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Andru [333]
3 years ago
12

Help with my geometry hw please :/

Mathematics
1 answer:
MrRa [10]3 years ago
7 0
What do you need help
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NEED ANSWER ASAP PLEASE
ollegr [7]
I don't get how it would be a system of equations.
3 0
3 years ago
Read 2 more answers
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.

6 0
3 years ago
Graph the system of linear inequalities <br><br> y&gt;x-3<br> y&lt;-x+2
Musya8 [376]

Answer:

it'll be a graph like this. the blue line is y<-x+2 and you would shade everything below this line because it's less than. the green is y>x-3 so you would shade everything above this line because it is greater than.

5 0
3 years ago
In spherical geometry, what is the term used for the shortest distance between two points?
sweet [91]
The correct answer for the question shown above is: Geodesic.

 The explanation of is shown below:
 1. You have that ,by definition, the spherical geometry studies figures on the surface of the spheres.
 2. And the termn known as "Geodesic" is define as <span>the shortest distance between two points on the surface of a sphere or a curved surface. </span>
3 0
3 years ago
Trapezoid CDEF is congruent to trapezoid TORS. If CF and DE are parallel, which pair of sides in trapezoid TQRS MUST also be par
kondaur [170]

Answer:

D

Step-by-step explanation:

TS and QR Is your answer

6 0
3 years ago
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