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 -5. 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 - 5y + 4
y² + (-4 - 1)y + (-4 x -1)
(y - 4)(y - 1)

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.)

-9b(b - x)
-9(4)(4 - 2)
-9(4)(2)
(-36)(2)
-72

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 6² + 9²
c² = 36 + 81
c² = 117
c = \( \sqrt{117} \)

You need to find the value of b so solve the first equation in terms of z:

-9b + z = -6
z = -6 + 9b

then substitute the result (-6 - -9b) into the second equation:

9b + 6(-6 + 9b) = -3
9b + (6 x -6) + (6 x 9b) = -3
9b - 36 + 54b = -3
9b + 54b = -3 + 36
63b = 33
b = \( \frac{33}{63} \)
b = \(\frac{11}{21}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 53° - 20° = 107°

So, d° = 20° + 107° = 127°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 53° = 127°