| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
What is \( 2 \)\( \sqrt{75} \) + \( 4 \)\( \sqrt{3} \)
| 14\( \sqrt{3} \) | |
| 6\( \sqrt{225} \) | |
| 8\( \sqrt{75} \) | |
| 6\( \sqrt{25} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{75} \) + 4\( \sqrt{3} \)
2\( \sqrt{25 \times 3} \) + 4\( \sqrt{3} \)
2\( \sqrt{5^2 \times 3} \) + 4\( \sqrt{3} \)
(2)(5)\( \sqrt{3} \) + 4\( \sqrt{3} \)
10\( \sqrt{3} \) + 4\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
10\( \sqrt{3} \) + 4\( \sqrt{3} \)Charlie loaned Roger $300 at an annual interest rate of 7%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $2 | |
| $36 | |
| $21 | |
| $78 |
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 $300
i = 0.07 x $300
i = $21
How many 14-passenger vans will it take to drive all 56 members of the football team to an away game?
| 15 vans | |
| 10 vans | |
| 4 vans | |
| 5 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{56}{14} \) = 4
Convert a-2 to remove the negative exponent.
| \( \frac{-1}{-2a} \) | |
| \( \frac{1}{a^{-2}} \) | |
| \( \frac{1}{a^2} \) | |
| \( \frac{-1}{a^{-2}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
a = 7 or a = -7 |
|
a = 7 |
|
none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).