Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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

z² + 3z - 54 = 0
(z - 6)(z + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 6) or (z + 9) must equal zero:

If (z - 6) = 0, z must equal 6
If (z + 9) = 0, z must equal -9

So the solution is that z = 6 or -9

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

c = πd
c = π(2 * r)
c = π(2 * 5)
c = 10π

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

Plugging these values into the slope-intercept equation:

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