C(x) = 200 - 7x + 0.345x^2
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
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42
10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745
The functions does not have real roots, then the costs never decrease to 0.
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.
The cost of the shirts is stable, so we can subtract $1150 - $84, which = $1066. Now we want to find how many watches we can buy with $1066, or how many times $99 fits into $1066. So divide 1066 by 99 to get 10.77. You can't buy 77ths of a watch, so round it down to 10 and you have your answer. Samantha can buy 10 watches.
Opposite angles of an inscribed quadrilateral are supplementary, so it is true that ...
... B. m∠A + m∠C = m∠B + m∠D . . . . . = 180°
<u>Answer-</u>
<em>The lines are two </em><em>coinciding lines</em><em> or the </em><em>same lines</em><em>.</em>
<u>Solution-</u>
The given line equations are
the first one,
the second one,
As we know two line equations
and
will be,
- Parallel if,

- Coincide if,

- Intersect if,

As here,


(C₁ and C₂ aren't considered as they are 0)
Therefore, the lines are two coinciding lines or the same lines.