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

5\( \sqrt{175} \) + 2\( \sqrt{7} \)
5\( \sqrt{25 \times 7} \) + 2\( \sqrt{7} \)
5\( \sqrt{5^2 \times 7} \) + 2\( \sqrt{7} \)
(5)(5)\( \sqrt{7} \) + 2\( \sqrt{7} \)
25\( \sqrt{7} \) + 2\( \sqrt{7} \)

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

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

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

\( \frac{6 x 5}{9 x 5} \) + \( \frac{4 x 3}{15 x 3} \)

\( \frac{30}{45} \) + \( \frac{12}{45} \)

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

\( \frac{30 + 12}{45} \) = \( \frac{42}{45} \) = \(\frac{14}{15}\)

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

5b⁶ - 6b⁶
(5 - 6)b⁶
-b⁶

If 81% of the town's 10,000 voters cast ballots the number of votes cast is:

(\( \frac{81}{100} \)) x 10,000 = \( \frac{810,000}{100} \) = 8,100

The mayor got 82% of the votes cast which is:

(\( \frac{82}{100} \)) x 8,100 = \( \frac{664,200}{100} \) = 6,642 votes.

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