| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
If the base of this triangle is 3 and the height is 8, what is the area?
| 45 | |
| 12 | |
| 105 | |
| 39 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 3 x 8 = \( \frac{24}{2} \) = 12
Simplify 3a x 5b.
| 15\( \frac{b}{a} \) | |
| 15\( \frac{a}{b} \) | |
| 15a2b2 | |
| 15ab |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
3a x 5b = (3 x 5) (a x b) = 15ab
Solve for z:
z2 - 8z + 9 = z - 5
| 2 or 7 | |
| 8 or 1 | |
| 4 or -7 | |
| 3 or -1 |
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 - 8z + 9 = z - 5
z2 - 8z + 9 + 5 = z
z2 - 8z - z + 14 = 0
z2 - 9z + 14 = 0
Next, factor the quadratic equation:
z2 - 9z + 14 = 0
(z - 2)(z - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 2) or (z - 7) must equal zero:
If (z - 2) = 0, z must equal 2
If (z - 7) = 0, z must equal 7
So the solution is that z = 2 or 7
The dimensions of this cube are height (h) = 4, length (l) = 5, and width (w) = 9. What is the volume?
| 162 | |
| 72 | |
| 210 | |
| 180 |
The volume of a cube is height x length x width:
v = h x l x w
v = 4 x 5 x 9
v = 180
The endpoints of this line segment are at (-2, 5) and (2, -7). What is the slope-intercept equation for this line?
| y = -2x + 1 | |
| y = 2\(\frac{1}{2}\)x + 0 | |
| y = 3x + 1 | |
| y = -3x - 1 |
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 -1. 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, 5) and (2, -7) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-7.0) - (5.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)Plugging these values into the slope-intercept equation:
y = -3x - 1