| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
If side a = 6, side b = 5, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{73} \) | |
| \( \sqrt{113} \) | |
| \( \sqrt{61} \) | |
| \( \sqrt{89} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 52
c2 = 36 + 25
c2 = 61
c = \( \sqrt{61} \)
The dimensions of this cylinder are height (h) = 8 and radius (r) = 8. What is the volume?
| 36π | |
| 196π | |
| 125π | |
| 512π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(82 x 8)
v = 512π
Which types of triangles will always have at least two sides of equal length?
equilateral and isosceles |
|
isosceles and right |
|
equilateral, isosceles and right |
|
equilateral and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
Factor y2 - 12y + 36
| (y - 6)(y + 6) | |
| (y + 6)(y + 6) | |
| (y - 6)(y - 6) | |
| (y + 6)(y - 6) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 36 as well and sum (Inside, Outside) to equal -12. For this problem, those two numbers are -6 and -6. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 12y + 36
y2 + (-6 - 6)y + (-6 x -6)
(y - 6)(y - 6)
If side x = 6cm, side y = 9cm, and side z = 14cm what is the perimeter of this triangle?
| 34cm | |
| 29cm | |
| 28cm | |
| 31cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 6cm + 9cm + 14cm = 29cm