3 years ago

An angle is geometric figure that consists of

Mathematics

1 answer:

docker41 [41]3 years ago

6 0

Answer:

the union of two rays that share a common endpoint.

Step-by-step explanation:

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WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"

Feliz [49]

Recall Euler's theorem: if $\gcd(a,n) = 1$ , then

$a^{\phi(n)} \equiv 1 \pmod n$

where $\phi$ is Euler's totient function.

We have $\gcd(9,32) = 1$ - in fact, $\gcd(9,32^k)=1$ for any $k\in\Bbb N$ since $9=3^2$ and $32=2^5$ share no common divisors - as well as $\phi(9) = 6$ .

Now,

$37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6$

where the $c_i$ are positive integer coefficients from the binomial expansion. By Euler's theorem,

$\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9$

so that

$32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9$

7 0

2 years ago

ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.

fomenos

Answer:

C. The graph of G(x) is the graph of F(x) flipped over the y-axis and compressed vertically.

Step-by-step explanation:

The negative in front of the 2 made the function flip over the y-axis. While the 2, compressed the function a little, making it so the function touched 2, vertically.

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3 years ago

Suppose a football team played 4 games and there were no ties. Which of the following would be a compound event? Explain!!

Tresset [83]

I would say D as it's the only different one

4 0

3 years ago

Read 2 more answers

PLEASE HELP!!! Number 2, and 4 please!! (YOU HAVE TO FIND THE SURFACE AREA OF THE PRISM)

Elenna [48]

The answer for 2 is 192. The answer for 4 is 672.

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