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The endpoints of this line segment are at (-2, 3) and (2, -3). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x + 0 | |
| y = 2x - 3 | |
| y = -x + 2 | |
| 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 0. 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, 3) and (2, -3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-3.0) - (3.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)Plugging these values into the slope-intercept equation:
y = -1\(\frac{1}{2}\)x + 0
Solve for c:
c2 - 64 = 0
| 8 or 1 | |
| 8 or -6 | |
| -1 or -2 | |
| 8 or -8 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 - 64 = 0
(c - 8)(c + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 8) or (c + 8) must equal zero:
If (c - 8) = 0, c must equal 8
If (c + 8) = 0, c must equal -8
So the solution is that c = 8 or -8
The endpoints of this line segment are at (-2, -1) and (2, 3). What is the slope of this line?
| -2 | |
| 2 | |
| 1 | |
| \(\frac{1}{2}\) |
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, 3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(3.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{4}{4} \)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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opposite sides and adjacent angles are equal |
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a parallelogram is a quadrilateral |
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the area of a parallelogram is base x height |
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).
Breaking apart a quadratic expression into a pair of binomials is called:
normalizing |
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factoring |
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deconstructing |
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squaring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.