Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and 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°).

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

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

b + y = 9
y = 9 - b

then substitute the result (9 - 1b) into the second equation:

9b + 2(9 - b) = -5
9b + (2 x 9) + (2 x -b) = -5
9b + 18 - 2b = -5
9b - 2b = -5 - 18
7b = -23
b = \( \frac{-23}{7} \)
b = -3\(\frac{2}{7}\)

A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.

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.)

8b(b - z)
8(2)(2 - 8)
8(2)(-6)
(16)(-6)
-96