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

6a + x = -5
x = -5 - 6a

then substitute the result (-5 - 6a) into the second equation:

-a - 2(-5 - 6a) = 4
-a + (-2 x -5) + (-2 x -6a) = 4
-a + 10 + 12a = 4
-a + 12a = 4 - 10
11a = -6
a = \( \frac{-6}{11} \)
a = -\(\frac{6}{11}\)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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, 5) and (2, 1) so the slope becomes:

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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

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.

9a x 7b = (9 x 7) (a x b) = 63ab