What is the value of x? show all of your work.

x = 9 cm

Step-by-step explanation:

The value of 'x' can be found using the Pythagorean Theorem.  This theorem applies to right triangles and uses the formula:

a² + b² = c², where 'a' and 'b' represent the legs of the triangle and 'c' represents the hypotenuse (diagonal)

Given the values from the triangle:

x² + 6² = (√117)²  or x² + 36 = 117

Subtract 36 from both sides:  x² + 36 - 36 = 117 - 36 or x² = 81

Take the square root:  √x² = √81

x = 9 cm

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a