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

6\( \sqrt{27} \) - 7\( \sqrt{3} \)
6\( \sqrt{9 \times 3} \) - 7\( \sqrt{3} \)
6\( \sqrt{3^2 \times 3} \) - 7\( \sqrt{3} \)
(6)(3)\( \sqrt{3} \) - 7\( \sqrt{3} \)
18\( \sqrt{3} \) - 7\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 have in common.

There are 2 5-passenger taxis available so that's 2 x 5 = 10 total seats. There are 12 people needing transportation leaving 12 - 10 = 2 who will have to find other transportation.

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

\( \frac{4}{8} \) ÷ \( \frac{3}{9} \) = \( \frac{4}{8} \) x \( \frac{9}{3} \)

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

\( \frac{4}{8} \) x \( \frac{9}{3} \) = \( \frac{4 x 9}{8 x 3} \) = \( \frac{36}{24} \) = 1\(\frac{1}{2}\)

The equation for this sequence is:

a_n = a_n-1 + 7

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 + 7
a₆ = 29 + 7
a₆ = 36