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 z:

4c + z = 9
z = 9 - 4c

then substitute the result (9 - 4c) into the second equation:

-6c - 2(9 - 4c) = -1
-6c + (-2 x 9) + (-2 x -4c) = -1
-6c - 18 + 8c = -1
-6c + 8c = -1 + 18
2c = 17
c = \( \frac{17}{2} \)
c = 8\(\frac{1}{2}\)

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 4)(y + 4)
(y x y) + (y x 4) + (4 x y) + (4 x 4)
y² + 4y + 4y + 16
y² + 8y + 16

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 = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

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 = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)