| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
How many hours does it take a car to travel 455 miles at an average speed of 65 miles per hour?
| 6 hours | |
| 2 hours | |
| 1 hour | |
| 7 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{455mi}{65mph} \)
7 hours
What is \( \sqrt{\frac{16}{64}} \)?
| 2 | |
| 1\(\frac{1}{4}\) | |
| \(\frac{3}{5}\) | |
| \(\frac{1}{2}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{16}{64}} \)
\( \frac{\sqrt{16}}{\sqrt{64}} \)
\( \frac{\sqrt{4^2}}{\sqrt{8^2}} \)
\(\frac{1}{2}\)
What is \( \frac{-9z^9}{4z^2} \)?
| -2\(\frac{1}{4}\)z-7 | |
| -2\(\frac{1}{4}\)z7 | |
| -2\(\frac{1}{4}\)z11 | |
| -2\(\frac{1}{4}\)z\(\frac{2}{9}\) |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-9z^9}{4z^2} \)
\( \frac{-9}{4} \) z(9 - 2)
-2\(\frac{1}{4}\)z7
Which of these numbers is a factor of 48?
| 1 | |
| 16 | |
| 48 | |
| 9 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
What is \( 9 \)\( \sqrt{32} \) - \( 8 \)\( \sqrt{2} \)
| 72\( \sqrt{16} \) | |
| \( \sqrt{16} \) | |
| 72\( \sqrt{2} \) | |
| 28\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
9\( \sqrt{32} \) - 8\( \sqrt{2} \)
9\( \sqrt{16 \times 2} \) - 8\( \sqrt{2} \)
9\( \sqrt{4^2 \times 2} \) - 8\( \sqrt{2} \)
(9)(4)\( \sqrt{2} \) - 8\( \sqrt{2} \)
36\( \sqrt{2} \) - 8\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
36\( \sqrt{2} \) - 8\( \sqrt{2} \)