The number of students taking German or Spanish is 7 + 13 = 20. Of that group of 20, 5 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 20 - 5 = 15 who are taking at least one language. 29 - 15 = 14 students who are not taking either language.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-3a⁷ + 9a⁷
(-3 + 9)a⁷
6a⁷

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 7}{5 x 7} \) - \( \frac{9 x 5}{7 x 5} \)

\( \frac{14}{35} \) - \( \frac{45}{35} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{14 - 45}{35} \) = \( \frac{-31}{35} \) = -\(\frac{31}{35}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

By buying two shirts, Roger will save $20 x \( \frac{50}{100} \) = \( \frac{$20 x 50}{100} \) = \( \frac{$1000}{100} \) = $10.00 on the second shirt.

So, his total cost will be
$20.00 + ($20.00 - $10.00)
$20.00 + $10.00
$30.00