| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
If \( \left|c + 0\right| \) + 6 = -7, which of these is a possible value for c?
| -12 | |
| 0 | |
| 13 | |
| 10 |
First, solve for \( \left|c + 0\right| \):
\( \left|c + 0\right| \) + 6 = -7
\( \left|c + 0\right| \) = -7 - 6
\( \left|c + 0\right| \) = -13
The value inside the absolute value brackets can be either positive or negative so (c + 0) must equal - 13 or --13 for \( \left|c + 0\right| \) to equal -13:
| c + 0 = -13 c = -13 + 0 c = -13 | c + 0 = 13 c = 13 + 0 c = 13 |
So, c = 13 or c = -13.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
|
PEDMAS |
|
distributive |
|
associative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
In a class of 19 students, 5 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 12 | |
| 16 | |
| 5 | |
| 19 |
The number of students taking German or Spanish is 5 + 14 = 19. Of that group of 19, 5 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 - 5 = 14 who are taking at least one language. 19 - 14 = 5 students who are not taking either language.
What is the greatest common factor of 76 and 44?
| 24 | |
| 9 | |
| 28 | |
| 4 |
The factors of 76 are [1, 2, 4, 19, 38, 76] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 the greatest factor 76 and 44 have in common.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
commutative property for multiplication |
|
commutative property for division |
|
distributive property for multiplication |
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.