The number of students taking German or Spanish is 8 + 9 = 17. Of that group of 17, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 17 - 2 = 15 who are taking at least one language. 27 - 15 = 12 students who are not taking either language.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 54 meters so the equation becomes: 2w + 2h = 54.

Putting these two equations together and solving for width (w):

2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9

Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m²

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{8} \) ÷ \( \frac{1}{8} \) = \( \frac{1}{8} \) x \( \frac{8}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{8} \) x \( \frac{8}{1} \) = \( \frac{1 x 8}{8 x 1} \) = \( \frac{8}{8} \) = 1

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).