| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
If angle a = 65° and angle b = 53° what is the length of angle d?
| 115° | |
| 154° | |
| 110° | |
| 129° |
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° - 65° - 53° = 62°
So, d° = 53° + 62° = 115°
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° - 65° = 115°
If the base of this triangle is 8 and the height is 4, what is the area?
| 18 | |
| 22\(\frac{1}{2}\) | |
| 66 | |
| 16 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 8 x 4 = \( \frac{32}{2} \) = 16
Factor y2 - 14y + 48
| (y - 8)(y - 6) | |
| (y - 8)(y + 6) | |
| (y + 8)(y + 6) | |
| (y + 8)(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 48 as well and sum (Inside, Outside) to equal -14. For this problem, those two numbers are -8 and -6. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 14y + 48
y2 + (-8 - 6)y + (-8 x -6)
(y - 8)(y - 6)
What is the circumference of a circle with a diameter of 15?
| 15π | |
| 7π | |
| 17π | |
| 10π |
The formula for circumference is circle diameter x π:
c = πd
c = 15π
Solve for x:
x2 + 13x + 42 = 0
| -6 or -7 | |
| 5 or -4 | |
| 6 or -4 | |
| 8 or 4 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
x2 + 13x + 42 = 0
(x + 6)(x + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 6) or (x + 7) must equal zero:
If (x + 6) = 0, x must equal -6
If (x + 7) = 0, x must equal -7
So the solution is that x = -6 or -7