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 volume of a cylinder is πr²h:

v = πr²h
v = π(9² x 2)
v = 162π

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, -7) and (2, -1) so the slope becomes:

Plugging these values into the slope-intercept equation:

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

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 + 8c + 39 = -4c + 4
c² + 8c + 39 - 4 = -4c
c² + 8c + 4c + 35 = 0
c² + 12c + 35 = 0

Next, factor the quadratic equation:

c² + 12c + 35 = 0
(c + 5)(c + 7) = 0

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

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

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

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)