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 9 as well and sum (Inside, Outside) to equal -10. For this problem, those two numbers are -9 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 10y + 9
y² + (-9 - 1)y + (-9 x -1)
(y - 9)(y - 1)

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(3 + 3)(5)
a = ½(6)(5)
a = ½(30) = \( \frac{30}{2} \)
a = 15

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with y° = 146, the value of d° is 146.

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

a(a - y)
1(-3)(-3 + 4)
1(-3)(1)
(-3)(1)
-3

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 50° - 53° = 77°