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3 years ago

PLEASE HELP!!!!!!! WORTH 40 POINTS AND WILL MARK BRAINLIEST!!!!

Mathematics

1 answer:

valentina_108 [34]3 years ago

7 0

Answer:

im pretty sure its c

Step-by-step explanation:

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In kite WXYZ, the measure of Measure of angle X = measure of angle Z = 86 degrees, and the Measure of angle Y = 72 degrees.

Varvara68 [4.7K]

Answer:

116

Step-by-step explanation:

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3 0

3 years ago

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

2 years ago

Describe the relationship between the terms in each arithmetic sequence. Then write the next three terms in each sequence.

11111nata11111 [884]

Answer:

For the first one: they increase in by 14, so the three could be 73,87,101

Second: Sequential, increasing by 20, next could be 110, 130, 150

Third: Increase by 27, next three could be 122,149,176

8 0

3 years ago

A. Are the expressions 3(m - 2) + 2(m - 2) and 5(m - 2) equivalent expressions?

Lena [83]

Answer:

Step A. 3(m - 2) + 2(m - 2) and 5(m - 2) are equivalent expressions.

Step-by-step explanation:

Step B. If you calculate 3(m - 2) + 2(m - 2) you will see it will equal to 5(m - 2) therefore, they are equal.

Hope I Helped I'm New! :D

8 0

3 years ago

Read 2 more answers

PLEASE HELP!!!!!! FAST!!!!!!!!

klio [65]

Answer:

%8.75 error

Step-by-step explanation:

14.6/n = 16/100

16n = 1460

n = 91.25

100-91.25 = 8.75

7 0

2 years ago

Read 2 more answers