To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -18 as well and sum (Inside, Outside) to equal 7. For this problem, those two numbers are -2 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 7y - 18
y² + (-2 + 9)y + (-2 x 9)
(y - 2)(y + 9)

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

c² = a² + b²
c² = 8² + 5²
c² = 64 + 25
c² = 89
c = \( \sqrt{89} \)

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

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, -7) so the slope becomes:

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 x° = 153, the value of c° is 27.