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For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
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c2 - a2 |
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a2 - c2 |
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c2 + a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
Solve for x:
4x - 6 = -4 - 7x
| -2\(\frac{2}{3}\) | |
| \(\frac{2}{11}\) | |
| -\(\frac{1}{4}\) | |
| -\(\frac{1}{2}\) |
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 equal sign and the answer on the other.
4x - 6 = -4 - 7x
4x = -4 - 7x + 6
4x + 7x = -4 + 6
11x = 2
x = \( \frac{2}{11} \)
x = \(\frac{2}{11}\)
Solve for a:
-9a + 3 = \( \frac{a}{-4} \)
| -\(\frac{7}{55}\) | |
| \(\frac{12}{35}\) | |
| \(\frac{8}{9}\) | |
| 1\(\frac{5}{9}\) |
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 equal sign and the answer on the other.
-9a + 3 = \( \frac{a}{-4} \)
-4 x (-9a + 3) = a
(-4 x -9a) + (-4 x 3) = a
36a - 12 = a
36a - 12 - a = 0
36a - a = 12
35a = 12
a = \( \frac{12}{35} \)
a = \(\frac{12}{35}\)
The endpoints of this line segment are at (-2, -1) and (2, 3). What is the slope-intercept equation for this line?
| y = -\(\frac{1}{2}\)x + 4 | |
| y = x - 1 | |
| y = -2\(\frac{1}{2}\)x - 4 | |
| y = x + 1 |
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 1. 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 = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(3.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{4}{4} \)Plugging these values into the slope-intercept equation:
y = x + 1
Which types of triangles will always have at least two sides of equal length?
equilateral and right |
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equilateral, isosceles and right |
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equilateral and isosceles |
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isosceles 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.