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

z² + 4z - 5 = 0
(z - 1)(z + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 1) or (z + 5) must equal zero:

If (z - 1) = 0, z must equal 1
If (z + 5) = 0, z must equal -5

So the solution is that z = 1 or -5

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

The formula for area is πr²:

a = πr²
a = π(4²)
a = 16π

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 -3. 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, -8) and (2, 2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 2\(\frac{1}{2}\)x - 3

You need to find the value of c so solve the first equation in terms of x:

8c + x = -3
x = -3 - 8c

then substitute the result (-3 - 8c) into the second equation:

-8c - 4(-3 - 8c) = -9
-8c + (-4 x -3) + (-4 x -8c) = -9
-8c + 12 + 32c = -9
-8c + 32c = -9 - 12
24c = -21
c = \( \frac{-21}{24} \)
c = -\(\frac{7}{8}\)