The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:

c = πd
c = π(2 * r)
c = π(2 * 11)
c = 22π

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.

6a + 5a = 11a

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 3) and (2, 1) so the slope becomes:

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -4 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -4 and 1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 3y - 4
y² + (-4 + 1)y + (-4 x 1)
(y - 4)(y + 1)