The volume of a cylinder is πr²h:

v = πr²h
v = π(4² x 8)
v = 128π

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

6a - 8 = \( \frac{a}{-2} \)
-2 x (6a - 8) = a
(-2 x 6a) + (-2 x -8) = a
-12a + 16 = a
-12a + 16 - a = 0
-12a - a = -16
-13a = -16
a = \( \frac{-16}{-13} \)
a = 1\(\frac{3}{13}\)

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 4. 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, 9) and (2, -1) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -2\(\frac{1}{2}\)x + 4

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 -35 as well and sum (Inside, Outside) to equal -2. For this problem, those two numbers are -7 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 2y - 35
y² + (-7 + 5)y + (-7 x 5)
(y - 7)(y + 5)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 9² + 6²
c² = 81 + 36
c² = 117
c = \( \sqrt{117} \)