The volume of a cylinder is πr²h:

v = πr²h
v = π(9² x 2)
v = 162π

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

-7a(a - z)
-7(5)(5 + 3)
-7(5)(8)
(-35)(8)
-280

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 16 as well and sum (Inside, Outside) to equal -10. For this problem, those two numbers are -8 and -2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 10y + 16
y² + (-8 - 2)y + (-8 x -2)
(y - 8)(y - 2)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 63° - 40° = 77°

So, d° = 40° + 77° = 117°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 63° = 117°

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.

9z + 3 = \( \frac{z}{6} \)
6 x (9z + 3) = z
(6 x 9z) + (6 x 3) = z
54z + 18 = z
54z + 18 - z = 0
54z - z = -18
53z = -18
z = \( \frac{-18}{53} \)
z = -\(\frac{18}{53}\)