| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
What is \( 8 \)\( \sqrt{48} \) - \( 5 \)\( \sqrt{3} \)
| 3\( \sqrt{-7} \) | |
| 3\( \sqrt{16} \) | |
| 3\( \sqrt{144} \) | |
| 27\( \sqrt{3} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{48} \) - 5\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) - 5\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) - 5\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) - 5\( \sqrt{3} \)
32\( \sqrt{3} \) - 5\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
32\( \sqrt{3} \) - 5\( \sqrt{3} \)Charlie loaned Roger $200 at an annual interest rate of 2%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $42 | |
| $6 | |
| $4 | |
| $45 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $200
i = 0.02 x $200
i = $4
What is \( \frac{1}{5} \) x \( \frac{1}{9} \)?
| \(\frac{12}{49}\) | |
| \(\frac{16}{63}\) | |
| \(\frac{1}{45}\) | |
| \(\frac{1}{28}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{5} \) x \( \frac{1}{9} \) = \( \frac{1 x 1}{5 x 9} \) = \( \frac{1}{45} \) = \(\frac{1}{45}\)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Roger buys two shirts, each with a regular price of $10, how much will he pay for both shirts?
| $16.00 | |
| $4.00 | |
| $13.50 | |
| $6.00 |
By buying two shirts, Roger will save $10 x \( \frac{40}{100} \) = \( \frac{$10 x 40}{100} \) = \( \frac{$400}{100} \) = $4.00 on the second shirt.
So, his total cost will be
$10.00 + ($10.00 - $4.00)
$10.00 + $6.00
$16.00
a(b + c) = ab + ac defines which of the following?
commutative property for division |
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distributive property for multiplication |
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commutative property for multiplication |
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distributive property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.