| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.66 |
| Score | 0% | 53% |
The dimensions of this trapezoid are a = 4, b = 3, c = 5, d = 6, and h = 2. What is the area?
| 14 | |
| 16\(\frac{1}{2}\) | |
| 9 | |
| 21 |
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(3 + 6)(2)
a = ½(9)(2)
a = ½(18) = \( \frac{18}{2} \)
a = 9
Which types of triangles will always have at least two sides of equal length?
equilateral, isosceles and right |
|
equilateral and right |
|
isosceles and right |
|
equilateral and isosceles |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
Solve for a:
-9a + 9 < \( \frac{a}{-7} \)
| a < -\(\frac{2}{19}\) | |
| a < -\(\frac{9}{14}\) | |
| a < 1\(\frac{1}{7}\) | |
| a < 1\(\frac{1}{62}\) |
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 < sign and the answer on the other.
-9a + 9 < \( \frac{a}{-7} \)
-7 x (-9a + 9) < a
(-7 x -9a) + (-7 x 9) < a
63a - 63 < a
63a - 63 - a < 0
63a - a < 63
62a < 63
a < \( \frac{63}{62} \)
a < 1\(\frac{1}{62}\)
Solve for b:
b2 - 11b + 30 = 0
| 9 or 9 | |
| 9 or -1 | |
| 2 or -6 | |
| 5 or 6 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 - 11b + 30 = 0
(b - 5)(b - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 5) or (b - 6) must equal zero:
If (b - 5) = 0, b must equal 5
If (b - 6) = 0, b must equal 6
So the solution is that b = 5 or 6
The dimensions of this cylinder are height (h) = 7 and radius (r) = 3. What is the volume?
| 294π | |
| 6π | |
| 2π | |
| 63π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(32 x 7)
v = 63π