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Umnica [9.8K]
2 years ago
8

Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).

Mathematics
1 answer:
svetoff [14.1K]2 years ago
4 0
Start by finding the sum of (-8 3/4) and (-2 5/6).  Find the least common denominator (LCD).  12 is the first thing that both 4 and 6 will evenly divide into, so we convert both fractions to 12ths:

-8 3/4 = -8 9/12 (multiply 4 by 3 to get 12, so multiply the numerator, 3, by 3 as well)
-2 5/6 = -2 10/12 (multiply 6 by 2 to get 12, so multiply the numerator, 5, by 2 as well)
-8 9/12 + -2 10/12 = -10 19/12
We must convert the improper fraction.  12 goes into 19 1 time with 7 left over, so 19/12 = 1 7/12
This means that -10 19/12 = -11 7/12
The opposite of 1 1/5 is -1 1/5.  Add this to -11 7/12.  Again find the LCD; in this case it is 60.
-1 1/5 = -1 12/60
-11 7/12 = -11 35/60
Adding these two we get -12 47/60.
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Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.

Range is the set of possible results for c(x), i.e. possible costs.

You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.

You can substitute some values for x to help you, for example:

x      y
0    200
1    200 -7 +0.345 = 193.345
2    200 - 14 + .345 (4) = 187.38
3    200 - 21 + .345(9) = 182.105
4    200 - 28 + .345(16) = 177.52
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10  200 - 70 + 0.345(100) =164.5
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The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.

Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.

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