| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
Which types of triangles will always have at least two sides of equal length?
isosceles and right |
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equilateral and right |
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equilateral, isosceles and right |
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equilateral and isosceles |
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.
The endpoints of this line segment are at (-2, 6) and (2, -2). What is the slope-intercept equation for this line?
| y = 2x + 3 | |
| y = -\(\frac{1}{2}\)x - 1 | |
| y = -2x + 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 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, 6) and (2, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (6.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)Plugging these values into the slope-intercept equation:
y = -2x + 2
The dimensions of this cube are height (h) = 4, length (l) = 1, and width (w) = 1. What is the volume?
| 360 | |
| 216 | |
| 60 | |
| 4 |
The volume of a cube is height x length x width:
v = h x l x w
v = 4 x 1 x 1
v = 4
Find the value of b:
-6b + x = 8
-3b + 5x = -4
| 1\(\frac{22}{53}\) | |
| -1\(\frac{17}{27}\) | |
| -\(\frac{2}{3}\) | |
| -1\(\frac{3}{5}\) |
You need to find the value of b so solve the first equation in terms of x:
-6b + x = 8
x = 8 + 6b
then substitute the result (8 - -6b) into the second equation:
-3b + 5(8 + 6b) = -4
-3b + (5 x 8) + (5 x 6b) = -4
-3b + 40 + 30b = -4
-3b + 30b = -4 - 40
27b = -44
b = \( \frac{-44}{27} \)
b = -1\(\frac{17}{27}\)
A cylinder with a radius (r) and a height (h) has a surface area of:
4π r2 |
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2(π r2) + 2π rh |
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π r2h |
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π r2h2 |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.