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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 40.4km + 9.0km
total distance = 49.5km

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

\( \left|z + 2\right| \) + 1 = 7
\( \left|z + 2\right| \) = 7 - 1
\( \left|z + 2\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (z + 2) must equal + 6 or -6 for \( \left|z + 2\right| \) to equal 6:

So, z = -8 or z = 4.

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

2\( \sqrt{112} \) + 2\( \sqrt{7} \)
2\( \sqrt{16 \times 7} \) + 2\( \sqrt{7} \)
2\( \sqrt{4^2 \times 7} \) + 2\( \sqrt{7} \)
(2)(4)\( \sqrt{7} \) + 2\( \sqrt{7} \)
8\( \sqrt{7} \) + 2\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 6 factors [1, 2, 4, 8, 16, 32] making 32 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{64} \) = \( \frac{\frac{32}{32}}{\frac{64}{32}} \) = \( \frac{1}{2} \)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.