The area of this shaded rectangle is 12(3) = 36.The sum of the areas of the three shaded rectangles is 60 + 45 + 36 = 141.32 . D
The denominator (3x + 4)(x − 5) is equal to 0 if 3 x + 4 = 0 or if x − 5 = 0. If 3 x + 4 = 0, then 3 x =
−4, and . If x − 5 = 0, then x = 5. The vertical asymptotes are and x = 5.
Values of x with large absolute values can be large positive values of x and can also be
negative values of x; both are far from 0 on the number line. For values of x with large
absolute values, in , x^2 , x, and 3x have much greater absolute values than −64, 4,
and −5. So when x approaches values that have a large absolute value,
approaches . So the horizontal asymptote is . Thus, x = −8 is not an
asymptote, while x = 5 and are asymptotes. (D) is correct.
33 . E
34 . B
The perpendicular distance from the center (h,k) of a circle to a line with the equation x = x 1
is |x 1 − h|. The perpendicular distance from the center (h,k) of a circle to a line with the
equation y = y 1 is |y 1 − k|. If you draw the radii of a circle that are tangent to both lines, the
distance from the center to the two lines will be the same because all radii of a circle are
equal. So you must find the answer choice that is the same positive distance from the lines
with the equations x = 5 and y = 7.Look at choice (A). The distance from (3,7) to the line with the equation x = 5 is |5 − 3| = |2| =
2 . The distance from (3,7) to the line with the equation y = 7 is |7 − 7| = 0. The distances from
(3,7) to the lines with the equations x = 5 and y = 7 are not equal; (A) is incorrect.