| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
Damon loaned Diane $1,400 at an annual interest rate of 7%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,470 | |
| $1,498 | |
| $1,512 | |
| $1,442 |
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
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,400 + $98The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
least common multiple |
|
greatest common factor |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
What is \( 5 \)\( \sqrt{20} \) - \( 7 \)\( \sqrt{5} \)
| -2\( \sqrt{20} \) | |
| -2\( \sqrt{21} \) | |
| 3\( \sqrt{5} \) | |
| 35\( \sqrt{20} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{20} \) - 7\( \sqrt{5} \)
5\( \sqrt{4 \times 5} \) - 7\( \sqrt{5} \)
5\( \sqrt{2^2 \times 5} \) - 7\( \sqrt{5} \)
(5)(2)\( \sqrt{5} \) - 7\( \sqrt{5} \)
10\( \sqrt{5} \) - 7\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
10\( \sqrt{5} \) - 7\( \sqrt{5} \)What is 7x2 + 8x2?
| 15x2 | |
| x2 | |
| -x-2 | |
| 15x-4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
7x2 + 8x2
(7 + 8)x2
15x2
What is the least common multiple of 4 and 6?
| 2 | |
| 13 | |
| 4 | |
| 12 |
The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 have in common.