| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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distributive property for division |
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distributive property for multiplication |
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commutative 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.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Frank buys two shirts, each with a regular price of $10, how much money will he save?
| $5.00 | |
| $2.00 | |
| $1.50 | |
| $3.50 |
By buying two shirts, Frank will save $10 x \( \frac{20}{100} \) = \( \frac{$10 x 20}{100} \) = \( \frac{$200}{100} \) = $2.00 on the second shirt.
If \( \left|b - 5\right| \) + 8 = 9, which of these is a possible value for b?
| -4 | |
| 0 | |
| -11 | |
| 6 |
First, solve for \( \left|b - 5\right| \):
\( \left|b - 5\right| \) + 8 = 9
\( \left|b - 5\right| \) = 9 - 8
\( \left|b - 5\right| \) = 1
The value inside the absolute value brackets can be either positive or negative so (b - 5) must equal + 1 or -1 for \( \left|b - 5\right| \) to equal 1:
| b - 5 = 1 b = 1 + 5 b = 6 | b - 5 = -1 b = -1 + 5 b = 4 |
So, b = 4 or b = 6.
What is \( \frac{8\sqrt{6}}{4\sqrt{2}} \)?
| \(\frac{1}{3}\) \( \sqrt{2} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{2}\) \( \sqrt{3} \) | |
| 2 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{8\sqrt{6}}{4\sqrt{2}} \)
\( \frac{8}{4} \) \( \sqrt{\frac{6}{2}} \)
2 \( \sqrt{3} \)
What is \( 4 \)\( \sqrt{48} \) + \( 3 \)\( \sqrt{3} \)
| 7\( \sqrt{48} \) | |
| 7\( \sqrt{16} \) | |
| 12\( \sqrt{3} \) | |
| 19\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
4\( \sqrt{48} \) + 3\( \sqrt{3} \)
4\( \sqrt{16 \times 3} \) + 3\( \sqrt{3} \)
4\( \sqrt{4^2 \times 3} \) + 3\( \sqrt{3} \)
(4)(4)\( \sqrt{3} \) + 3\( \sqrt{3} \)
16\( \sqrt{3} \) + 3\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
16\( \sqrt{3} \) + 3\( \sqrt{3} \)