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

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 - 11x + 9 = -3x - 3
x² - 11x + 9 + 3 = -3x
x² - 11x + 3x + 12 = 0
x² - 8x + 12 = 0

Next, factor the quadratic equation:

x² - 8x + 12 = 0
(x - 2)(x - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 2) or (x - 6) must equal zero:

If (x - 2) = 0, x must equal 2
If (x - 6) = 0, x must equal 6

So the solution is that x = 2 or 6

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

-6a + x = -4
x = -4 + 6a

then substitute the result (-4 - -6a) into the second equation:

-a - 9(-4 + 6a) = -8
-a + (-9 x -4) + (-9 x 6a) = -8
-a + 36 - 54a = -8
-a - 54a = -8 - 36
-55a = -44
a = \( \frac{-44}{-55} \)
a = \(\frac{4}{5}\)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).