The distance on the y-axis from point A to point B is the difference in the y-coordinates of points A and B. Since point A is (−2,8) and point B is (5,3), the distance in the y-direction is 8 − 3 = 5.

To solve this problem, distribute the −1 and combine like terms, as follows:
(5x³ + 3xz² − 17z) − (4xz² + 5z − 2x³)
5x³ + 3xz² − 17z − 4xz² − 5z + 2x³
(5x³ + 2x³) + (3xz² − 4xz²) + (−17z − 5z)
7x³ − xz² − 22z

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.

To solve this problem, substitute −3 for x in 2x² − 6x + 7:
2(−3)² − 6(−3) + 7
2(9) − (−18) + 7
18 + 18 + 7 = 43

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.

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

To solve this problem,substitute −5 for x in the expression 2x² + 6x:
2(−5)² + 6(−5)
2(25) − 30
50 − 30 = 20

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.

To solve this problem, first perform the subtractions and then evaluate the absolute values:
|5 − 3|−|2 − 6|
|2|−|− 4|
2 − 4 = −2

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