| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
What is \( 3 \)\( \sqrt{63} \) - \( 8 \)\( \sqrt{7} \)
| 24\( \sqrt{9} \) | |
| -5\( \sqrt{40} \) | |
| -5\( \sqrt{441} \) | |
| \( \sqrt{7} \) |
To subtract these radicals together their radicands must be the same:
3\( \sqrt{63} \) - 8\( \sqrt{7} \)
3\( \sqrt{9 \times 7} \) - 8\( \sqrt{7} \)
3\( \sqrt{3^2 \times 7} \) - 8\( \sqrt{7} \)
(3)(3)\( \sqrt{7} \) - 8\( \sqrt{7} \)
9\( \sqrt{7} \) - 8\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
9\( \sqrt{7} \) - 8\( \sqrt{7} \)A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 20% | |
| 32\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%
A tiger in a zoo has consumed 104 pounds of food in 8 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 195 pounds?
| 15 | |
| 3 | |
| 13 | |
| 7 |
If the tiger has consumed 104 pounds of food in 8 days that's \( \frac{104}{8} \) = 13 pounds of food per day. The tiger needs to consume 195 - 104 = 91 more pounds of food to reach 195 pounds total. At 13 pounds of food per day that's \( \frac{91}{13} \) = 7 more days.
The __________ is the greatest factor that divides two integers.
greatest common multiple |
|
greatest common factor |
|
absolute value |
|
least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If a car travels 200 miles in 4 hours, what is the average speed?
| 30 mph | |
| 50 mph | |
| 45 mph | |
| 55 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)