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

2\( \sqrt{9} \) x 4\( \sqrt{6} \)
(2 x 4)\( \sqrt{9 \times 6} \)
8\( \sqrt{54} \)

Now we need to simplify the radical:

8\( \sqrt{54} \)
8\( \sqrt{6 \times 9} \)
8\( \sqrt{6 \times 3^2} \)
(8)(3)\( \sqrt{6} \)
24\( \sqrt{6} \)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-4a⁵ + 1a⁵
(-4 + 1)a⁵
-3a⁵

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.3km + 40.1km + 11.0km
total distance = 51.4km

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 $100
i = 0.01 x $100

No payments were made so the total amount due is the original amount + the accumulated interest:

First, solve for \( \left|y - 3\right| \):

\( \left|y - 3\right| \) + 4 = 8
\( \left|y - 3\right| \) = 8 - 4
\( \left|y - 3\right| \) = 4

The value inside the absolute value brackets can be either positive or negative so (y - 3) must equal + 4 or -4 for \( \left|y - 3\right| \) to equal 4:

So, y = -1 or y = 7.