To add these radicals together their radicands must be the same:

6\( \sqrt{125} \) + 7\( \sqrt{5} \)
6\( \sqrt{25 \times 5} \) + 7\( \sqrt{5} \)
6\( \sqrt{5^2 \times 5} \) + 7\( \sqrt{5} \)
(6)(5)\( \sqrt{5} \) + 7\( \sqrt{5} \)
30\( \sqrt{5} \) + 7\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 12 people needing transportation leaving 12 - 8 = 4 who will have to find other transportation.

The number of students taking German or Spanish is 13 + 6 = 19. Of that group of 19, 6 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 19 - 6 = 13 who are taking at least one language. 25 - 13 = 12 students who are not taking either language.

The equation for this sequence is:

a_n = a_n-1 + 4

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4
a₆ = 17 + 4
a₆ = 21

If 61% of the town's 28,000 voters cast ballots the number of votes cast is:

(\( \frac{61}{100} \)) x 28,000 = \( \frac{1,708,000}{100} \) = 17,080

The mayor got 79% of the votes cast which is:

(\( \frac{79}{100} \)) x 17,080 = \( \frac{1,349,320}{100} \) = 13,493 votes.