| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
How many 2\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 10 gallon tank to fill it exactly halfway?
| 5 | |
| 9 | |
| 2 | |
| 7 |
To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:
cans = \( \frac{5 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 2
If \( \left|x + 4\right| \) + 3 = 1, which of these is a possible value for x?
| -6 | |
| 6 | |
| -12 | |
| 18 |
First, solve for \( \left|x + 4\right| \):
\( \left|x + 4\right| \) + 3 = 1
\( \left|x + 4\right| \) = 1 - 3
\( \left|x + 4\right| \) = -2
The value inside the absolute value brackets can be either positive or negative so (x + 4) must equal - 2 or --2 for \( \left|x + 4\right| \) to equal -2:
| x + 4 = -2 x = -2 - 4 x = -6 | x + 4 = 2 x = 2 - 4 x = -2 |
So, x = -2 or x = -6.
Convert a-5 to remove the negative exponent.
| \( \frac{5}{a} \) | |
| \( \frac{1}{a^5} \) | |
| \( \frac{-5}{-a} \) | |
| \( \frac{-5}{a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is -y4 + 8y4?
| 9y-4 | |
| 9y4 | |
| 7y4 | |
| -9y-4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-1y4 + 8y4
(-1 + 8)y4
7y4
What is the least common multiple of 4 and 6?
| 10 | |
| 18 | |
| 9 | |
| 12 |
The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 have in common.