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

4c - 2x = -9c - 7x + 9
4c = -9c - 7x + 9 + 2x
4c + 9c = -7x + 9 + 2x
13c = -5x + 9
c = \( \frac{-5x + 9}{13} \)
c = \( \frac{-5x}{13} \) + \( \frac{9}{13} \)
c = -\(\frac{5}{13}\)x + \(\frac{9}{13}\)

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:

(y - 9)(y + 2)
(y x y) + (y x 2) + (-9 x y) + (-9 x 2)
y² + 2y - 9y - 18
y² - 7y - 18

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

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° - 60° - 69° = 51°

So, d° = 69° + 51° = 120°

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° - 60° = 120°

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.