| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
What is \( \frac{-9a^7}{2a^2} \)?
| -4\(\frac{1}{2}\)a3\(\frac{1}{2}\) | |
| -\(\frac{2}{9}\)a5 | |
| -\(\frac{2}{9}\)a-5 | |
| -4\(\frac{1}{2}\)a5 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-9a^7}{2a^2} \)
\( \frac{-9}{2} \) a(7 - 2)
-4\(\frac{1}{2}\)a5
If a rectangle is twice as long as it is wide and has a perimeter of 6 meters, what is the area of the rectangle?
| 128 m2 | |
| 98 m2 | |
| 2 m2 | |
| 8 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.
Putting these two equations together and solving for width (w):
2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1
Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m2
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
16 members of a bridal party need transported to a wedding reception but there are only 3 4-passenger taxis available to take them. How many will need to find other transportation?
| 5 | |
| 6 | |
| 1 | |
| 4 |
There are 3 4-passenger taxis available so that's 3 x 4 = 12 total seats. There are 16 people needing transportation leaving 16 - 12 = 4 who will have to find other transportation.
Bob loaned Betty $1,300 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,391 | |
| $1,378 | |
| $1,365 | |
| $1,313 |
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 $1,300
i = 0.06 x $1,300
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,300 + $78