The factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 the greatest factor 48 and 36 have in common.

Latoya scored 77% on the test meaning she earned 77% of the possible points on the test. There were 60 possible points on the test so she earned 60 x 0.77 = 46 points. Each question is worth 2 points so she got \( \frac{46}{2} \) = 23 questions right.

First, solve for \( \left|y + 2\right| \):

\( \left|y + 2\right| \) - 9 = 6
\( \left|y + 2\right| \) = 6 + 9
\( \left|y + 2\right| \) = 15

The value inside the absolute value brackets can be either positive or negative so (y + 2) must equal + 15 or -15 for \( \left|y + 2\right| \) to equal 15:

So, y = -17 or y = 13.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

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

\( \frac{2 x 7}{5 x 7} \) + \( \frac{4 x 5}{7 x 5} \)

\( \frac{14}{35} \) + \( \frac{20}{35} \)

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

\( \frac{14 + 20}{35} \) = \( \frac{34}{35} \) = \(\frac{34}{35}\)

The equation for this sequence is:

a_n = a_n-1 + 9

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 + 9
a₆ = 37 + 9
a₆ = 46