| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
What is \( 7 \)\( \sqrt{45} \) + \( 4 \)\( \sqrt{5} \)
| 11\( \sqrt{5} \) | |
| 25\( \sqrt{5} \) | |
| 28\( \sqrt{225} \) | |
| 11\( \sqrt{45} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{45} \) + 4\( \sqrt{5} \)
7\( \sqrt{9 \times 5} \) + 4\( \sqrt{5} \)
7\( \sqrt{3^2 \times 5} \) + 4\( \sqrt{5} \)
(7)(3)\( \sqrt{5} \) + 4\( \sqrt{5} \)
21\( \sqrt{5} \) + 4\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
21\( \sqrt{5} \) + 4\( \sqrt{5} \)What is the next number in this sequence: 1, 2, 3, 4, 5, __________ ?
| 6 | |
| 14 | |
| 0 | |
| 13 |
The equation for this sequence is:
an = an-1 + 1
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 1
a6 = 5 + 1
a6 = 6
What is -9z3 x 8z6?
| -72z6 | |
| -z18 | |
| -72z9 | |
| -z9 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-9z3 x 8z6
(-9 x 8)z(3 + 6)
-72z9
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 49 | |
| 40 | |
| 39 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
Damon loaned Bob $900 at an annual interest rate of 5%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $90 | |
| $9 | |
| $30 | |
| $45 |
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 $900
i = 0.05 x $900
i = $45