| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.67 |
| Score | 0% | 53% |
A quadrilateral is a shape with __________ sides.
3 |
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5 |
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4 |
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2 |
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 c:
3c - 4 < 4 + 2c
| c < -\(\frac{1}{3}\) | |
| c < 8 | |
| c < 1\(\frac{1}{3}\) | |
| c < \(\frac{5}{9}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.
3c - 4 < 4 + 2c
3c < 4 + 2c + 4
3c - 2c < 4 + 4
c < 8
The endpoints of this line segment are at (-2, -8) and (2, 4). What is the slope-intercept equation for this line?
| y = 2x + 2 | |
| y = -2\(\frac{1}{2}\)x + 4 | |
| y = 1\(\frac{1}{2}\)x - 1 | |
| y = 3x - 2 |
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 -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, -8) and (2, 4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(4.0) - (-8.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)Plugging these values into the slope-intercept equation:
y = 3x - 2
Find the value of a:
-6a + y = 1
-8a + 8y = 4
| 1\(\frac{3}{14}\) | |
| -\(\frac{1}{10}\) | |
| -2\(\frac{1}{4}\) | |
| 1\(\frac{22}{25}\) |
You need to find the value of a so solve the first equation in terms of y:
-6a + y = 1
y = 1 + 6a
then substitute the result (1 - -6a) into the second equation:
-8a + 8(1 + 6a) = 4
-8a + (8 x 1) + (8 x 6a) = 4
-8a + 8 + 48a = 4
-8a + 48a = 4 - 8
40a = -4
a = \( \frac{-4}{40} \)
a = -\(\frac{1}{10}\)
Which of the following is not required to define the slope-intercept equation for a line?
\({\Delta y \over \Delta x}\) |
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x-intercept |
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y-intercept |
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slope |
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.