The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² + 4a - 11 = 5a + 1
a² + 4a - 11 - 1 = 5a
a² + 4a - 5a - 12 = 0
a² - a - 12 = 0

Next, factor the quadratic equation:

a² - a - 12 = 0
(a + 3)(a - 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 3) or (a - 4) must equal zero:

If (a + 3) = 0, a must equal -3
If (a - 4) = 0, a must equal 4

So the solution is that a = -3 or 4

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(4 + 7)(5)
a = ½(11)(5)
a = ½(55) = \( \frac{55}{2} \)
a = 27\(\frac{1}{2}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

8a + 8a = 16a

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

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 20° - 28° = 132°

So, d° = 28° + 132° = 160°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 20° = 160°