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Salsk061 [2.6K]
1 year ago
9

An online shopping club has 4,600 members when it charges ​$9 per month for membership. For each ​$1 monthly increase in members

hip​ fee, the club loses approximately 200 of its existing members. Write and simplify a function R to represent the monthly revenue received by the club when x represents the price increase.
Hint – Monthly Revenue = # of members • monthly fee
ℙ !!​
Mathematics
1 answer:
rjkz [21]1 year ago
7 0

Answer: R  = (4600 - 200x) ( 9 + 1x)

Step-by-step explanation:

We have that

Revenue  =  Members  *  (Cost Per Member)

Where x represents the number of $1  increases

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I think I have the correct answers but will anyone try to solve these questions so I can see if we got the same answer.
Andre45 [30]

Because you seem to have an understanding of the material, I will write my math, but no explanations for my work. Comment on this answer for an explanation, or if I did something wrong.

1. Find the length of the South side of the field.

(5x+2)+(x^2-9)+(x^2-7x+12)\\5x+2+x^2-9+x^2-7x+12\\2x^2+5x+2-9-7x+12\\2x^2-2x+2-9+12\\2x^2-2x+5

2.Find the perimeter of the pumpkin field.

2(5x+2)+2(5x-2)\\(5x+2)+(5x+2)+(5x-2)+(5x-2)\\20x+4-4\\20x

3. Find the perimeter of the whole field.

2(4x+5x-2)+2(5x+2+x^2-9+x^2-7x+12)\\2(9x-2)+2(2x^2-2x-5)\\18x-4+4x^2-4x+10\\4x^2+14x+6

4. If x=30ft, what is the total perimeter?

P=4x^2+14x+6\\P=4(30)^2+14(30)+6\\P=4(900)+420+6\\P=1026ft

Random Tangent:

If you want to involve y in finding these answers for whatever reason, your math is going to get messy. Here's what I tried before I realized you could multiply each side by 2 to get the total perimeter:

xy+1+x+6=4x+5x-2\\xy-8x=-9\\x(y-8)=-9\\y-8=-\frac{9}{x}\\y=-\frac{9}{x}+8

Now the other side. This one's even worse.

xy-1+6x+x=5x+2+x^2-9+x^2-7x+12\\xy+9x-2x^2=5\\x(y+9+2x)=5\\2x+9+y=\frac{5}{x}\\y=\frac{5}{x}-2x-9

At this point, was realizing I wasn't going about the problem correctly, but did one last try by setting y=y. At this point in the equation, I simply had to stop, both due to complexity and technological problems.

\frac{5}{x}-2x-9=-\frac{9}{x}+8\\\frac{14}{x}=2x+17\\ 14=2x^2+17x\\0=2x^2+17x-13\\

I could possibly continue to solve, but I don't see a point. It was clear that this was NOT the right path to take finding the perimeter. It was here I realized that I could just multiply the two sides without y in them by 2 and--without as much difficulty--reach the correct answer.

6 0
3 years ago
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