First, solve for \( \left|b + 0\right| \):

\( \left|b + 0\right| \) + 9 = 4
\( \left|b + 0\right| \) = 4 - 9
\( \left|b + 0\right| \) = -5

The value inside the absolute value brackets can be either positive or negative so (b + 0) must equal - 5 or --5 for \( \left|b + 0\right| \) to equal -5:

So, b = 5 or b = -5.

If 39% of the town's 17,000 voters cast ballots the number of votes cast is:

(\( \frac{39}{100} \)) x 17,000 = \( \frac{663,000}{100} \) = 6,630

The mayor got 65% of the votes cast which is:

(\( \frac{65}{100} \)) x 6,630 = \( \frac{430,950}{100} \) = 4,310 votes.

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{56} \) = \( \frac{\frac{40}{8}}{\frac{56}{8}} \) = \( \frac{5}{7} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{6 x 5}{3 x 5} \) + \( \frac{7 x 3}{5 x 3} \)

\( \frac{30}{15} \) + \( \frac{21}{15} \)

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

\( \frac{30 + 21}{15} \) = \( \frac{51}{15} \) = 3\(\frac{2}{5}\)

Jennifer scored 97% on the test meaning she earned 97% of the possible points on the test. There were 300 possible points on the test so she earned 300 x 0.97 = 291 points. Each question is worth 3 points so she got \( \frac{291}{3} \) = 97 questions right.