| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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If side a = 8, side b = 9, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{145} \) | |
| \( \sqrt{73} \) | |
| \( \sqrt{10} \) | |
| \( \sqrt{106} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 82 + 92
c2 = 64 + 81
c2 = 145
c = \( \sqrt{145} \)
Factor y2 + 14y + 45
| (y - 5)(y - 9) | |
| (y + 5)(y - 9) | |
| (y - 5)(y + 9) | |
| (y + 5)(y + 9) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 45 as well and sum (Inside, Outside) to equal 14. For this problem, those two numbers are 5 and 9. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 + 14y + 45
y2 + (5 + 9)y + (5 x 9)
(y + 5)(y + 9)
Solve for a:
a2 + 13a + 12 = 3a + 3
| 6 or 1 | |
| 7 or 2 | |
| -1 or -9 | |
| 8 or 6 |
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:
a2 + 13a + 12 = 3a + 3
a2 + 13a + 12 - 3 = 3a
a2 + 13a - 3a + 9 = 0
a2 + 10a + 9 = 0
Next, factor the quadratic equation:
a2 + 10a + 9 = 0
(a + 1)(a + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 1) or (a + 9) must equal zero:
If (a + 1) = 0, a must equal -1
If (a + 9) = 0, a must equal -9
So the solution is that a = -1 or -9
Which types of triangles will always have at least two sides of equal length?
equilateral and isosceles |
|
equilateral, isosceles and right |
|
equilateral and right |
|
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.
Solve -2c + c = -3c - 5z - 6 for c in terms of z.
| -1\(\frac{3}{11}\)z - \(\frac{7}{11}\) | |
| -\(\frac{1}{4}\)z + 2 | |
| -z - \(\frac{1}{5}\) | |
| -6z - 6 |
To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.
-2c + z = -3c - 5z - 6
-2c = -3c - 5z - 6 - z
-2c + 3c = -5z - 6 - z
c = -6z - 6