The finances of a group of pet owners were analyzed to determine how much they were spending on their pet(s) each year. A graph
of that data is shown:
Would (3, 7.2) be a realistic solution for the function? Explain.
A. Yes, it is realistic to have 7.2 owners who spend $300 dollars on their pet(s).
B. No, it is not realistic to have 3 owners.
C. Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
D. No, it is not realistic that owners spend $720 a year on their pet(s).
Would (3, 7.2) be a realistic solution for the function? Explain.
A. Yes, it is realistic to have 7.2 owners who spend $300 dollars on their pet(s).
B. No, it is not realistic to have 3 owners.
C. Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
D. No, it is not realistic that owners spend $720 a year on their pet(s).
1 answer:
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Answer:
Step-by-step explanation:
Let
Subbing in:
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
Group together in groups of 2:
Now factor out what's common within each set of parenthesis:
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
Remember that
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring gives us that x = 1 and -1. The other set is a bit more tricky. If
then
and
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
±
which will simplify down to
±
Those are the 4 solutions to the quartic equation.