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2 years ago

What is the perimeter of a rectangle with a length of

Mathematics

2 answers:

solong [7]2 years ago

8 0

Answer:

Step-by-step explanation:

boyakko [2]2 years ago

4 0

The perimeter would be 28x-4

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

2 years ago

All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of 25. By wh

elena-s [515]

5

reason is because if you’re pentagon has lines of 5 then the area would be 25

8 0

1 year ago

I'm bad at math so uh yeahhh

____ [38]

Answer and Step-by-step explanation:

Since we know that lines l and m are parallel (we are just proving that they are parallel), we can see that the two angles given are corresponding angles, so they are congruent to each other.

123 = 2x + 7

Subtract 7 from both sides.

116 = 2x

Now, divide both sides by 2.

58 = x

So, the value of x is 58.

#teamtrees #PAW (Plant And Water)

4 0

2 years ago

When Devon cashed a $450 check at the bank, the teller gave him 18 bills, all $20 bills and $50 bills. Which system of equations

Neporo4naja [7]

B is the answer to the equation

7 0

2 years ago

Look

pochemuha

Answer:

Have mercy on me, have mercy on my soul

Don't let my heart turn cold

Have mercy on me, have mercy on my soul

Don't let my heart turn cold

Have mercy on many men

Many, many, many, many men

Wish death 'pon me

Yeah, I don't cry no mo'

I don't look to the sky no mo'

'Cause I got it on me

I got it on me

You can run up if you want

Mercy on me

Step-by-step explanation:

I love that song

3 0

3 years ago