| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
Which of the following statements about a parallelogram is not true?
the perimeter of a parallelogram is the sum of the lengths of all sides |
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the area of a parallelogram is base x height |
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a parallelogram is a quadrilateral |
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opposite sides and adjacent angles are equal |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
The endpoints of this line segment are at (-2, -1) and (2, -5). What is the slope-intercept equation for this line?
| y = 3x + 2 | |
| y = \(\frac{1}{2}\)x + 4 | |
| y = -x - 3 | |
| y = -\(\frac{1}{2}\)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 -3. 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, -5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-5.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{-4}{4} \)Plugging these values into the slope-intercept equation:
y = -x - 3
If side a = 4, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{128} \) | |
| \( \sqrt{97} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{32} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 42
c2 = 16 + 16
c2 = 32
c = \( \sqrt{32} \)
What is 5a6 - 4a6?
| 20a12 | |
| 1a6 | |
| a12 | |
| 1 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
5a6 - 4a6 = 1a6
Find the value of a:
2a + x = 1
3a + x = -8
| -9 | |
| -4\(\frac{2}{5}\) | |
| -\(\frac{11}{67}\) | |
| 1\(\frac{1}{26}\) |
You need to find the value of a so solve the first equation in terms of x:
2a + x = 1
x = 1 - 2a
then substitute the result (1 - 2a) into the second equation:
3a + 1(1 - 2a) = -8
3a + (1 x 1) + (1 x -2a) = -8
3a + 1 - 2a = -8
3a - 2a = -8 - 1
a = -9
a = \( \frac{-9}{1} \)
a = -9