| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
Convert z-2 to remove the negative exponent.
| \( \frac{2}{z} \) | |
| \( \frac{-2}{-z} \) | |
| \( \frac{1}{z^{-2}} \) | |
| \( \frac{1}{z^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A triathlon course includes a 400m swim, a 30.2km bike ride, and a 5.7km run. What is the total length of the race course?
| 41.1km | |
| 36.3km | |
| 46.4km | |
| 36.9km |
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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 30.2km + 5.7km
total distance = 36.3km
What is \( \frac{35\sqrt{21}}{5\sqrt{7}} \)?
| \(\frac{1}{7}\) \( \sqrt{3} \) | |
| 7 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{7} \) | |
| 3 \( \sqrt{7} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{35\sqrt{21}}{5\sqrt{7}} \)
\( \frac{35}{5} \) \( \sqrt{\frac{21}{7}} \)
7 \( \sqrt{3} \)
Frank loaned Charlie $900 at an annual interest rate of 9%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $18 | |
| $81 | |
| $72 | |
| $10 |
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 $900
i = 0.09 x $900
i = $81
Simplify \( \sqrt{32} \)
| 6\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| 2\( \sqrt{4} \) | |
| 4\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)