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.

(7a)(6ab) - (6a²)(9b)
(7 x 6)(a x a x b) - (6 x 9)(a² x b)
(42)(a¹⁺¹ x b) - (54)(a²b)
42a²b - 54a²b
-12a²b

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(7 + 2)(3)
a = ½(9)(3)
a = ½(27) = \( \frac{27}{2} \)
a = 13\(\frac{1}{2}\)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• 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°)

Applying these relationships starting with a° = 13, the value of y° is 167.

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 7² + 6²
c² = 49 + 36
c² = 85
c = \( \sqrt{85} \)

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