| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
Convert a-4 to remove the negative exponent.
| \( \frac{4}{a} \) | |
| \( \frac{1}{a^4} \) | |
| \( \frac{-1}{-4a^{4}} \) | |
| \( \frac{-4}{-a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( 6 \)\( \sqrt{18} \) + \( 2 \)\( \sqrt{2} \)
| 8\( \sqrt{2} \) | |
| 8\( \sqrt{18} \) | |
| 8\( \sqrt{36} \) | |
| 20\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
6\( \sqrt{18} \) + 2\( \sqrt{2} \)
6\( \sqrt{9 \times 2} \) + 2\( \sqrt{2} \)
6\( \sqrt{3^2 \times 2} \) + 2\( \sqrt{2} \)
(6)(3)\( \sqrt{2} \) + 2\( \sqrt{2} \)
18\( \sqrt{2} \) + 2\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
18\( \sqrt{2} \) + 2\( \sqrt{2} \)a(b + c) = ab + ac defines which of the following?
distributive property for division |
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distributive property for multiplication |
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commutative property for division |
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commutative property for multiplication |
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.
How many hours does it take a car to travel 150 miles at an average speed of 75 miles per hour?
| 6 hours | |
| 5 hours | |
| 3 hours | |
| 2 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{150mi}{75mph} \)
2 hours
If \( \left|x - 8\right| \) + 6 = -8, which of these is a possible value for x?
| 7 | |
| -6 | |
| -7 | |
| -8 |
First, solve for \( \left|x - 8\right| \):
\( \left|x - 8\right| \) + 6 = -8
\( \left|x - 8\right| \) = -8 - 6
\( \left|x - 8\right| \) = -14
The value inside the absolute value brackets can be either positive or negative so (x - 8) must equal - 14 or --14 for \( \left|x - 8\right| \) to equal -14:
| x - 8 = -14 x = -14 + 8 x = -6 | x - 8 = 14 x = 14 + 8 x = 22 |
So, x = 22 or x = -6.