is not true, so eliminate (A). In (B), d = 2, and the equation becomes . Solve both sides of the equation to get
, or . Reduce both fractions to get .Eliminate (B). In (C), d = 4 and the equation becomes .Solve both sides of the equation to get , or .Reduce both fractions to get = . The correct answer is (C).11. D All the answer choices are equal to 4 (which is r^2 , making r = 2), so you need to focus on
where the center of the circle lies. If the circle is tangent to both the x-axis (which is
equivalent to the line y = 0) and the line x = 4, then the center must be 2 units from y = 0 and
2 units from x = 4. Choices (A) and (B) both have centers with an x value of −2 (remember
the standard form of the circle equation is (x − h)^2 + (y – k)^2 = r^2 , where (h, k) is the center
and r is the radius), which is 6 units from x = 4. Eliminate (A) and (B). Choice (C) has a
center at (2, −4). The x-value is 2 units from x = 4; however, the y-value is 4 units from y =
Eliminate (C) and choose (D).
B According to the question, Reactant A does not react unless B gets to a certain
concentration. Therefore, the correct answer will have an initial flat line for A while the
line for B is rising. Only graph (B) shows this initial relationship. Therefore, the correct
answer is (B).
A All of the answer choices have the same lines graphed, so this question is really about the
shading. Plugging In is probably the easiest way to approach this problem. Start with (0, 0)
because this is an easy value to check. This works in all three equations since 0 ≤ 8, –3 ≤ 0,
and 1 ≥ 0. Therefore, this value needs to be shaded as a possible answer. Eliminate (B),
(C), and (D) because they do not include this point. The correct answer is (A).
B The question says that tan BCA is , so draw segment CA. Since tan = , . Let
AB = 3x and BC = 4x. The question says that the area of the rectangle is 48. The formula forthe area of the rectangle is A = lw. Plug in A = 48, l = 3x, and w = 4x into the formula to get48 = (3x)(4x). Simplify the right side to get 48 = 12x^2 . Divide both sides by 12 to get 4 =x^2 . Then take the square root of both sides to get x = 2. Therefore, AB = 3x = 3(2) = 6, andBC = 4x = 4(2) = 8. The question asks for the length of BD, which is the diagonal of therectangle and equal to diagonal AC. The diagonal of the rectangle is the hypotenuse of a