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mixer [17]
3 years ago
7

Can someone help me solv for x?

Mathematics
1 answer:
Alexxx [7]3 years ago
5 0

Answer:

AB=AC

X²+8 =33

X²=33-8

X²=25.

X=√25

X=5

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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
PLEASE NO LINKS OR SITES!!!! JUST ANSWERS. THANK YOU!
kap26 [50]

Answer:2/16

Step-by-step explanation:

8 0
3 years ago
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Which equation shows y-5=x converted to slope intercept form.
andreyandreev [35.5K]

Answer:

C) y = x + 5

Step-by-step explanation

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8 0
3 years ago
If a turtle can move 1/7 of a km every hour, then how many hours would it take for a turtle to go 5 km?
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Answer:

it take 1/7 km in 1 hour then,

1 km it take 7 hours

so, it cover 5 km in 35 hours

1/7 km ------- 1 hour

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3 years ago
HELLLP<br> Simplify the following expression.
Yanka [14]
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x^-m=1/(x^m)
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so

(3^-4)(3^2)=
3^(-4+2)=
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1/(3^2)=
1/9

the answer is A


7 0
3 years ago
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