| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
A trapezoid is a quadrilateral with one set of __________ sides.
equal length |
|
parallel |
|
right angle |
|
equal angle |
A trapezoid is a quadrilateral with one set of parallel sides.
If a = c = 4, b = d = 7, and the blue angle = 80°, what is the area of this parallelogram?
| 28 | |
| 42 | |
| 24 | |
| 40 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 4 x 7
a = 28
Solve for b:
-3b + 5 = \( \frac{b}{3} \)
| \(\frac{12}{35}\) | |
| \(\frac{8}{11}\) | |
| -1\(\frac{11}{14}\) | |
| 1\(\frac{1}{2}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
-3b + 5 = \( \frac{b}{3} \)
3 x (-3b + 5) = b
(3 x -3b) + (3 x 5) = b
-9b + 15 = b
-9b + 15 - b = 0
-9b - b = -15
-10b = -15
b = \( \frac{-15}{-10} \)
b = 1\(\frac{1}{2}\)
Solve for b:
b2 - 7b + 10 = 0
| 6 or 2 | |
| 2 or 5 | |
| 7 or 5 | |
| -4 or -8 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 - 7b + 10 = 0
(b - 2)(b - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 2) or (b - 5) must equal zero:
If (b - 2) = 0, b must equal 2
If (b - 5) = 0, b must equal 5
So the solution is that b = 2 or 5
If side a = 6, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{65} \) | |
| \( \sqrt{61} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{80} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 72
c2 = 36 + 49
c2 = 85
c = \( \sqrt{85} \)