| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
What is the area of a circle with a radius of 2?
| 8π | |
| 2π | |
| 4π | |
| 9π |
The formula for area is πr2:
a = πr2
a = π(22)
a = 4π
The dimensions of this cube are height (h) = 2, length (l) = 7, and width (w) = 7. What is the volume?
| 162 | |
| 72 | |
| 98 | |
| 80 |
The volume of a cube is height x length x width:
v = h x l x w
v = 2 x 7 x 7
v = 98
The endpoints of this line segment are at (-2, 9) and (2, -1). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x + 4 | |
| y = -2\(\frac{1}{2}\)x - 4 | |
| y = -2x + 4 | |
| y = 3x - 3 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 4. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 9) and (2, -1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-1.0) - (9.0)}{(2) - (-2)} \) = \( \frac{-10}{4} \)Plugging these values into the slope-intercept equation:
y = -2\(\frac{1}{2}\)x + 4
A quadrilateral is a shape with __________ sides.
3 |
|
2 |
|
5 |
|
4 |
A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.
Solve for a:
a2 + 2a - 68 = a + 4
| 3 or -5 | |
| 8 or -9 | |
| 5 or -7 | |
| 3 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:
a2 + 2a - 68 = a + 4
a2 + 2a - 68 - 4 = a
a2 + 2a - a - 72 = 0
a2 + a - 72 = 0
Next, factor the quadratic equation:
a2 + a - 72 = 0
(a - 8)(a + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 8) or (a + 9) must equal zero:
If (a - 8) = 0, a must equal 8
If (a + 9) = 0, a must equal -9
So the solution is that a = 8 or -9