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2 years ago

I need help somebody please?

Mathematics

2 answers:

BaLLatris [955]2 years ago

6 0

Answer:

(R, G, Y, O)

Step-by-step explanation:

because it is the order in which the problem presents it

shtirl [24]2 years ago

6 0

The answer is D because all of them are 1

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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

1 year ago

Anyone know the answer ? Please is it a function or relation?

levacccp [35]

Answer: i think its a function

Step-by-step explanation:

3 0

2 years ago

Which word is used to name the bold number?

prohojiy [21]

If 3 is the bold number then the answer is D. <span>#TeamAlvaxic</span>

7 0

3 years ago

Genni has a rectangular garden with a length of 3x+4 and a width of 6x-10.

Nitella [24]

Answer:

equation in terms of x is 18x - 12

x = 3

area = 104 sq. feet

you want only the ans right?

if you need explaination comment down.

GOOD LUCK FOR THE FUTURE! :)

3 0

2 years ago

Read 2 more answers

Last one I need help in will give BRAINLY (don’t send me links)

iren2701 [21]

Answer:

x=11

Step-by-step explanation:

4x+11=5x (angle adb and edf are the same)

11=5x-4x

11=x

x=11

if you want you can check by doing...

(14*11-29)+(5*11)=180

4 0

2 years ago