Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(7a)(7ab) + (2a²)(9b)
(7 x 7)(a x a x b) + (2 x 9)(a² x b)
(49)(a¹⁺¹ x b) + (18)(a²b)
49a²b + 18a²b
67a²b

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:

a² - 9a + 31 = 2a + 1
a² - 9a + 31 - 1 = 2a
a² - 9a - 2a + 30 = 0
a² - 11a + 30 = 0

Next, factor the quadratic equation:

a² - 11a + 30 = 0
(a - 5)(a - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 5) or (a - 6) must equal zero:

If (a - 5) = 0, a must equal 5
If (a - 6) = 0, a must equal 6

So the solution is that a = 5 or 6

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

sa = 2πr² + 2πrh
sa = 2π(6²) + 2π(6 x 4)
sa = 2π(36) + 2π(24)
sa = (2 x 36)π + (2 x 24)π
sa = 72π + 48π
sa = 120π