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.

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

8a x 2b = (8 x 2) (a x b) = 16ab

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 + 15c + 22 = 3c - 5
c² + 15c + 22 + 5 = 3c
c² + 15c - 3c + 27 = 0
c² + 12c + 27 = 0

Next, factor the quadratic equation:

c² + 12c + 27 = 0
(c + 3)(c + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 3) or (c + 9) must equal zero:

If (c + 3) = 0, c must equal -3
If (c + 9) = 0, c must equal -9

So the solution is that c = -3 or -9

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° = 40, the value of d° is 140.

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

8a + 2a = 10a