| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
What is 9z4 + z4?
| 10z4 | |
| 8z-4 | |
| 10z8 | |
| 8z4 |
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:
9z4 + 1z4
(9 + 1)z4
10z4
Solve for \( \frac{4!}{3!} \)
| 5 | |
| 4 | |
| 336 | |
| \( \frac{1}{56} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
4
What is \( \frac{21\sqrt{12}}{7\sqrt{6}} \)?
| 3 \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{2}} \) | |
| 2 \( \sqrt{3} \) | |
| 3 \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{21\sqrt{12}}{7\sqrt{6}} \)
\( \frac{21}{7} \) \( \sqrt{\frac{12}{6}} \)
3 \( \sqrt{2} \)
What is \( 2 \)\( \sqrt{20} \) - \( 6 \)\( \sqrt{5} \)
| -4\( \sqrt{100} \) | |
| -2\( \sqrt{5} \) | |
| -4\( \sqrt{4} \) | |
| -4\( \sqrt{20} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{20} \) - 6\( \sqrt{5} \)
2\( \sqrt{4 \times 5} \) - 6\( \sqrt{5} \)
2\( \sqrt{2^2 \times 5} \) - 6\( \sqrt{5} \)
(2)(2)\( \sqrt{5} \) - 6\( \sqrt{5} \)
4\( \sqrt{5} \) - 6\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
4\( \sqrt{5} \) - 6\( \sqrt{5} \)A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Bob buys two shirts, each with a regular price of $43, how much money will he save?
| $17.20 | |
| $19.35 | |
| $8.60 | |
| $21.50 |
By buying two shirts, Bob will save $43 x \( \frac{50}{100} \) = \( \frac{$43 x 50}{100} \) = \( \frac{$2150}{100} \) = $21.50 on the second shirt.