| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.90 |
| Score | 0% | 58% |
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 = -\(\frac{1}{2}\)x + 3 | |
| y = -2\(\frac{1}{2}\)x + 1 | |
| y = -1\(\frac{1}{2}\)x + 0 |
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
Which types of triangles will always have at least two sides of equal length?
equilateral, isosceles and right |
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isosceles and right |
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equilateral and isosceles |
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equilateral and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
A quadrilateral is a shape with __________ sides.
5 |
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4 |
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2 |
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3 |
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 a:
a2 - 10a + 14 = -a - 4
| 3 or 6 | |
| 4 or 2 | |
| -8 or -8 | |
| 2 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:
a2 - 10a + 14 = -a - 4
a2 - 10a + 14 + 4 = -a
a2 - 10a + a + 18 = 0
a2 - 9a + 18 = 0
Next, factor the quadratic equation:
a2 - 9a + 18 = 0
(a - 3)(a - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 6) must equal zero:
If (a - 3) = 0, a must equal 3
If (a - 6) = 0, a must equal 6
So the solution is that a = 3 or 6
Solve for x:
x2 + x - 56 = 0
| -1 or -3 | |
| 7 or -8 | |
| -1 or -5 | |
| 6 or 3 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
x2 + x - 56 = 0
(x - 7)(x + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 7) or (x + 8) must equal zero:
If (x - 7) = 0, x must equal 7
If (x + 8) = 0, x must equal -8
So the solution is that x = 7 or -8