| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
If \( \left|y + 2\right| \) + 2 = 7, which of these is a possible value for y?
| 4 | |
| -7 | |
| -3 | |
| -1 |
First, solve for \( \left|y + 2\right| \):
\( \left|y + 2\right| \) + 2 = 7
\( \left|y + 2\right| \) = 7 - 2
\( \left|y + 2\right| \) = 5
The value inside the absolute value brackets can be either positive or negative so (y + 2) must equal + 5 or -5 for \( \left|y + 2\right| \) to equal 5:
| y + 2 = 5 y = 5 - 2 y = 3 | y + 2 = -5 y = -5 - 2 y = -7 |
So, y = -7 or y = 3.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 35% | |
| 15% | |
| 37\(\frac{1}{2}\)% | |
| 20% |
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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 9:1 | |
| 25:2 | |
| 3:6 | |
| 3:1 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
What is -7c4 x 9c6?
| 2c10 | |
| -63c-2 | |
| -63c10 | |
| 2c6 |
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:
-7c4 x 9c6
(-7 x 9)c(4 + 6)
-63c10
What is \( \frac{7}{2} \) + \( \frac{8}{10} \)?
| 1 \( \frac{4}{10} \) | |
| \( \frac{8}{16} \) | |
| 4\(\frac{3}{10}\) | |
| 2 \( \frac{4}{10} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 5}{2 x 5} \) + \( \frac{8 x 1}{10 x 1} \)
\( \frac{35}{10} \) + \( \frac{8}{10} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 8}{10} \) = \( \frac{43}{10} \) = 4\(\frac{3}{10}\)