At New years you decide to join a gym to lose all those calories gained during winter break and youre comparing two different gyms. The first gym, gym A has a 12$ initiation fee and then costs 10$ per month. The second gym , gym B has a 20$ initiation fee and then costs 6$ per month. Create an equation that aims to find when these two gyms will cost the same amount of money

Given:

For gym A, initiation fee = $12 and cost = $10 per month.

For gym B, initiation fee = $20 and cost = $6 per month.

To find:

The equation that aims to find when these two gyms will cost the same amount of money,

Solution:

Let the number of months be x.

Cost function = Initiation fee + (cost)(x)

Cost function for gym A is

Cost function for gym B is

Cost of these two gyms are equal if f(x)=g(x).

Therefore, the required equation is .

On solving this equation, we get

Hence, after 2 months the cost of these two gyms are same.

it would be 6xy and -16xy.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: