| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.69 |
| Score | 0% | 74% |
If \( \left|c + 7\right| \) - 2 = 0, which of these is a possible value for c?
| -12 | |
| -9 | |
| 11 | |
| -23 |
First, solve for \( \left|c + 7\right| \):
\( \left|c + 7\right| \) - 2 = 0
\( \left|c + 7\right| \) = 0 + 2
\( \left|c + 7\right| \) = 2
The value inside the absolute value brackets can be either positive or negative so (c + 7) must equal + 2 or -2 for \( \left|c + 7\right| \) to equal 2:
| c + 7 = 2 c = 2 - 7 c = -5 | c + 7 = -2 c = -2 - 7 c = -9 |
So, c = -9 or c = -5.
4! = ?
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
4 x 3 |
|
4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
What is \( \frac{4}{5} \) ÷ \( \frac{3}{9} \)?
| \(\frac{1}{9}\) | |
| \(\frac{2}{9}\) | |
| 2\(\frac{2}{5}\) | |
| \(\frac{4}{63}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{5} \) ÷ \( \frac{3}{9} \) = \( \frac{4}{5} \) x \( \frac{9}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{9}{3} \) = \( \frac{4 x 9}{5 x 3} \) = \( \frac{36}{15} \) = 2\(\frac{2}{5}\)
How many hours does it take a car to travel 540 miles at an average speed of 60 miles per hour?
| 8 hours | |
| 5 hours | |
| 9 hours | |
| 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 = \( \frac{540mi}{60mph} \)
9 hours
Damon loaned Christine $500 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $530 | |
| $515 | |
| $505 | |
| $525 |
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 $500
i = 0.06 x $500
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $500 + $30