Amy can run 3.5 miles in x minutes. At that pace, how many minutes would it take her to run 10.5 miles?

Solution
Which one of the following lines has the smallest slope?

Solution
To find which equation has the smallest slope, first convert any equations to slope intercept form (y = mx + b, where m is the slope and b is the yintercept) if they are not already in that form. In choice E, dividing both sides of 7y = 3x − 7 by 7 yields y = \(\frac{3x}{7}\) − 1, which has a slope of ^{3}⁄_{7}. When compared to the other slopes, ^{1}⁄_{2} is the smallest (the next closest is ^{1}⁄_{2}, which is only slightly larger than ^{3}⁄_{7}).
What is the slope of any line parallel to the yaxis in the (x, y) coordinate plane?

Solution
Any line parallel to the yaxis is a vertical line. Vertical lines have slopes that are undefined. Remember that the definition of slope is rise/run; vertical lines have no run and thus dividing rise by run is dividing by 0, making the quotient undefined.
What value of t will satisfy the equation 0.1(t + 3, 420) = t?

Solution
To solve this problem, first distribute then combine like terms. Distribute
0.1 as follows:
0.1(t + 3,420) = t
0.1t + 342 = t.
342 = 0.9t.
t = \(\frac{342}{0.9}\) = 380
If 5−2x>5, which of the following is a possible value of x?

Solution
Given that 5 − 2x > 5, then either 5 − 2x > 5 or 5 − 2x < −5. In the case that 5 − 2x > 5, −2x > 0 making x < 0 (when you divide by a negative number remember to switch the direction of the inequality). In the case that 5 − 2x < −5, then −2x < −10 making x > 5. Thus the range for x is x < 0 or x > 5. Of the answer choices, only 6 fits into the range for x.
In a certain music store, CDs were put on display and assigned prices for May. Each month after that, the price was 20% less than the price for the previous month. If the price of a CD was d dollars in May, what was the price in August?

Solution
Between May and August, there were 3 price decreases (in June, July, and August). If the price was decreased by 20%, then the resulting price was 80% of the previous month’s price. Thus, in June the price was 0.8d; in July the price was 0.8(0.8d); in August the price was 0.8(0.8(0.8d)), which is equivalent to (0.8)3d, or 0.512d.
If ^{a2x}⁄_{ay} = a^{4} for all a ≠ 0, which of the following must be true?

Solution
To divide ^{ax}⁄_{ay} , subtract the exponents. Thus ^{ax}⁄_{ay} = a^{x−y}. If a^{x}⁄_{ay} = a^{4}, the a^{x−y} = a^{4}, making x − y = 4.
In the (x, y) coordinate plane, what is the yintercept of the line 5x + 3y = 8?

Solution
To solve this problem, convert 5x + 3y = 8 to the slopeintercept form, y = mx + b, where m is the slope and b is the yintercept. To do so, first subtract 5x from both sides to get 3y = −5x + 8. Dividing the entire equation by 3 yields y = −\(\frac{5x}{3}\)+^{8}⁄_{3}. Thus ^{8}⁄_{3}
If cos A = ^{4}⁄_{5}, and sin A = ^{3}⁄_{5}, then tan A = ?

Solution
To solve this problem, it may be helpful to draw a picture in which one angle of a right triangle is labeled A, as shown below:
Because cos A = ^{4}⁄_{5}, let the side adjacent to angle A be 4 and the hypotenuse be 5. Likewise, since sin A = ^{3}⁄_{5}, let the side opposite angle A be 3 and the hypotenuse be 5. It follows then that tan A =side opposite divided by side adjacent, or ^{3}⁄_{4}
For all x > 0,^{1}⁄_{x} + ^{3}⁄_{4} = ?

Solution
In order to add ^{1}⁄_{x} + ^{3}⁄_{4}, the fractions must have a common denominator. To achieve a common denominator, multiply ^{1}⁄_{x} by ^{4}⁄_{4} and ^{3}⁄_{4} by ^{x}⁄_{x} to get \(\frac{4}{4x}+\frac{3x}{4x}\), which equals \(\frac{(4 + 3x)}{4x}\)