| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
If side a = 7, side b = 2, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{97} \) | |
| \( \sqrt{34} \) | |
| \( \sqrt{80} \) | |
| \( \sqrt{53} \) |
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 = \( \sqrt{53} \)
The dimensions of this cylinder are height (h) = 5 and radius (r) = 7. What is the volume?
| 245π | |
| 100π | |
| 54π | |
| 125π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(72 x 5)
v = 245π
The dimensions of this cube are height (h) = 6, length (l) = 1, and width (w) = 8. What is the volume?
| 48 | |
| 648 | |
| 8 | |
| 96 |
The volume of a cube is height x length x width:
v = h x l x w
v = 6 x 1 x 8
v = 48
If angle a = 68° and angle b = 43° what is the length of angle c?
| 110° | |
| 93° | |
| 69° | |
| 91° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 68° - 43° = 69°
Find the value of c:
8c + z = 1
c + 9z = -1
| \(\frac{3}{4}\) | |
| 8 | |
| \(\frac{28}{33}\) | |
| \(\frac{10}{71}\) |
You need to find the value of c so solve the first equation in terms of z:
8c + z = 1
z = 1 - 8c
then substitute the result (1 - 8c) into the second equation:
c + 9(1 - 8c) = -1
c + (9 x 1) + (9 x -8c) = -1
c + 9 - 72c = -1
c - 72c = -1 - 9
-71c = -10
c = \( \frac{-10}{-71} \)
c = \(\frac{10}{71}\)