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 formula for circumference is circle diameter x π:

c = πd
c = 9π

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:

c² + 19c + 59 = 3c - 4
c² + 19c + 59 + 4 = 3c
c² + 19c - 3c + 63 = 0
c² + 16c + 63 = 0

Next, factor the quadratic equation:

c² + 16c + 63 = 0
(c + 7)(c + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 7) or (c + 9) must equal zero:

If (c + 7) = 0, c must equal -7
If (c + 9) = 0, c must equal -9

So the solution is that c = -7 or -9

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

When solving an equation with two variables, 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.)