If 38% of the town's 46,000 voters cast ballots the number of votes cast is:

(\( \frac{38}{100} \)) x 46,000 = \( \frac{1,748,000}{100} \) = 17,480

The mayor got 81% of the votes cast which is:

(\( \frac{81}{100} \)) x 17,480 = \( \frac{1,415,880}{100} \) = 14,159 votes.

The number of students taking German or Spanish is 8 + 13 = 21. Of that group of 21, 4 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 21 - 4 = 17 who are taking at least one language. 23 - 17 = 6 students who are not taking either language.

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).

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 have in common.

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:

-5z⁶ + 7z⁶
(-5 + 7)z⁶
2z⁶