The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² + 8y + 12 = 0
(y + 2)(y + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 2) or (y + 6) must equal zero:

If (y + 2) = 0, y must equal -2
If (y + 6) = 0, y must equal -6

So the solution is that y = -2 or -6

The volume of a cylinder is πr²h:

v = πr²h
v = π(1² x 6)
v = 6π

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

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 = \( \sqrt{a} \) = \( \sqrt{36} \) = 6

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 = 6² + 6²
c² = 72
c = \( \sqrt{72} \) = \( \sqrt{36 x 2} \) = \( \sqrt{36} \) \( \sqrt{2} \)
c = 6\( \sqrt{2} \)

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)(2ab) - (7a²)(4b)
(8 x 2)(a x a x b) - (7 x 4)(a² x b)
(16)(a¹⁺¹ x b) - (28)(a²b)
16a²b - 28a²b
-12a²b