| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
What is 6a - 5a?
| 1 | |
| 30a | |
| 30a2 | |
| 1a |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
6a - 5a = 1a
For this diagram, the Pythagorean theorem states that b2 = ?
c2 + a2 |
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a2 - c2 |
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c - a |
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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, \(c = \sqrt{a + b}\)
Order the following types of angle from least number of degrees to most number of degrees.
right, acute, obtuse |
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right, obtuse, acute |
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acute, obtuse, right |
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acute, right, obtuse |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
If the area of this square is 4, what is the length of one of the diagonals?
| 4\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{4} \) = 2
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 22 + 22
c2 = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)
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 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.