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).

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 53° - 25° = 102°

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, \(c = \sqrt{a + b}\)

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 -14 as well and sum (Inside, Outside) to equal -5. For this problem, those two numbers are -7 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 5y - 14
y² + (-7 + 2)y + (-7 x 2)
(y - 7)(y + 2)

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

b² + 5b + 6 = 0
(b + 2)(b + 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 2) or (b + 3) must equal zero:

If (b + 2) = 0, b must equal -2
If (b + 3) = 0, b must equal -3

So the solution is that b = -2 or -3