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 + 7)(y + 4)
(y x y) + (y x 4) + (7 x y) + (7 x 4)
y² + 4y + 7y + 28
y² + 11y + 28

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

-4a + 3 > \( \frac{a}{5} \)
5 x (-4a + 3) > a
(5 x -4a) + (5 x 3) > a
-20a + 15 > a
-20a + 15 - a > 0
-20a - a > -15
-21a > -15
a > \( \frac{-15}{-21} \)
a > \(\frac{5}{7}\)

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(5 + 6)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22

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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

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 = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 2 x 3 = \( \frac{6}{2} \) = 3