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, \(c = \sqrt{a + b}\)

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

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 - 6c + 20 = 4c - 1
c² - 6c + 20 + 1 = 4c
c² - 6c - 4c + 21 = 0
c² - 10c + 21 = 0

Next, factor the quadratic equation:

c² - 10c + 21 = 0
(c - 3)(c - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 3) or (c - 7) must equal zero:

If (c - 3) = 0, c must equal 3
If (c - 7) = 0, c must equal 7

So the solution is that c = 3 or 7

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 40° - 64° = 76°

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².