| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
If \( \left|b - 5\right| \) + 0 = -7, which of these is a possible value for b?
| -2 | |
| 7 | |
| 3 | |
| 6 |
First, solve for \( \left|b - 5\right| \):
\( \left|b - 5\right| \) + 0 = -7
\( \left|b - 5\right| \) = -7 + 0
\( \left|b - 5\right| \) = -7
The value inside the absolute value brackets can be either positive or negative so (b - 5) must equal - 7 or --7 for \( \left|b - 5\right| \) to equal -7:
| b - 5 = -7 b = -7 + 5 b = -2 | b - 5 = 7 b = 7 + 5 b = 12 |
So, b = 12 or b = -2.
How many 1 gallon cans worth of fuel would you need to pour into an empty 10 gallon tank to fill it exactly halfway?
| 2 | |
| 5 | |
| 6 | |
| 9 |
To fill a 10 gallon tank exactly halfway you'll need 5 gallons of fuel. Each fuel can holds 1 gallons so:
cans = \( \frac{5 \text{ gallons}}{1 \text{ gallons}} \) = 5
What is -8a4 x 9a4?
| a8 | |
| -72a4 | |
| -72a8 | |
| a4 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-8a4 x 9a4
(-8 x 9)a(4 + 4)
-72a8
Which of the following is not an integer?
0 |
|
-1 |
|
1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
Convert y-4 to remove the negative exponent.
| \( \frac{-4}{y} \) | |
| \( \frac{1}{y^4} \) | |
| \( \frac{4}{y} \) | |
| \( \frac{-1}{-4y^{4}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.