| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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distributive property for division |
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distributive property for multiplication |
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commutative property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
What is the greatest common factor of 60 and 28?
| 26 | |
| 2 | |
| 4 | |
| 27 |
The factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 60 and 28 have in common.
Which of the following statements about exponents is false?
b0 = 1 |
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b1 = b |
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b1 = 1 |
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all of these are false |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
Simplify \( \sqrt{12} \)
| 2\( \sqrt{3} \) | |
| 9\( \sqrt{6} \) | |
| 8\( \sqrt{6} \) | |
| 4\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{12} \)
\( \sqrt{4 \times 3} \)
\( \sqrt{2^2 \times 3} \)
2\( \sqrt{3} \)
In a class of 28 students, 14 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 13 | |
| 11 | |
| 10 |
The number of students taking German or Spanish is 14 + 5 = 19. Of that group of 19, 4 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 19 - 4 = 15 who are taking at least one language. 28 - 15 = 13 students who are not taking either language.