| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.64 |
| Score | 0% | 53% |
If side a = 7, side b = 6, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{41} \) | |
| \( \sqrt{113} \) | |
| \( \sqrt{65} \) | |
| \( \sqrt{85} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 72 + 62
c2 = 49 + 36
c2 = 85
c = \( \sqrt{85} \)
If angle a = 41° and angle b = 48° what is the length of angle d?
| 154° | |
| 111° | |
| 115° | |
| 139° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 41° - 48° = 91°
So, d° = 48° + 91° = 139°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 41° = 139°
The dimensions of this cube are height (h) = 7, length (l) = 9, and width (w) = 4. What is the surface area?
| 158 | |
| 254 | |
| 212 | |
| 38 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 9 x 4) + (2 x 4 x 7) + (2 x 9 x 7)
sa = (72) + (56) + (126)
sa = 254
What is the circumference of a circle with a radius of 18?
| 9π | |
| 36π | |
| 26π | |
| 19π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 18)
c = 36π
The formula for the area of a circle is which of the following?
c = π r |
|
c = π d2 |
|
c = π d |
|
c = π r2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.