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 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

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

\( \frac{4 x 7}{3 x 7} \) + \( \frac{2 x 3}{7 x 3} \)

\( \frac{28}{21} \) + \( \frac{6}{21} \)

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

\( \frac{28 + 6}{21} \) = \( \frac{34}{21} \) = 1\(\frac{13}{21}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

First, solve for \( \left|y + 9\right| \):

\( \left|y + 9\right| \) - 1 = -4
\( \left|y + 9\right| \) = -4 + 1
\( \left|y + 9\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (y + 9) must equal - 3 or --3 for \( \left|y + 9\right| \) to equal -3:

So, y = -6 or y = -12.

By buying two shirts, Roger will save $24 x \( \frac{15}{100} \) = \( \frac{$24 x 15}{100} \) = \( \frac{$360}{100} \) = $3.60 on the second shirt.

So, his total cost will be
$24.00 + ($24.00 - $3.60)
$24.00 + $20.40
$44.40