| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
Charlie loaned Charlie $1,400 at an annual interest rate of 7%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $40 | |
| $98 | |
| $14 | |
| $54 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,400
i = 0.07 x $1,400
i = $98
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
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none of these is correct |
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a = 7 or a = -7 |
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a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
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commutative property for division |
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distributive property for division |
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commutative 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.
What is \( \frac{3}{2} \) + \( \frac{4}{6} \)?
| 1 \( \frac{8}{6} \) | |
| 2\(\frac{1}{6}\) | |
| 1 \( \frac{2}{6} \) | |
| 1 \( \frac{8}{16} \) |
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 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{2 x 3} \) + \( \frac{4 x 1}{6 x 1} \)
\( \frac{9}{6} \) + \( \frac{4}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{9 + 4}{6} \) = \( \frac{13}{6} \) = 2\(\frac{1}{6}\)
What is \( \frac{9}{6} \) - \( \frac{2}{14} \)?
| 2 \( \frac{6}{42} \) | |
| 2 \( \frac{4}{12} \) | |
| 1\(\frac{5}{14}\) | |
| 2 \( \frac{8}{14} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 7}{6 x 7} \) - \( \frac{2 x 3}{14 x 3} \)
\( \frac{63}{42} \) - \( \frac{6}{42} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{63 - 6}{42} \) = \( \frac{57}{42} \) = 1\(\frac{5}{14}\)