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).

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

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-3x + 3 = \( \frac{x}{4} \)
4 x (-3x + 3) = x
(4 x -3x) + (4 x 3) = x
-12x + 12 = x
-12x + 12 - x = 0
-12x - x = -12
-13x = -12
x = \( \frac{-12}{-13} \)
x = \(\frac{12}{13}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a⁵ - 5a⁵ = 2a⁵

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² + 12y + 27 = 0
(y + 3)(y + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 3) or (y + 9) must equal zero:

If (y + 3) = 0, y must equal -3
If (y + 9) = 0, y must equal -9

So the solution is that y = -3 or -9