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valkas [14]
3 years ago
11

What is the solution of the following system of equation: 2X+Y=17 AND Y=X+14 ?

Mathematics
1 answer:
Inessa [10]3 years ago
6 0

Answer:

I do't know how to solve this.

Step-by-step explanation:

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Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

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3 years ago
What is the word form for 2.51 and expanded form
Nimfa-mama [501]
Word Form:
Two and fifty-one hundredths

Expanded Form:
2 + 0.5 + 0.01

Hope I Helped You!!! :-)

Have A Good Day!!!
6 0
3 years ago
Select all the equations for which (-6,-1) is a solution. *
ella [17]
1 and 4 hope this helps!
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Without using a calculator, order the following numbers from least to greatest
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The square root of 78 is a number which when multiplied by itself results in 78. The square root of 78 is denoted by √78. 78 can be expressed as 78 = 2 × 3 × 13. Hence, on simplifying square root of 78 is written as √78

so the least number is root 78 , 9 , 10
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On neatly scaled axes, graph and then write an equation in terms of u and y for the distance Leslie travels. Let I represent tim
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Leslie: y= 2x

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