A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

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 - 7)
(y x y) + (y x -7) + (9 x y) + (9 x -7)
y² - 7y + 9y - 63
y² + 2y - 63

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

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

-7a - 9z = 2a - 2z + 3
-7a = 2a - 2z + 3 + 9z
-7a - 2a = -2z + 3 + 9z
-9a = 7z + 3
a = \( \frac{7z + 3}{-9} \)
a = \( \frac{7z}{-9} \) + \( \frac{3}{-9} \)
a = -\(\frac{7}{9}\)z - \(\frac{1}{3}\)

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.