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

c² = a² + b²
c² = 4² + 8²
c² = 16 + 64
c² = 80
c = \( \sqrt{80} \)

The volume of a cube is height x length x width:

v = h x l x w
v = 5 x 4 x 8
v = 160

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 -18 as well and sum (Inside, Outside) to equal 7. For this problem, those two numbers are -2 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 7y - 18
y² + (-2 + 9)y + (-2 x 9)
(y - 2)(y + 9)

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.

8c + 9 = -9 - 5c
8c = -9 - 5c - 9
8c + 5c = -9 - 9
13c = -18
c = \( \frac{-18}{13} \)
c = -1\(\frac{5}{13}\)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

y² - 7y + 4 = 2y - 4
y² - 7y + 4 + 4 = 2y
y² - 7y - 2y + 8 = 0
y² - 9y + 8 = 0

Next, factor the quadratic equation:

y² - 9y + 8 = 0
(y - 1)(y - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 1) or (y - 8) must equal zero:

If (y - 1) = 0, y must equal 1
If (y - 8) = 0, y must equal 8

So the solution is that y = 1 or 8