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.

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 > sign and the answer on the other.

-5z + 7 > \( \frac{z}{1} \)
1 x (-5z + 7) > z
(1 x -5z) + (1 x 7) > z
-5z + 7 > z
-5z + 7 - z > 0
-5z - z > -7
-6z > -7
z > \( \frac{-7}{-6} \)
z > 1\(\frac{1}{6}\)

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).

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -54 as well and sum (Inside, Outside) to equal 3. For this problem, those two numbers are -6 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 3y - 54
y² + (-6 + 9)y + (-6 x 9)
(y - 6)(y + 9)

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

9a + 9y = -3a + 5y + 6
9a = -3a + 5y + 6 - 9y
9a + 3a = 5y + 6 - 9y
12a = -4y + 6
a = \( \frac{-4y + 6}{12} \)
a = \( \frac{-4y}{12} \) + \( \frac{6}{12} \)
a = -\(\frac{1}{3}\)y + \(\frac{1}{2}\)