In the standard (x,y) coordinate plane shown below, what is the distance on the yaxis, in units, from point A to point B?

Solution
The distance on the yaxis from point A to point B is the difference in the ycoordinates of points A and B. Since point A is (−2,8) and point B is (5,3), the distance in the ydirection is 8 − 3 = 5.
(5x^{3} + 3xz^{2} − 17z) − (4xz^{2} + 5z − 2x^{3}) = ?

Solution
To solve this problem, distribute the −1 and combine like terms, as follows:
(5x^{3} + 3xz^{2} − 17z) − (4xz^{2} + 5z − 2x^{3})
5x^{3} + 3xz^{2} − 17z − 4xz^{2} − 5z + 2x^{3}
(5x^{3} + 2x^{3}) + (3xz^{2} − 4xz^{2}) + (−17z − 5z)
7x^{3} − xz^{2} − 22z
A map is drawn so that 1.2 inches represents 50 miles. About how many miles do 1.4 inches represent?

Solution
To solve this problem, set up a proportion between the length in inches and the length in miles represented. Let the x be the number of miles represented by 1.4 inches. Since 1.2 inches represents 50 miles, \(\frac{50}{1.2}\)
= \(\frac{x}{1.4}\). Multiplying both sides of the proportion by 1.4
yields x = \(\frac{(50)(1.4)}{1.2}\) ≈ 58 miles.
If f (x) = 2x^{2} DO YOUR FIGURING HERE. 2 − 6x + 7, then f (−3) =?

Solution
To solve this problem, substitute −3 for x in 2x^{2} − 6x + 7:
2(−3)^{2} − 6(−3) + 7
2(9) − (−18) + 7
18 + 18 + 7 = 43
In the figure below, S and T are points on RU. What is the ratio of the area of square STVX to the area of parallelogram RUVY?

Solution
Recall that the area of a parallelogram is equivalent to base × height. Since STVX is a square, all sides of STVX will be equal. Likewise, since the height of the parallelogram is equal to the height of the square, the height of the parallelogram is 3. The area of the square STVX is 32 = 9. The area of the parallelogram is therefore (8 + 3)(3) = (11)(3), or 33. Thus the ratio of the area of square STVX to the area of parallelogram RUVY is 9:33, or 3:11.
For what value of a is b = 4 a solution to the equation b − 2 = ab + 16?

Solution
To solve this problem, substitute 4 for b in the equation b − 2 = ab + 16:
4 − 2 = 4a + 16
2 − 16 = 4a + 16 − 16
\(\frac{(−14)}{4}=\frac{(4a)}{4}\)
a = −\(\frac{14}{4}\)= −3.5
If x = −5, what is the value of 2x^{2} + 6x?

Solution
To solve this problem,substitute −5 for x in the expression 2x^{2} + 6x:
2(−5)^{2} + 6(−5)
2(25) − 30
50 − 30 = 20
If Ryan traveled 20 miles in 4 hours and Jeff traveled twice as far in half the time, what was Jeff’s average speed, in miles per hour?

Solution
Since Jeff traveled twice as far as Ryan in half the time, Jeff traveled 40 miles in 2 hours. Jeff’s average speed is equivalent to 40 miles ÷ 2 hours, or 20 miles per hour.
5 − 3−2 − 6 = ?

Solution
To solve this problem, first perform the subtractions and then evaluate the absolute values:
5 − 3−2 − 6
2−− 4
2 − 4 = −2
A pie recipe calls for ^{1}⁄_{3} cup sugar to make one 9inch pie. According to this recipe, how many cups of sugar should be used to make three 9inch pies?

Solution
If a pie recipe calls for ^{1}⁄_{3} cup sugar to make one 9inch pie, making three 9inch pies will require 3(^{1}⁄_{3}), or 1 cup of sugar.