| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
The dimensions of this trapezoid are a = 5, b = 5, c = 8, d = 3, and h = 4. What is the area?
| 22\(\frac{1}{2}\) | |
| 30 | |
| 16 | |
| 27\(\frac{1}{2}\) |
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(5 + 3)(4)
a = ½(8)(4)
a = ½(32) = \( \frac{32}{2} \)
a = 16
The dimensions of this cylinder are height (h) = 3 and radius (r) = 2. What is the volume?
| 343π | |
| 81π | |
| 12π | |
| 18π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(22 x 3)
v = 12π
If a = c = 1, b = d = 8, and the blue angle = 77°, what is the area of this parallelogram?
| 28 | |
| 18 | |
| 35 | |
| 8 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 1 x 8
a = 8
If b = 2 and y = -2, what is the value of 2b(b - y)?
| 12 | |
| -112 | |
| 16 | |
| -108 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
2b(b - y)
2(2)(2 + 2)
2(2)(4)
(4)(4)
16
Solve for x:
x2 + x - 21 = 2x - 1
| -2 or -2 | |
| 7 or -2 | |
| -4 or 5 | |
| 2 or 2 |
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:
x2 + x - 21 = 2x - 1
x2 + x - 21 + 1 = 2x
x2 + x - 2x - 20 = 0
x2 - x - 20 = 0
Next, factor the quadratic equation:
x2 - x - 20 = 0
(x + 4)(x - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 4) or (x - 5) must equal zero:
If (x + 4) = 0, x must equal -4
If (x - 5) = 0, x must equal 5
So the solution is that x = -4 or 5