| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
The dimensions of this trapezoid are a = 6, b = 8, c = 9, d = 5, and h = 5. What is the area?
| 22\(\frac{1}{2}\) | |
| 32\(\frac{1}{2}\) | |
| 13\(\frac{1}{2}\) | |
| 24 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(8 + 5)(5)
a = ½(13)(5)
a = ½(65) = \( \frac{65}{2} \)
a = 32\(\frac{1}{2}\)
Solve for a:
-2a - 1 = 4 + 4a
| -\(\frac{3}{4}\) | |
| -\(\frac{5}{6}\) | |
| 1\(\frac{1}{2}\) | |
| 6 |
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.
-2a - 1 = 4 + 4a
-2a = 4 + 4a + 1
-2a - 4a = 4 + 1
-6a = 5
a = \( \frac{5}{-6} \)
a = -\(\frac{5}{6}\)
If a = c = 1, b = d = 2, and the blue angle = 59°, what is the area of this parallelogram?
| 5 | |
| 20 | |
| 54 | |
| 2 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 1 x 2
a = 2
If a = 1, b = 9, c = 4, and d = 5, what is the perimeter of this quadrilateral?
| 19 | |
| 17 | |
| 21 | |
| 15 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 9 + 4 + 5
p = 19
Solve for z:
z2 + 2z + 11 = -5z - 1
| 7 or -4 | |
| -3 or -4 | |
| 8 or 1 | |
| -1 or -7 |
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:
z2 + 2z + 11 = -5z - 1
z2 + 2z + 11 + 1 = -5z
z2 + 2z + 5z + 12 = 0
z2 + 7z + 12 = 0
Next, factor the quadratic equation:
z2 + 7z + 12 = 0
(z + 3)(z + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 3) or (z + 4) must equal zero:
If (z + 3) = 0, z must equal -3
If (z + 4) = 0, z must equal -4
So the solution is that z = -3 or -4