| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
If \( \left|x + 0\right| \) + 6 = -5, which of these is a possible value for x?
| 15 | |
| 2 | |
| -2 | |
| 11 |
First, solve for \( \left|x + 0\right| \):
\( \left|x + 0\right| \) + 6 = -5
\( \left|x + 0\right| \) = -5 - 6
\( \left|x + 0\right| \) = -11
The value inside the absolute value brackets can be either positive or negative so (x + 0) must equal - 11 or --11 for \( \left|x + 0\right| \) to equal -11:
| x + 0 = -11 x = -11 + 0 x = -11 | x + 0 = 11 x = 11 + 0 x = 11 |
So, x = 11 or x = -11.
a(b + c) = ab + ac defines which of the following?
commutative property for division |
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commutative property for multiplication |
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distributive 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.
What is (x2)5?
| 2x5 | |
| x-3 | |
| 5x2 | |
| x10 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(x2)5A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Ezra buys two shirts, each with a regular price of $47, how much money will he save?
| $11.75 | |
| 49 | |
| $7.05 | |
| $21.15 |
By buying two shirts, Ezra will save $47 x \( \frac{15}{100} \) = \( \frac{$47 x 15}{100} \) = \( \frac{$705}{100} \) = $7.05 on the second shirt.
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 20 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?
| 20 | |
| 31 | |
| 50 | |
| 46 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{55}{100} \) = \( \frac{55 x 20}{100} \) = \( \frac{1100}{100} \) = 11 shots
The center makes 35% 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 = \( \frac{11}{\frac{35}{100}} \) = 11 x \( \frac{100}{35} \) = \( \frac{11 x 100}{35} \) = \( \frac{1100}{35} \) = 31 shots
to make the same number of shots as the guard and thus score the same number of points.