| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.76 |
| Score | 0% | 55% |
What is \( 7 \)\( \sqrt{28} \) + \( 7 \)\( \sqrt{7} \)
| 49\( \sqrt{7} \) | |
| 49\( \sqrt{196} \) | |
| 21\( \sqrt{7} \) | |
| 14\( \sqrt{28} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{28} \) + 7\( \sqrt{7} \)
7\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
7\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(7)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
14\( \sqrt{7} \) + 7\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
14\( \sqrt{7} \) + 7\( \sqrt{7} \)What is -6a2 - 7a2?
| a-4 | |
| -13a2 | |
| a4 | |
| -13a-2 |
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:
-6a2 - 7a2
(-6 - 7)a2
-13a2
A circular logo is enlarged to fit the lid of a jar. The new diameter is 60% larger than the original. By what percentage has the area of the logo increased?
| 22\(\frac{1}{2}\)% | |
| 30% | |
| 37\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% |
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 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%
A bread recipe calls for 2\(\frac{7}{8}\) cups of flour. If you only have \(\frac{1}{2}\) cup, how much more flour is needed?
| 2\(\frac{3}{8}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 1\(\frac{3}{4}\) cups | |
| 2\(\frac{1}{8}\) cups |
The amount of flour you need is (2\(\frac{7}{8}\) - \(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{23}{8} \) - \( \frac{4}{8} \)) cups
\( \frac{19}{8} \) cups
2\(\frac{3}{8}\) cups
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Frank buys two shirts, each with a regular price of $38, how much will he pay for both shirts?
| $68.40 | |
| $7.60 | |
| $57.00 | |
| $39.90 |
By buying two shirts, Frank will save $38 x \( \frac{20}{100} \) = \( \frac{$38 x 20}{100} \) = \( \frac{$760}{100} \) = $7.60 on the second shirt.
So, his total cost will be
$38.00 + ($38.00 - $7.60)
$38.00 + $30.40
$68.40