| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
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c - a |
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c2 - a2 |
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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, \(c = \sqrt{a + b}\)
If a = 1, b = 6, c = 7, and d = 6, what is the perimeter of this quadrilateral?
| 21 | |
| 20 | |
| 15 | |
| 16 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 6 + 7 + 6
p = 20
If the length of AB equals the length of BD, point B __________ this line segment.
bisects |
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intersects |
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midpoints |
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trisects |
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.
A(n) __________ is two expressions separated by an equal sign.
formula |
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problem |
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equation |
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expression |
An equation is two expressions separated by an equal sign. The key to solving equations is to 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.
Find the value of a:
3a + z = 7
-9a + 5z = -6
| -2 | |
| -1\(\frac{17}{18}\) | |
| 1\(\frac{17}{24}\) | |
| -\(\frac{33}{47}\) |
You need to find the value of a so solve the first equation in terms of z:
3a + z = 7
z = 7 - 3a
then substitute the result (7 - 3a) into the second equation:
-9a + 5(7 - 3a) = -6
-9a + (5 x 7) + (5 x -3a) = -6
-9a + 35 - 15a = -6
-9a - 15a = -6 - 35
-24a = -41
a = \( \frac{-41}{-24} \)
a = 1\(\frac{17}{24}\)