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 + 1)(y - 2)
(y x y) + (y x -2) + (1 x y) + (1 x -2)
y² - 2y + y - 2
y² - y - 2

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 0. 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, -3) and (2, 3) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 1\(\frac{1}{2}\)x + 0

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.

8a - 9 < \( \frac{a}{6} \)
6 x (8a - 9) < a
(6 x 8a) + (6 x -9) < a
48a - 54 < a
48a - 54 - a < 0
48a - a < 54
47a < 54
a < \( \frac{54}{47} \)
a < 1\(\frac{7}{47}\)

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

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, \(c = \sqrt{a + b}\)