| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
What is 3z3 + 7z3?
| -4z3 | |
| 10z3 | |
| 4z3 | |
| 10z9 |
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:
3z3 + 7z3
(3 + 7)z3
10z3
What is \( 4 \)\( \sqrt{80} \) - \( 2 \)\( \sqrt{5} \)
| 2\( \sqrt{5} \) | |
| 2\( \sqrt{9} \) | |
| 2\( \sqrt{400} \) | |
| 14\( \sqrt{5} \) |
To subtract these radicals together their radicands must be the same:
4\( \sqrt{80} \) - 2\( \sqrt{5} \)
4\( \sqrt{16 \times 5} \) - 2\( \sqrt{5} \)
4\( \sqrt{4^2 \times 5} \) - 2\( \sqrt{5} \)
(4)(4)\( \sqrt{5} \) - 2\( \sqrt{5} \)
16\( \sqrt{5} \) - 2\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
16\( \sqrt{5} \) - 2\( \sqrt{5} \)On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 45% 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?
| 46 | |
| 43 | |
| 32 | |
| 41 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{45}{100} \) = \( \frac{45 x 30}{100} \) = \( \frac{1350}{100} \) = 13 shots
The center makes 30% 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 = \( \frac{13}{\frac{30}{100}} \) = 13 x \( \frac{100}{30} \) = \( \frac{13 x 100}{30} \) = \( \frac{1300}{30} \) = 43 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \sqrt{\frac{9}{4}} \)?
| \(\frac{2}{9}\) | |
| 1\(\frac{1}{2}\) | |
| 1 | |
| \(\frac{1}{2}\) |
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:
\( \sqrt{\frac{9}{4}} \)
\( \frac{\sqrt{9}}{\sqrt{4}} \)
\( \frac{\sqrt{3^2}}{\sqrt{2^2}} \)
\( \frac{3}{2} \)
1\(\frac{1}{2}\)
What is \( \frac{8}{4} \) - \( \frac{3}{8} \)?
| 1\(\frac{5}{8}\) | |
| 1 \( \frac{9}{18} \) | |
| 2 \( \frac{9}{8} \) | |
| \( \frac{1}{8} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 2}{4 x 2} \) - \( \frac{3 x 1}{8 x 1} \)
\( \frac{16}{8} \) - \( \frac{3}{8} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{16 - 3}{8} \) = \( \frac{13}{8} \) = 1\(\frac{5}{8}\)