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 sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 37° - 49° = 94°

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 = \( \sqrt{a} \) = \( \sqrt{36} \) = 6

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 = 6² + 6²
c² = 72
c = \( \sqrt{72} \) = \( \sqrt{36 x 2} \) = \( \sqrt{36} \) \( \sqrt{2} \)
c = 6\( \sqrt{2} \)

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 - 21x + 69 = -4x - 3
x² - 21x + 69 + 3 = -4x
x² - 21x + 4x + 72 = 0
x² - 17x + 72 = 0

Next, factor the quadratic equation:

x² - 17x + 72 = 0
(x - 8)(x - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 8) or (x - 9) must equal zero:

If (x - 8) = 0, x must equal 8
If (x - 9) = 0, x must equal 9

So the solution is that x = 8 or 9

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.