The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr²
a = π(4²)
a = 16π

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

y² - 15y + 25 = -5y + 1
y² - 15y + 25 - 1 = -5y
y² - 15y + 5y + 24 = 0
y² - 10y + 24 = 0

Next, factor the quadratic equation:

y² - 10y + 24 = 0
(y - 4)(y - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 4) or (y - 6) must equal zero:

If (y - 4) = 0, y must equal 4
If (y - 6) = 0, y must equal 6

So the solution is that y = 4 or 6

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 4 x 7
a = 28

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 -4 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -4 and 1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 3y - 4
y² + (-4 + 1)y + (-4 x 1)
(y - 4)(y + 1)