To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-z + 7 = 6 - 2z
-z = 6 - 2z - 7
-z + 2z = 6 - 7
z = -1

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

Plugging these values into the slope-intercept equation:

y = 2x + 0

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

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).

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

6c + x = -2
x = -2 - 6c

then substitute the result (-2 - 6c) into the second equation:

7c - 4(-2 - 6c) = 9
7c + (-4 x -2) + (-4 x -6c) = 9
7c + 8 + 24c = 9
7c + 24c = 9 - 8
31c = 1
c = \( \frac{1}{31} \)
c = \(\frac{1}{31}\)