Over the summer, 2 people visited the beach, 3 people visited a state park, and 5 people flew across the country. If Connor's cl
2 answers:
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Answer:
Part A : 2y( x³ + 9x - 5x² - 45 ), Part B : 2y( x - 5 )( x² + 9 )
Step-by-step explanation:
Part A : Let's break every term down here to their " prime factors ", and see what is common among them,
2x³y + 18xy − 10x²y − 90y -
2x³y = 2 x³
y,
18xy = 2 3
3
x
y,
− 10x²y = 2 - 5
x²
y, - so as you can see for this example I purposely broke down - 10 into 2 and - 5. I could have placed the negative on the 2, but as that value was must likely common among all the terms, I decided to place it on the 5. The same goes for " − 90y. " I placed the negative there on the 5 once more.
− 90y = 2 - 5
3
3
y
The terms common among each term are 2 and y. Therefore, the GCF ( greatest common factor ) is 2x. Let's now factor the expression using this value.
2y( x³ + 9x - 5x² - 45 )
Part B : Let's simply factor this entire expression. Of course starting with the " factored " expression : 2y( x³ + 9x - 5x² - 45 ),
- Factor out "
" by grouping,
- Factor 9 from 9x - 45 and x² from x³ - 5x²,
- Factor out common term x - 5,
- And our solution is thus 2y( x - 5 )( x² + 9 )
Answer:
The value is
Step-by-step explanation:
From the question we are told that
The amount charge per year is
The number of members it will have at this amount is
The amount amount increase that will lead to the loss of a single member is
Generally the total amount the club would obtain from its members is mathematically represented as
Now let x denote the number of member lost
Hence
=>
=>
Thus the number of members that be removed to give the maximum income from dues is obtained by differentiating the above equation and equating it to zero
=>
So from we have
So the amount the club should charge is