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

-4a + x = -4
x = -4 + 4a

then substitute the result (-4 - -4a) into the second equation:

4a + 1(-4 + 4a) = 8
4a + (1 x -4) + (1 x 4a) = 8
4a - 4 + 4a = 8
4a + 4a = 8 + 4
8a = 12
a = \( \frac{12}{8} \)
a = 1\(\frac{1}{2}\)

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 d° = 155, the value of a° is 25.

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)(7ab) - (4a²)(5b)
(4 x 7)(a x a x b) - (4 x 5)(a² x b)
(28)(a¹⁺¹ x b) - (20)(a²b)
28a²b - 20a²b
8a²b

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{36} \) = 6

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 6² + 6²
c² = 72
c = \( \sqrt{72} \) = \( \sqrt{36 x 2} \) = \( \sqrt{36} \) \( \sqrt{2} \)
c = 6\( \sqrt{2} \)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).