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2 years ago

What expression is equivalent to 10q+5

Mathematics

1 answer:

lawyer [7]2 years ago

4 0

➽━━━━━━━━━━━━━──➸

☺ Hello mate__ ❤

◾◾here is your answer

given expression is 10q+5

we multiply by 2 this expression, we get

(10q+5)2 = 20q+10

so 20 q+ 10 is answer!!☺

➽━━━━━━━━━━━━━──➸

I hope, this will help you.☺

Thank you______❤

✿┅═══❁✿ Be Brainly✿❁═══┅✿

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Answer:

Let us use mathematical induction to prove the statement. So, we are going to start checking the statement for the first natural numbers.

$n=1$ : Our set is $\{x_1\}$ . So, obviously, $x_1$ is the maximum and minimum of our set. Then, the statement is true for $n=1$ .

$n=2$ : Our set is $\{x_1,x_2\}$ . Necessarily, $x_1$ or $x_1>x_2$ . In both cases, there is a minimum and a maximum.

Once we have our statement checked for the initial cases, we state our <em>induction hypothesis</em>:

For every finite set A of $n$ elements there exists a maximum and a minimum.

Now, let us prove the that the above assertion is true for sets with $n+1$ elements.

Our set is $A=\{x_1,x_2,\ldots,x_n,x_{n+1}\}$ and we want to find

$\max\{x_1,x_2,\ldots,x_n,x_{n+1}\}$ .

Notice that this problem is equivalent to solve

$\max\{\max\{x_1,x_2,\ldots,x_n\},x_{n+1}\}$ ,

i.e, to find the maximum among $n+1$ numbers, we can find first the miximum among $n$ and then compare with the other one.

Now, using our induction hypothesis we know that there is a maximum in the set $\{x_1,x_2,\ldots,x_n\}$ , because it has $n$ elements. Let us write

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So, in order to find the maximum of A, we have to find the maximum of $\A'={x',x_{n+1}\}$ . As we have checked at the beginning, there is a maximum in $A'$ , and it is the maximum of A.

Hence, we have completed the prove for the existence of the maximum of a set with $n+1$ elements. The prove for the existence of the minimum is analogue, we just need to change ‘‘maximum’’ for ‘‘minimum’’.

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