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°).

The volume of a cylinder is πr²h:

v = πr²h
v = π(5² x 4)
v = 100π

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:

b² - 2b - 25 = -5b + 3
b² - 2b - 25 - 3 = -5b
b² - 2b + 5b - 28 = 0
b² + 3b - 28 = 0

Next, factor the quadratic equation:

b² + 3b - 28 = 0
(b - 4)(b + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 4) or (b + 7) must equal zero:

If (b - 4) = 0, b must equal 4
If (b + 7) = 0, b must equal -7

So the solution is that b = 4 or -7

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 5)(y - 1)
(y x y) + (y x -1) + (-5 x y) + (-5 x -1)
y² - y - 5y + 5
y² - 6y + 5

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 7 x 9) + (2 x 9 x 8) + (2 x 7 x 8)
sa = (126) + (144) + (112)
sa = 382