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.

2a + 2a = 4a

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

sa = 2πr² + 2πrh
sa = 2π(2²) + 2π(2 x 5)
sa = 2π(4) + 2π(10)
sa = (2 x 4)π + (2 x 10)π
sa = 8π + 20π
sa = 28π

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-3a + z = 3a - 9z + 3
-3a = 3a - 9z + 3 - z
-3a - 3a = -9z + 3 - z
-6a = -10z + 3
a = \( \frac{-10z + 3}{-6} \)
a = \( \frac{-10z}{-6} \) + \( \frac{3}{-6} \)
a = 1\(\frac{2}{3}\)z - \(\frac{1}{2}\)

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

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 < sign and the answer on the other.

-5c + 1 < \( \frac{c}{3} \)
3 x (-5c + 1) < c
(3 x -5c) + (3 x 1) < c
-15c + 3 < c
-15c + 3 - c < 0
-15c - c < -3
-16c < -3
c < \( \frac{-3}{-16} \)
c < \(\frac{3}{16}\)