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

c² = a² + b²
c² = 7² + 7²
c² = 49 + 49
c² = 98
c = \( \sqrt{98} \)

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 - 5c - 27 = -3c - 3
c² - 5c - 27 + 3 = -3c
c² - 5c + 3c - 24 = 0
c² - 2c - 24 = 0

Next, factor the quadratic equation:

c² - 2c - 24 = 0
(c + 4)(c - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 4) or (c - 6) must equal zero:

If (c + 4) = 0, c must equal -4
If (c - 6) = 0, c must equal 6

So the solution is that c = -4 or 6

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• 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°)

Applying these relationships starting with c° = 39, the value of b° is 141.

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.