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°).

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

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 + 8c - 21 = 2c - 5
c² + 8c - 21 + 5 = 2c
c² + 8c - 2c - 16 = 0
c² + 6c - 16 = 0

Next, factor the quadratic equation:

c² + 6c - 16 = 0
(c - 2)(c + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 8) must equal zero:

If (c - 2) = 0, c must equal 2
If (c + 8) = 0, c must equal -8

So the solution is that c = 2 or -8

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

c² = a² + b²
c² = 3² + 7²
c² = 9 + 49
c² = 58
c = \( \sqrt{58} \)