| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.54 |
| Score | 0% | 71% |
If side a = 7, side b = 2, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{90} \) | |
| \( \sqrt{97} \) | |
| \( \sqrt{82} \) | |
| \( \sqrt{53} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 72 + 22
c2 = 49 + 4
c2 = 53
c = \( \sqrt{53} \)
What is 7a8 - 2a8?
| 9 | |
| 5a16 | |
| 9a16 | |
| 5a8 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
7a8 - 2a8 = 5a8
The dimensions of this cube are height (h) = 7, length (l) = 7, and width (w) = 6. What is the volume?
| 105 | |
| 196 | |
| 294 | |
| 24 |
The volume of a cube is height x length x width:
v = h x l x w
v = 7 x 7 x 6
v = 294
Solve for x:
x2 + 2x - 24 = 0
| 1 or 1 | |
| 6 or 4 | |
| 4 or -6 | |
| -2 or -6 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
x2 + 2x - 24 = 0
(x - 4)(x + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 4) or (x + 6) must equal zero:
If (x - 4) = 0, x must equal 4
If (x + 6) = 0, x must equal -6
So the solution is that x = 4 or -6
If AD = 17 and BD = 11, AB = ?
| 6 | |
| 18 | |
| 5 | |
| 16 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD