The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 2. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -4) and (2, 8) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 3x + 2

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 10 as well and sum (Inside, Outside) to equal -7. For this problem, those two numbers are -5 and -2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 7y + 10
y² + (-5 - 2)y + (-5 x -2)
(y - 5)(y - 2)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(4²) + 2π(4 x 6)
sa = 2π(16) + 2π(24)
sa = (2 x 16)π + (2 x 24)π
sa = 32π + 48π
sa = 80π