| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.34 |
| Score | 0% | 67% |
What is \( \frac{49\sqrt{30}}{7\sqrt{6}} \)?
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{5}} \) | |
| \(\frac{1}{5}\) \( \sqrt{7} \) | |
| 7 \( \sqrt{5} \) | |
| \(\frac{1}{7}\) \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{49\sqrt{30}}{7\sqrt{6}} \)
\( \frac{49}{7} \) \( \sqrt{\frac{30}{6}} \)
7 \( \sqrt{5} \)
What is the distance in miles of a trip that takes 1 hour at an average speed of 40 miles per hour?
| 525 miles | |
| 225 miles | |
| 40 miles | |
| 420 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 40mph \times 1h \)
40 miles
What is \( 7 \)\( \sqrt{32} \) + \( 7 \)\( \sqrt{2} \)
| 35\( \sqrt{2} \) | |
| 14\( \sqrt{2} \) | |
| 14\( \sqrt{32} \) | |
| 14\( \sqrt{64} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{32} \) + 7\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) + 7\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) + 7\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) + 7\( \sqrt{2} \)
28\( \sqrt{2} \) + 7\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
28\( \sqrt{2} \) + 7\( \sqrt{2} \)What is \( \sqrt{\frac{49}{81}} \)?
| \(\frac{3}{5}\) | |
| \(\frac{2}{3}\) | |
| \(\frac{2}{9}\) | |
| \(\frac{7}{9}\) |
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:
\( \sqrt{\frac{49}{81}} \)
\( \frac{\sqrt{49}}{\sqrt{81}} \)
\( \frac{\sqrt{7^2}}{\sqrt{9^2}} \)
\(\frac{7}{9}\)
Alex loaned Betty $1,400 at an annual interest rate of 1%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,414 | |
| $1,484 | |
| $1,456 | |
| $1,526 |
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 $1,400
i = 0.01 x $1,400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,400 + $14