| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
If \( \left|c - 5\right| \) - 1 = 5, which of these is a possible value for c?
| 4 | |
| -7 | |
| -4 | |
| -1 |
First, solve for \( \left|c - 5\right| \):
\( \left|c - 5\right| \) - 1 = 5
\( \left|c - 5\right| \) = 5 + 1
\( \left|c - 5\right| \) = 6
The value inside the absolute value brackets can be either positive or negative so (c - 5) must equal + 6 or -6 for \( \left|c - 5\right| \) to equal 6:
| c - 5 = 6 c = 6 + 5 c = 11 | c - 5 = -6 c = -6 + 5 c = -1 |
So, c = -1 or c = 11.
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
least common factor |
|
greatest common factor |
|
absolute value |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 20% | |
| 35% | |
| 27\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
What is 4y6 - 3y6?
| 7y-12 | |
| 7y12 | |
| y6 | |
| y-6 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
4y6 - 3y6
(4 - 3)y6
y6
Simplify \( \sqrt{125} \)
| 5\( \sqrt{5} \) | |
| 2\( \sqrt{5} \) | |
| 7\( \sqrt{10} \) | |
| 6\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)