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 c° = 26, the value of x° is 154.

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:

y² + 10y + 33 = -2y - 3
y² + 10y + 33 + 3 = -2y
y² + 10y + 2y + 36 = 0
y² + 12y + 36 = 0

Next, factor the quadratic equation:

y² + 12y + 36 = 0
(y + 6)(y + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (y + 6) must equal zero:

If (y + 6) = 0, y must equal -6

So the solution is that y = -6

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

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° - 66° - 25° = 89°

So, d° = 25° + 89° = 114°

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° - 66° = 114°

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.

(4a)(8ab) + (3a²)(5b)
(4 x 8)(a x a x b) + (3 x 5)(a² x b)
(32)(a¹⁺¹ x b) + (15)(a²b)
32a²b + 15a²b
47a²b