| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
What is \( 9 \)\( \sqrt{28} \) + \( 2 \)\( \sqrt{7} \)
| 18\( \sqrt{7} \) | |
| 20\( \sqrt{7} \) | |
| 11\( \sqrt{4} \) | |
| 18\( \sqrt{4} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{28} \) + 2\( \sqrt{7} \)
9\( \sqrt{4 \times 7} \) + 2\( \sqrt{7} \)
9\( \sqrt{2^2 \times 7} \) + 2\( \sqrt{7} \)
(9)(2)\( \sqrt{7} \) + 2\( \sqrt{7} \)
18\( \sqrt{7} \) + 2\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
18\( \sqrt{7} \) + 2\( \sqrt{7} \)If \( \left|y - 2\right| \) + 0 = 1, which of these is a possible value for y?
| -15 | |
| -11 | |
| 0 | |
| 1 |
First, solve for \( \left|y - 2\right| \):
\( \left|y - 2\right| \) + 0 = 1
\( \left|y - 2\right| \) = 1 + 0
\( \left|y - 2\right| \) = 1
The value inside the absolute value brackets can be either positive or negative so (y - 2) must equal + 1 or -1 for \( \left|y - 2\right| \) to equal 1:
| y - 2 = 1 y = 1 + 2 y = 3 | y - 2 = -1 y = -1 + 2 y = 1 |
So, y = 1 or y = 3.
How many 7-passenger vans will it take to drive all 44 members of the football team to an away game?
| 13 vans | |
| 14 vans | |
| 7 vans | |
| 6 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{44}{7} \) = 6\(\frac{2}{7}\)
So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.
What is \( \frac{3}{8} \) x \( \frac{2}{7} \)?
| \(\frac{2}{35}\) | |
| \(\frac{6}{7}\) | |
| \(\frac{3}{28}\) | |
| \(\frac{2}{15}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{2}{7} \) = \( \frac{3 x 2}{8 x 7} \) = \( \frac{6}{56} \) = \(\frac{3}{28}\)
What is \( \frac{1}{6} \) ÷ \( \frac{4}{9} \)?
| \(\frac{1}{42}\) | |
| \(\frac{2}{35}\) | |
| \(\frac{3}{8}\) | |
| 1\(\frac{1}{2}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{6} \) ÷ \( \frac{4}{9} \) = \( \frac{1}{6} \) x \( \frac{9}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{6} \) x \( \frac{9}{4} \) = \( \frac{1 x 9}{6 x 4} \) = \( \frac{9}{24} \) = \(\frac{3}{8}\)