To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(2ab) + (6a²)(5b)
(8 x 2)(a x a x b) + (6 x 5)(a² x b)
(16)(a¹⁺¹ x b) + (30)(a²b)
16a²b + 30a²b
46a²b

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

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.

-6b + 6 < \( \frac{b}{6} \)
6 x (-6b + 6) < b
(6 x -6b) + (6 x 6) < b
-36b + 36 < b
-36b + 36 - b < 0
-36b - b < -36
-37b < -36
b < \( \frac{-36}{-37} \)
b < \(\frac{36}{37}\)

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -2. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -4) and (2, 0) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = x - 2

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)