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Travka [436]
3 years ago
12

At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

but after that, each month at the gym costs $22. After how many months will the cost of both gyms be thge same?
Mathematics
1 answer:
mart [117]3 years ago
5 0

Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

f(x)=mx+b

where

m\rightarrow slope of line

b\rightarrow y-intercept

Let linear function to calculate total cost of gym be:

c(n)=mn+b

where

c\rightarrow total cost of gym

m\rightarrow cost per month (slope)

n\rightarrow number of months

b\rightarrow start-up fee (y-intercept)

For Gym 1

m=20 , b=12

c(n)=20n+12

For Gym 2

m=22 , b=4

c(n)=22n+4

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months (n)

20n+12=22n+4

\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}

So,

In 4 months the cost of both gyms will be the same.

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Pull terms out from under the radical, assuming positive real numbers.

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3 years ago
An element with mass 800 grams decays by 8.2% per day. How much of the element is remaining after 15 days,
Serjik [45]

Given:

The initial mass of an element is 800 grams.

Decay rate = 8.2% per day

Number of days = 15

To find:

The remaining element after 15 days.

Solution:

The exponential decay model is

y=a(1-r)^t

Where, a is the initial value r is the rate of interest and t is time period.

Putting a=800,r=0.082,t=15 in the above formula, we get

y=800(1-0.082)^{15}

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7 0
3 years ago
HELP!!!!!!!!!!!!! Please
Arturiano [62]

Probability helps us to know the chances of an event occurring. There are six possible outcomes.

<h3>What is Probability?</h3>

Probability helps us to know the chances of an event occurring.

\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

A.) The outcomes that are possible from the first spinner is 1, 2, and 3, while the outcomes possible from the second spinner are 2, Red and blue.

All the possible outcomes from this two spinner are,

(B,1), (B,2), (B,3), (R,1), (R,2), and (R,3).

Hence, there are six possible outcomes.

B.) The letters that can be used are A and B. The numbers that can be used are 1, 2, 3, and 4.

All the possible out comes are,

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Learn more about Probability:

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3 0
2 years ago
Help i made it worth a lot of points
raketka [301]

Answer:

36x^6/y^10

Step-by-step explanation:

First evaluate the parentheses, 6x^3 x 6x^3 = 36x^6

y^5 x y^5 = y^10 ; remember m^k x m^r = m^k+r

final answer should be 36x^6/y^10

hope this helps :')

4 0
2 years ago
Read 2 more answers
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