| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
If angle a = 49° and angle b = 60° what is the length of angle d?
| 111° | |
| 145° | |
| 131° | |
| 112° |
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° - 49° - 60° = 71°
So, d° = 60° + 71° = 131°
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° - 49° = 131°
If side x = 8cm, side y = 6cm, and side z = 13cm what is the perimeter of this triangle?
| 35cm | |
| 29cm | |
| 27cm | |
| 25cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 8cm + 6cm + 13cm = 27cm
Solve for c:
c2 - 12c + 11 = -2c - 5
| 5 or -8 | |
| 4 or -1 | |
| 2 or 8 | |
| 7 or 4 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
c2 - 12c + 11 = -2c - 5
c2 - 12c + 11 + 5 = -2c
c2 - 12c + 2c + 16 = 0
c2 - 10c + 16 = 0
Next, factor the quadratic equation:
c2 - 10c + 16 = 0
(c - 2)(c - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c - 8) must equal zero:
If (c - 2) = 0, c must equal 2
If (c - 8) = 0, c must equal 8
So the solution is that c = 2 or 8
If AD = 26 and BD = 17, AB = ?
| 9 | |
| 13 | |
| 3 | |
| 2 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BDBreaking apart a quadratic expression into a pair of binomials is called:
normalizing |
|
factoring |
|
squaring |
|
deconstructing |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.