To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{9 x 3}{8 x 3} \) + \( \frac{7 x 2}{12 x 2} \)

\( \frac{27}{24} \) + \( \frac{14}{24} \)

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

\( \frac{27 + 14}{24} \) = \( \frac{41}{24} \) = 1\(\frac{17}{24}\)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $700
i = 0.03 x $700
i = $21

To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{9} \) x 9\( \sqrt{2} \)
(3 x 9)\( \sqrt{9 \times 2} \)
27\( \sqrt{18} \)

Now we need to simplify the radical:

27\( \sqrt{18} \)
27\( \sqrt{2 \times 9} \)
27\( \sqrt{2 \times 3^2} \)
(27)(3)\( \sqrt{2} \)
81\( \sqrt{2} \)

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 6h \)
360 miles

First, solve for \( \left|x - 5\right| \):

\( \left|x - 5\right| \) + 5 = -9
\( \left|x - 5\right| \) = -9 - 5
\( \left|x - 5\right| \) = -14

The value inside the absolute value brackets can be either positive or negative so (x - 5) must equal - 14 or --14 for \( \left|x - 5\right| \) to equal -14:

So, x = 19 or x = -9.