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 b° = 144, the value of y° is 144.

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

You need to find the value of a so solve the first equation in terms of x:

9a + x = 5
x = 5 - 9a

then substitute the result (5 - 9a) into the second equation:

2a - 9(5 - 9a) = 5
2a + (-9 x 5) + (-9 x -9a) = 5
2a - 45 + 81a = 5
2a + 81a = 5 + 45
83a = 50
a = \( \frac{50}{83} \)
a = \(\frac{50}{83}\)

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.

(2a)(7ab) + (4a²)(6b)
(2 x 7)(a x a x b) + (4 x 6)(a² x b)
(14)(a¹⁺¹ x b) + (24)(a²b)
14a²b + 24a²b
38a²b

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:

x² - 3x - 7 = 2x - 1
x² - 3x - 7 + 1 = 2x
x² - 3x - 2x - 6 = 0
x² - 5x - 6 = 0

Next, factor the quadratic equation:

x² - 5x - 6 = 0
(x + 1)(x - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x - 6) must equal zero:

If (x + 1) = 0, x must equal -1
If (x - 6) = 0, x must equal 6

So the solution is that x = -1 or 6