When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 2)
sa = 2π(1) + 2π(2)
sa = (2 x 1)π + (2 x 2)π
sa = 2π + 4π
sa = 6π

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:

b² + 6b - 26 = 5b + 4
b² + 6b - 26 - 4 = 5b
b² + 6b - 5b - 30 = 0
b² + b - 30 = 0

Next, factor the quadratic equation:

b² + b - 30 = 0
(b - 5)(b + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 5) or (b + 6) must equal zero:

If (b - 5) = 0, b must equal 5
If (b + 6) = 0, b must equal -6

So the solution is that b = 5 or -6

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 12cm + 7cm + 5cm = 24cm