At which root does the graph of f(x)=(x+4)^6(x+7)^5 cross the x-axis ?
2 answers:
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In Graph x-axis represents number of visits and y-axis represents cost.
As graph comes up to be a linear one, so we can clearly say that cost is increasing linearly in multiples of 5.5 with increase in number of visits.
Example :
If museum is visited once then cost (y) = 5.5 x 1 = 5.5
If museum is visited twice then cost (y) = 5.5 x 2 = 11
If museum is visited thrice then cost (y) = 5.5 x 3 = 16.5
... cost (y) goes on in creasing when number of visits (x) increase with multiples of 5.5
Answer:
11 music lessons.
Step-by-step explanation:
We know that membership costs $165 and members pay $25 per music lesson.
So, we can write the following expression:
The 165 represents the one-time membership fee and the 25m represents the cost for m music lessons.
We know that non-members pay no membership fee but their cost per lesson is $40. So:
Represents the cost for non-members for m music lessons.
We want to find how many music lessons would have to be taken for the cost to be the same for both members and non-members. So, we can set the expressions equal to each other:
And solve for m. Let's subtract 25m from both sides:
Now, divide both sides by 15:
So, at the 11th music lesson, members and non-members will pay the same.
Further Notes:
This means that if a person would only like to take 10 or less lessons, the non-membership is best because there is no initial fee.
However, if a person would like to take 12 or more lessons, than the membership is best because the membership has a lower cost per lesson than the non-membership.
And we're done!