| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
What is \( 9 \)\( \sqrt{45} \) + \( 9 \)\( \sqrt{5} \)
| 18\( \sqrt{5} \) | |
| 18\( \sqrt{225} \) | |
| 81\( \sqrt{45} \) | |
| 36\( \sqrt{5} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{45} \) + 9\( \sqrt{5} \)
9\( \sqrt{9 \times 5} \) + 9\( \sqrt{5} \)
9\( \sqrt{3^2 \times 5} \) + 9\( \sqrt{5} \)
(9)(3)\( \sqrt{5} \) + 9\( \sqrt{5} \)
27\( \sqrt{5} \) + 9\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
27\( \sqrt{5} \) + 9\( \sqrt{5} \)Simplify \( \frac{28}{60} \).
| \( \frac{7}{15} \) | |
| \( \frac{5}{8} \) | |
| \( \frac{4}{7} \) | |
| \( \frac{1}{2} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{60} \) = \( \frac{\frac{28}{4}}{\frac{60}{4}} \) = \( \frac{7}{15} \)
Which of the following is an improper fraction?
\({a \over 5} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
A bread recipe calls for 2 cups of flour. If you only have \(\frac{1}{8}\) cup, how much more flour is needed?
| 1\(\frac{7}{8}\) cups | |
| \(\frac{1}{2}\) cups | |
| 2\(\frac{3}{8}\) cups | |
| 3\(\frac{5}{8}\) cups |
The amount of flour you need is (2 - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{16}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups
In a class of 26 students, 13 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 8 are taking both courses. How many students are not enrolled in either course?
| 25 | |
| 17 | |
| 7 | |
| 16 |
The number of students taking German or Spanish is 13 + 14 = 27. Of that group of 27, 8 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 27 - 8 = 19 who are taking at least one language. 26 - 19 = 7 students who are not taking either language.