Simplify the expression to a polynomial in standard form: (x-1)^4
1 answer:
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Answer:
(a) P(x) = 300 x - 3600
(b) P(340) = $ 98400
(c) At least 12 items must be sold to avoid losing money.
Step-by-step explanation:
Part (a):
The Profit function is the difference between the revenue function (R(x)) and the Cost (C(x)) function:
P(x) = R(x) - C(x)
P(x) = 384 x - [84 x + 3600]
P(x) = 384 x - 84 x - 3600
P(x) = 300 x - 3600
Part (b):
The profit on 340 items is:
P(340) = 300 (340) - 3600
P(340) = 102000 - 3600
P(340) = $ 98400
Part (c):
To avoid losing money, the profit P(x) has to be larger or equal than zero. That is:
P(x) 0
300 x -3600 0
300 x 3600
x 3600/300
x 12
So at least 12 items must be sold to avoid losing money.
Check the picture below, so, those red ones are the midpoints you found.
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) \stackrel{midpoint}{JK}&({{ -1}}\quad ,&{{ 2}})\quad % (c,d) \stackrel{midpoint}{ML}&({{ 2}}\quad ,&{{ -2}}) \end{array} \\\\\\ d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\implies d_2=\sqrt{[2-(-1)]^2+[-2-2]^2} \\\\\\ d_2=\sqrt{(2+1)^2+(-4)^2}\implies d_2=\sqrt{9+16}\implies d_2=5](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%5Cstackrel%7Bmidpoint%7D%7BJK%7D%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0A%5Cstackrel%7Bmidpoint%7D%7BML%7D%26%28%7B%7B%202%7D%7D%5Cquad%20%2C%26%7B%7B%20-2%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%5Cimplies%20d_2%3D%5Csqrt%7B%5B2-%28-1%29%5D%5E2%2B%5B-2-2%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad_2%3D%5Csqrt%7B%282%2B1%29%5E2%2B%28-4%29%5E2%7D%5Cimplies%20d_2%3D%5Csqrt%7B9%2B16%7D%5Cimplies%20d_2%3D5)
now, that many units are each distance for those "medians", hmmm now, recall that each unit is meant to be 10 meters, so, just multiply each by 10, to get how many meters long each one is.
now, that many units are each distance for those "medians", hmmm now, recall that each unit is meant to be 10 meters, so, just multiply each by 10, to get how many meters long each one is.