| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
|
c2 + a2 |
|
c - a |
|
c2 - a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
If side a = 9, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{40} \) | |
| \( \sqrt{34} \) | |
| \( \sqrt{37} \) | |
| \( \sqrt{130} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 92 + 72
c2 = 81 + 49
c2 = 130
c = \( \sqrt{130} \)
If the base of this triangle is 5 and the height is 9, what is the area?
| 72 | |
| 22\(\frac{1}{2}\) | |
| 42 | |
| 50 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 5 x 9 = \( \frac{45}{2} \) = 22\(\frac{1}{2}\)
What is 4a + 9a?
| 36a2 | |
| 36a | |
| 13a | |
| -5 |
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.
4a + 9a = 13a
The dimensions of this cube are height (h) = 3, length (l) = 3, and width (w) = 3. What is the volume?
| 40 | |
| 32 | |
| 27 | |
| 240 |
The volume of a cube is height x length x width:
v = h x l x w
v = 3 x 3 x 3
v = 27