| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
If a = c = 5, b = d = 6, and the blue angle = 57°, what is the area of this parallelogram?
| 4 | |
| 48 | |
| 28 | |
| 30 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 5 x 6
a = 30
The endpoints of this line segment are at (-2, -1) and (2, -7). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x - 4 | |
| y = 3x + 1 | |
| y = -x + 2 | |
| y = 2\(\frac{1}{2}\)x + 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, -1) and (2, -7) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-7.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)Plugging these values into the slope-intercept equation:
y = -1\(\frac{1}{2}\)x - 4
Simplify 5a x 7b.
| 35\( \frac{b}{a} \) | |
| 35\( \frac{a}{b} \) | |
| 35a2b2 | |
| 35ab |
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.
5a x 7b = (5 x 7) (a x b) = 35ab
If side a = 3, side b = 8, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{10} \) | |
| \( \sqrt{37} \) | |
| \( \sqrt{130} \) | |
| \( \sqrt{73} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 82
c2 = 9 + 64
c2 = 73
c = \( \sqrt{73} \)
If BD = 26 and AD = 29, AB = ?
| 14 | |
| 3 | |
| 19 | |
| 10 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD