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hodyreva [135]
3 years ago
6

The owner of a new restaurant is ordering tables and chairs. he wants to have only tables for two and tables for 4. the total nu

mber of people can be seated in rest is 120, then write an equation to represent the situation. What do the variables represent?
Mathematics
1 answer:
Papessa [141]3 years ago
7 0

Answer:

4 M + 2 N = 120

Step-by-step explanation:

If we name "M" the number of tables for four people, and "N" the number of tables for two people, then the total number of people to be seated using M tables (of four people) would be the product "4 * M".

Similarly, the total number of people to be seated if the owner has N number of two person tables, would be: "2 * N".

Therefore, if the owner has M four people tables and N two person tables, the total number of people seated at the restaurant would be the addition:

4 * M + 2 * N. Since he wants this number to be 120, we complete the equation making this expression equal to 120:

4 * M + 2 * N = 120

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Express the terms of the following sequence by giving a recursive formula.
emmasim [6.3K]

The recursive formula for given sequence is: a_n = a_{n-1}-7

And the terms will be expressed as:

a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\

Step-by-step explanation:

First of all, we have to determine if the given sequence  is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7

Hence,

The recursive formula for given sequence is: a_n = a_{n-1}-7

And the terms will be expressed as:

a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

  • brainly.com/question/10341324
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#LearnwithBrainly

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Answer:

5(7d-5)

Step-by-step explanation:

taking 5 common from  35d-25

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47% of those who received a certificate were men

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