| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
What is 3\( \sqrt{8} \) x 4\( \sqrt{2} \)?
| 7\( \sqrt{16} \) | |
| 12\( \sqrt{8} \) | |
| 48 | |
| 7\( \sqrt{8} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{8} \) x 4\( \sqrt{2} \)
(3 x 4)\( \sqrt{8 \times 2} \)
12\( \sqrt{16} \)
Now we need to simplify the radical:
12\( \sqrt{16} \)
12\( \sqrt{4^2} \)
(12)(4)
48
What is \( \frac{1}{5} \) ÷ \( \frac{1}{7} \)?
| \(\frac{2}{45}\) | |
| 1\(\frac{2}{5}\) | |
| \(\frac{16}{25}\) | |
| \(\frac{1}{49}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{5} \) ÷ \( \frac{1}{7} \) = \( \frac{1}{5} \) x \( \frac{7}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{5} \) x \( \frac{7}{1} \) = \( \frac{1 x 7}{5 x 1} \) = \( \frac{7}{5} \) = 1\(\frac{2}{5}\)
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 9:2 | |
| 3:1 | |
| 3:4 | |
| 5:8 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
What is -2x5 + 5x5?
| 7x-5 | |
| 3x5 | |
| 3x25 | |
| -7x-5 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-2x5 + 5x5
(-2 + 5)x5
3x5
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 65% of his shots. If the guard takes 30 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 42 | |
| 56 | |
| 79 | |
| 70 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{65}{100} \) = \( \frac{65 x 30}{100} \) = \( \frac{1950}{100} \) = 19 shots
The center makes 45% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{19}{\frac{45}{100}} \) = 19 x \( \frac{100}{45} \) = \( \frac{19 x 100}{45} \) = \( \frac{1900}{45} \) = 42 shots
to make the same number of shots as the guard and thus score the same number of points.