1.
a gym has two membership plans.
the gold plan costs 50 dollars per month and 3 dollars per visit.
the platinum plan costs 20 dollars per month and 6 dollars per visit.

The number of visit so that both plan cost same is 10 .

Both the plan has equivalent choice of benefit

Step-by-step explanation:

Given as :

A gym has two membership plans.

For Gold plan

The charge per month = $50  

The charge per visit = $3

For Platinum plan

The charge per month = $20  

The charge per visit = $6

Let The number of visit for which each plan be same = n visits

Now, According to question

∵ Each plan cost to be same

So,

The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit

I.e $50 + $3 × n = $20 + $6 × n

Or, $50 - $20 =  $6 × n  -  $3 × n

Or, $30 = ($6 - $3) × n  

Or, $30 = $3 × n  

∴ n =

I.e n = 10

So, The number of visits = n = 10

Now, For Gold plan

The charge per month = $50  

The charge per visit = $3 × 10 = $30

So, Total charge for gold plan = $50 + $30 = $80

Similarly For Platinum plan

The charge per month = $20  

The charge per visit = $6×10 = $60

So, For Platinum plan ,total charge = $20 + $60 = $80

Hence, The number of visit so that both plan cost same is 10

and both the plan has equivalent benefit. Answer

d. vertex

step-by-step explanation:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this