| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
If side a = 6, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{45} \) | |
| \( \sqrt{58} \) | |
| \( \sqrt{52} \) | |
| 5 |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 42
c2 = 36 + 16
c2 = 52
c = \( \sqrt{52} \)
Simplify (y + 6)(y - 2)
| y2 - 8y + 12 | |
| y2 - 4y - 12 | |
| y2 + 4y - 12 | |
| y2 + 8y + 12 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 6)(y - 2)
(y x y) + (y x -2) + (6 x y) + (6 x -2)
y2 - 2y + 6y - 12
y2 + 4y - 12
If b = 6 and x = -5, what is the value of -2b(b - x)?
| -140 | |
| -132 | |
| 24 | |
| -630 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
-2b(b - x)
-2(6)(6 + 5)
-2(6)(11)
(-12)(11)
-132
A(n) __________ is two expressions separated by an equal sign.
formula |
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equation |
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problem |
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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.
Solve -7a + 6a = 8a + 7z + 1 for a in terms of z.
| -2z + 3\(\frac{1}{2}\) | |
| 4z + 6 | |
| -\(\frac{3}{4}\)z + 1\(\frac{1}{8}\) | |
| -\(\frac{1}{15}\)z - \(\frac{1}{15}\) |
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.
-7a + 6z = 8a + 7z + 1
-7a = 8a + 7z + 1 - 6z
-7a - 8a = 7z + 1 - 6z
-15a = z + 1
a = \( \frac{z + 1}{-15} \)
a = \( \frac{z}{-15} \) + \( \frac{1}{-15} \)
a = -\(\frac{1}{15}\)z - \(\frac{1}{15}\)