Answer:
![4x^3+7x^2+5x+2](https://tex.z-dn.net/?f=4x%5E3%2B7x%5E2%2B5x%2B2)
Step-by-step explanation:
Given:
![f(x)=4x^2+5x-3](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E2%2B5x-3)
![g(x)=4x^3+3x^2+5](https://tex.z-dn.net/?f=g%28x%29%3D4x%5E3%2B3x%5E2%2B5)
![\begin{aligned}\implies (f+g)(x)=f(x)+g(x) & = (4x^2+5x-3) + (4x^3+3x^2+5) \\& = 4x^2+5x-3+4x^3+3x^2+5 \\& = 4x^3+4x^2+3x^2+5x-3+5 \\& = 4x^3+7x^2+5x+2 \\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%28f%2Bg%29%28x%29%3Df%28x%29%2Bg%28x%29%20%26%20%3D%20%284x%5E2%2B5x-3%29%20%2B%20%284x%5E3%2B3x%5E2%2B5%29%20%5C%5C%26%20%3D%204x%5E2%2B5x-3%2B4x%5E3%2B3x%5E2%2B5%20%5C%5C%26%20%3D%204x%5E3%2B4x%5E2%2B3x%5E2%2B5x-3%2B5%20%5C%5C%26%20%3D%204x%5E3%2B7x%5E2%2B5x%2B2%20%5C%5C%5Cend%7Baligned%7D)
Answer:
- the owner should increase prices to increase revenue (up to n=5)
- a) c(n) = 50+5n; q(n) = 200-10n
- b) R(n) =50(10+n)(20-n)
- c) see below for a graph
Step-by-step explanation:
a. The cost of a ticket after n price increases of $5 each will be ...
c(n) = 50 +5n
The number of season-ticket holders (q) after n price increases will be ...
q(n) = 200 -10n
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b. The revenue after n price increases will be ...
R(n) = c(n)·q(n) = (50 +5n)(200 -10n)
R(n) = 50(10 +n)(20 -n)
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c. See the attachment for a graph
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d. The theater owner should raise the price of a season ticket to increase revenue. The number of $5 price increases should not exceed 5 if revenue is to increase. Above that number, revenue will decrease.
The missing term is -1155.
Step-by-step explanation:
Given expression is
68 * 27 - 81 + ? = 600
Let the missing term be x
![68*27-81+x=600\\1836-81+x=600\\1755+x=600](https://tex.z-dn.net/?f=68%2A27-81%2Bx%3D600%5C%5C1836-81%2Bx%3D600%5C%5C1755%2Bx%3D600)
Subtracting 1755 from both sides
![1755-1755+x=600-1755\\x=-1155](https://tex.z-dn.net/?f=1755-1755%2Bx%3D600-1755%5C%5Cx%3D-1155)
Therefore,
The missing term is -1155.
Keywords: multiplication, addition
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