| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.83 |
| Score | 0% | 57% |
If side a = 5, side b = 8, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{65} \) | |
| \( \sqrt{130} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{162} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 82
c2 = 25 + 64
c2 = 89
c = \( \sqrt{89} \)
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
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c2 + a2 |
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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, \(c = \sqrt{a + b}\)
Solve for z:
z2 - 12z - 14 = -4z - 5
| -4 or -8 | |
| -1 or 9 | |
| 2 or -7 | |
| -1 or -3 |
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:
z2 - 12z - 14 = -4z - 5
z2 - 12z - 14 + 5 = -4z
z2 - 12z + 4z - 9 = 0
z2 - 8z - 9 = 0
Next, factor the quadratic equation:
z2 - 8z - 9 = 0
(z + 1)(z - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 1) or (z - 9) must equal zero:
If (z + 1) = 0, z must equal -1
If (z - 9) = 0, z must equal 9
So the solution is that z = -1 or 9
What is 9a - 5a?
| 14a2 | |
| 4 | |
| 4a | |
| 45a2 |
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.
9a - 5a = 4a
If the length of AB equals the length of BD, point B __________ this line segment.
midpoints |
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bisects |
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trisects |
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intersects |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.