| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
A tiger in a zoo has consumed 126 pounds of food in 9 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 196 pounds?
| 6 | |
| 1 | |
| 5 | |
| 12 |
If the tiger has consumed 126 pounds of food in 9 days that's \( \frac{126}{9} \) = 14 pounds of food per day. The tiger needs to consume 196 - 126 = 70 more pounds of food to reach 196 pounds total. At 14 pounds of food per day that's \( \frac{70}{14} \) = 5 more days.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Ezra buys two shirts, each with a regular price of $24, how much will he pay for both shirts?
| $40.80 | |
| $16.80 | |
| $32.40 | |
| $36.00 |
By buying two shirts, Ezra will save $24 x \( \frac{30}{100} \) = \( \frac{$24 x 30}{100} \) = \( \frac{$720}{100} \) = $7.20 on the second shirt.
So, his total cost will be
$24.00 + ($24.00 - $7.20)
$24.00 + $16.80
$40.80
What is \( \frac{12\sqrt{16}}{4\sqrt{8}} \)?
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{3}} \) | |
| 2 \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{2} \) | |
| 2 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{16}}{4\sqrt{8}} \)
\( \frac{12}{4} \) \( \sqrt{\frac{16}{8}} \)
3 \( \sqrt{2} \)
What is \( 4 \)\( \sqrt{45} \) + \( 4 \)\( \sqrt{5} \)
| 16\( \sqrt{225} \) | |
| 8\( \sqrt{9} \) | |
| 16\( \sqrt{5} \) | |
| 8\( \sqrt{5} \) |
To add these radicals together their radicands must be the same:
4\( \sqrt{45} \) + 4\( \sqrt{5} \)
4\( \sqrt{9 \times 5} \) + 4\( \sqrt{5} \)
4\( \sqrt{3^2 \times 5} \) + 4\( \sqrt{5} \)
(4)(3)\( \sqrt{5} \) + 4\( \sqrt{5} \)
12\( \sqrt{5} \) + 4\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
12\( \sqrt{5} \) + 4\( \sqrt{5} \)If \( \left|z - 1\right| \) - 7 = 7, which of these is a possible value for z?
| 3 | |
| -13 | |
| -17 | |
| 18 |
First, solve for \( \left|z - 1\right| \):
\( \left|z - 1\right| \) - 7 = 7
\( \left|z - 1\right| \) = 7 + 7
\( \left|z - 1\right| \) = 14
The value inside the absolute value brackets can be either positive or negative so (z - 1) must equal + 14 or -14 for \( \left|z - 1\right| \) to equal 14:
| z - 1 = 14 z = 14 + 1 z = 15 | z - 1 = -14 z = -14 + 1 z = -13 |
So, z = -13 or z = 15.