| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.57 |
| Score | 0% | 71% |
If a = 6, b = 6, c = 2, and d = 3, what is the perimeter of this quadrilateral?
| 17 | |
| 19 | |
| 11 | |
| 27 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 6 + 6 + 2 + 3
p = 17
If angle a = 67° and angle b = 60° what is the length of angle c?
| 70° | |
| 68° | |
| 53° | |
| 93° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 67° - 60° = 53°
Breaking apart a quadratic expression into a pair of binomials is called:
squaring |
|
factoring |
|
normalizing |
|
deconstructing |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
If angle a = 27° and angle b = 63° what is the length of angle d?
| 127° | |
| 153° | |
| 119° | |
| 142° |
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° - 27° - 63° = 90°
So, d° = 63° + 90° = 153°
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° - 27° = 153°
If the area of this square is 16, what is the length of one of the diagonals?
| \( \sqrt{2} \) | |
| 7\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 42 + 42
c2 = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)