| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.82 |
| Score | 0% | 56% |
What is 9\( \sqrt{5} \) x 5\( \sqrt{3} \)?
| 14\( \sqrt{15} \) | |
| 45\( \sqrt{15} \) | |
| 14\( \sqrt{5} \) | |
| 14\( \sqrt{3} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
9\( \sqrt{5} \) x 5\( \sqrt{3} \)
(9 x 5)\( \sqrt{5 \times 3} \)
45\( \sqrt{15} \)
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
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PEDMAS |
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associative |
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commutative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Bob buys two shirts, each with a regular price of $13, how much money will he save?
| $4.55 | |
| $0.65 | |
| $3.25 | |
| $2.60 |
By buying two shirts, Bob will save $13 x \( \frac{35}{100} \) = \( \frac{$13 x 35}{100} \) = \( \frac{$455}{100} \) = $4.55 on the second shirt.
If \( \left|a - 4\right| \) - 1 = -1, which of these is a possible value for a?
| 4 | |
| -4 | |
| 22 | |
| -13 |
First, solve for \( \left|a - 4\right| \):
\( \left|a - 4\right| \) - 1 = -1
\( \left|a - 4\right| \) = -1 + 1
\( \left|a - 4\right| \) = 0
The value inside the absolute value brackets can be either positive or negative so (a - 4) must equal + 0 or -0 for \( \left|a - 4\right| \) to equal 0:
| a - 4 = 0 a = 0 + 4 a = 4 | a - 4 = 0 a = 0 + 4 a = 4 |
So, a = 4 or a = 4.
If a mayor is elected with 87% of the votes cast and 36% of a town's 19,000 voters cast a vote, how many votes did the mayor receive?
| 5,951 | |
| 4,583 | |
| 6,088 | |
| 3,762 |
If 36% of the town's 19,000 voters cast ballots the number of votes cast is:
(\( \frac{36}{100} \)) x 19,000 = \( \frac{684,000}{100} \) = 6,840
The mayor got 87% of the votes cast which is:
(\( \frac{87}{100} \)) x 6,840 = \( \frac{595,080}{100} \) = 5,951 votes.