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|---|---|---|
| Questions | 5 | 5 |
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For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
|
c - a |
|
c2 + a2 |
|
a2 - c2 |
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 the base of this triangle is 8 and the height is 1, what is the area?
| 4 | |
| 36 | |
| 71\(\frac{1}{2}\) | |
| 31\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 8 x 1 = \( \frac{8}{2} \) = 4
Solve -a + 8a = -9a - 5z - 5 for a in terms of z.
| -1\(\frac{5}{8}\)z - \(\frac{5}{8}\) | |
| -\(\frac{4}{5}\)z - \(\frac{4}{5}\) | |
| 1\(\frac{4}{11}\)z + \(\frac{8}{11}\) | |
| \(\frac{1}{4}\)z - \(\frac{1}{4}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
-a + 8z = -9a - 5z - 5
-a = -9a - 5z - 5 - 8z
-a + 9a = -5z - 5 - 8z
8a = -13z - 5
a = \( \frac{-13z - 5}{8} \)
a = \( \frac{-13z}{8} \) + \( \frac{-5}{8} \)
a = -1\(\frac{5}{8}\)z - \(\frac{5}{8}\)
What is 8a8 + 5a8?
| 13a16 | |
| 40a16 | |
| 13a8 | |
| a816 |
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.
8a8 + 5a8 = 13a8
The dimensions of this cylinder are height (h) = 2 and radius (r) = 2. What is the surface area?
| 70π | |
| 126π | |
| 16π | |
| 192π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(22) + 2π(2 x 2)
sa = 2π(4) + 2π(4)
sa = (2 x 4)π + (2 x 4)π
sa = 8π + 8π
sa = 16π