| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
If angle a = 53° and angle b = 20° what is the length of angle d?
| 127° | |
| 119° | |
| 113° | |
| 121° |
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° - 53° - 20° = 107°
So, d° = 20° + 107° = 127°
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° - 53° = 127°
Solve for a:
a2 + 3a - 4 = 0
| 1 or -4 | |
| 4 or -3 | |
| 5 or -1 | |
| -5 or -5 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
a2 + 3a - 4 = 0
(a - 1)(a + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 1) or (a + 4) must equal zero:
If (a - 1) = 0, a must equal 1
If (a + 4) = 0, a must equal -4
So the solution is that a = 1 or -4
If a = 3, b = 7, c = 6, and d = 4, what is the perimeter of this quadrilateral?
| 15 | |
| 23 | |
| 20 | |
| 24 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 3 + 7 + 6 + 4
p = 20
Which types of triangles will always have at least two sides of equal length?
equilateral, isosceles and right |
|
isosceles and right |
|
equilateral and right |
|
equilateral and isosceles |
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 - 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)