| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
If angle a = 45° and angle b = 34° what is the length of angle d?
| 147° | |
| 135° | |
| 111° | |
| 125° |
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° - 45° - 34° = 101°
So, d° = 34° + 101° = 135°
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° - 45° = 135°
Breaking apart a quadratic expression into a pair of binomials is called:
factoring |
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normalizing |
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deconstructing |
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squaring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
If a = c = 4, b = d = 6, what is the area of this rectangle?
| 16 | |
| 6 | |
| 24 | |
| 12 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 4 x 6
a = 24
If side a = 1, side b = 1, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{13} \) | |
| 5 | |
| \( \sqrt{58} \) | |
| \( \sqrt{2} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 12 + 12
c2 = 1 + 1
c2 = 2
c = \( \sqrt{2} \)
Solve for b:
b2 + 8b - 20 = 3b + 4
| 3 or -7 | |
| 3 or -8 | |
| 9 or -7 | |
| -7 or -9 |
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:
b2 + 8b - 20 = 3b + 4
b2 + 8b - 20 - 4 = 3b
b2 + 8b - 3b - 24 = 0
b2 + 5b - 24 = 0
Next, factor the quadratic equation:
b2 + 5b - 24 = 0
(b - 3)(b + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 3) or (b + 8) must equal zero:
If (b - 3) = 0, b must equal 3
If (b + 8) = 0, b must equal -8
So the solution is that b = 3 or -8