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lana [24]
2 years ago
7

The manager of a furniture factory finds that it costs $3000 to manufacture 80 chairs in one day and $4800 to produce 280 chairs

in one day. (a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear. C
Mathematics
1 answer:
Delicious77 [7]2 years ago
8 0

9514 1404 393

Answer:

  C = 9x +2280

Step-by-step explanation:

The 2-point form of the equation for a line can be a place to start.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  C = (4800 -3000)/(280 -80)(x -80) +3000 . . . . . use given values

  C = 1800/200(x -80) +3000 . . . . simplify some

  C = 9x -720 +3000 . . . . eliminate parentheses

  C = 9x +2280

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What's happening is that every subtraction can be written as "addition of the opposite."

18-5 = 18 + (-5)

One reason this is done in the work you showed is that they're trying to show why you distribute the negative and the 1 into the parentheses, why you multiply everything in the parentheses by "-1" and not just 1.

The other reason is to later to be able to move the individual terms around, so you'll be able to combine like terms.

When you move terms around, the sign has to stay attached to the term, so writing all the subtractions as addition helps keep the sign attached.

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