To subtract these radicals together their radicands must be the same:

6\( \sqrt{80} \) - 4\( \sqrt{5} \)
6\( \sqrt{16 \times 5} \) - 4\( \sqrt{5} \)
6\( \sqrt{4^2 \times 5} \) - 4\( \sqrt{5} \)
(6)(4)\( \sqrt{5} \) - 4\( \sqrt{5} \)
24\( \sqrt{5} \) - 4\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The equation for this sequence is:

a_n = a_n-1 + 8

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 + 8
a₆ = 33 + 8
a₆ = 41

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 = 0.09 x $700
i = $63

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

\( \left|x + 5\right| \) - 1 = 5
\( \left|x + 5\right| \) = 5 + 1
\( \left|x + 5\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (x + 5) must equal + 6 or -6 for \( \left|x + 5\right| \) to equal 6:

So, x = -11 or x = 1.