Answer:
The correct answer is B. Linear Relationship
Write the coeeficientes of the polynomial in order:
| 1 - 5 6 - 30
|
|
|
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After some trials you probe with 5
| 1 - 5 6 - 30
|
|
5 | 5 0 30
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1 0 6 0 <---- residue
Given that the residue is 0, 5 is a root.
The quotient is x^2 + 6 = 0, which does not have a real root.
Therefore, 5 is the only root. You can prove it by solving the polynomial x^2 + 6 = 0.
Answer: choice A. 40 liters
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Explanation:
x = number of liters of the 50% alcohol solution
If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).
So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below
0.50*x + 36 = 0.70*(40+x)
0.50*x + 36 = 0.70*(40)+0.70*(x)
0.50*x + 36 = 28+0.70*x
36 - 28 = 0.70*x - 0.50x
8 = 0.20x
0.20x = 8
x = 8/0.20
x = 40
So that is why the answer is choice A. 40 liters
