PQ)(QR)For a right triangle with fixed hypotenuse d, the product PQ QR is maximized whengiving the maximum possible area:The area of the circle isOne-third of the circle's area isCompare the maximum triangle area to one-third of the circle's area:Multiply both sides by 12:3d2 vs. d2.Since 3 < ,Thus, even the largest possible triangle area is always less than one-third of the circle's area.Quantity B is always greater.
If r = 3x and , then r2 =
Answer(s): C
Given r = 3x and x =4/rSubstitute into the first equation:Multiply both sides by :r2 = 12
S is a set of n consecutive even integers.What is the range of the integers in S, in terms of n?
Answer(s): E
A set of n consecutive even integers has the form k, k + 2, k + 4, ..., k + 2(n - 1).Range = (largest) (smallest)= (k + 2(n - 1)) - k = 2(n - 1).So, the range is 2(n - 1).
In the xy-plane, the circle shown is the graph of x2 + x2 = 4.Which of the following best represents the graph of the circle and the line y x + 2 = 0?
1. Circle: x2 + 2 = 4 is a circle of radius 2 centered at the origin.2. Line: x + 2 = 0 --> = x 2slope - +1 (rises up to the right)y-intercept (0, 2) - the lowest point on the circle x-intercept (2, 0) - the right-most point on the circle3. Therefore the line must pass through the bottom point (0, 2) and the right-most point (2, 0) of the circle, tilting upward with positive slope and lying below the center (0, 0).
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