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erik [133]
3 years ago
12

Does anyone know the answer to these questions???

Mathematics
2 answers:
Alika [10]3 years ago
4 0

Answer:

  • 2 is -1/3
  • 3 is y ≥-13
  • I don't know number 4 sorry :(
  • Step-by-step explanation:

Dmitriy789 [7]3 years ago
3 0

Answer:b b c

Step-by-step explanation:

fjsiwjensksnsfhnsnazkxisj done

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When are the x-intercept and the y-intercept of a graph identical?
vova2212 [387]

at the origin

they are same

7 0
3 years ago
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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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Grayson's mistake was that he multiplied 4 and 3 and then used the exponent he had to square 3 and then multiply it by 4.

Emily's mistake was that she added 2 to 36 instead of multiplying it by -2

Pat's mistake was that he forget to make y into -2 instead of 2

The right way to do this is 4(3^2)+2(-2)
(3^2)=9 9×4=36 2(-2)=-4 -4+9=5
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