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

z² - 6z - 7 = 0
(z + 1)(z - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 1) or (z - 7) must equal zero:

If (z + 1) = 0, z must equal -1
If (z - 7) = 0, z must equal 7

So the solution is that z = -1 or 7

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

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 combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

3a + 8a = 11a

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, -2) and (2, -4) so the slope becomes:

Plugging these values into the slope-intercept equation:

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