| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.34 |
| Score | 0% | 67% |
If \( \left|x + 6\right| \) - 6 = 3, which of these is a possible value for x?
| 7 | |
| 9 | |
| -12 | |
| -15 |
First, solve for \( \left|x + 6\right| \):
\( \left|x + 6\right| \) - 6 = 3
\( \left|x + 6\right| \) = 3 + 6
\( \left|x + 6\right| \) = 9
The value inside the absolute value brackets can be either positive or negative so (x + 6) must equal + 9 or -9 for \( \left|x + 6\right| \) to equal 9:
| x + 6 = 9 x = 9 - 6 x = 3 | x + 6 = -9 x = -9 - 6 x = -15 |
So, x = -15 or x = 3.
What is \( \frac{7}{3} \) - \( \frac{6}{11} \)?
| 1 \( \frac{7}{33} \) | |
| \( \frac{2}{33} \) | |
| 1\(\frac{26}{33}\) | |
| 2 \( \frac{4}{10} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 11}{3 x 11} \) - \( \frac{6 x 3}{11 x 3} \)
\( \frac{77}{33} \) - \( \frac{18}{33} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{77 - 18}{33} \) = \( \frac{59}{33} \) = 1\(\frac{26}{33}\)
Convert a-4 to remove the negative exponent.
| \( \frac{-1}{-4a} \) | |
| \( \frac{1}{a^4} \) | |
| \( \frac{-4}{-a} \) | |
| \( \frac{-1}{a^{-4}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
distributive property for multiplication |
|
commutative property for division |
|
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.
Damon loaned Christine $300 at an annual interest rate of 5%. If no payments are made, what is the total amount owed at the end of the first year?
| $306 | |
| $318 | |
| $315 | |
| $324 |
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 $300
i = 0.05 x $300
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $300 + $15