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.

(2a)(7ab) + (2a²)(2b)
(2 x 7)(a x a x b) + (2 x 2)(a² x b)
(14)(a¹⁺¹ x b) + (4)(a²b)
14a²b + 4a²b
18a²b

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -4. 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, -1) and (2, -7) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -1\(\frac{1}{2}\)x - 4

The volume of a cylinder is πr²h:

v = πr²h
v = π(4² x 8)
v = 128π

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

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

y² + 12y + 35 = 0
(y + 5)(y + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 5) or (y + 7) must equal zero:

If (y + 5) = 0, y must equal -5
If (y + 7) = 0, y must equal -7

So the solution is that y = -5 or -7