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kodGreya [7K]
3 years ago
5

WHO IS SUPER GOOD AT MATH? I NEED HELP REALLY FAST! BRAINLIEST ANSWER AWARDED TO CORRECT ANSWER WITH AT LEAST A LITTLE EXPLANATI

ON
Describe the vector as an ordered pair. Round the coordinates to the nearest tenth. The diagram is not drawn to scale.

Mathematics
1 answer:
erastova [34]3 years ago
7 0
The answer to your question is D
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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
Which are the solutions of the quadratic equation? x2 = 9x + 6
Lelechka [254]
X^2 = 9x + 6
x^2 - 9x - 6 = 0
use quadratic formula : (-b (+-) sqrt b^2 - 4ac) / (2a)
a = 1, b = -9, c = -6
now we sub

x = (-(-9) (+-) sqrt -9^2 - 4(1)(-6)) / 2(1)
x = 9 (+-) sqrt 81 + 24)/2
x = 9 (+-) sqrt 105) / 2
x = 9/2 + 1/2 sqrt 105 or x = 9/2 - 1/2 sqrt 105

8 0
3 years ago
Read 2 more answers
The difference between 31 and a number is 7
astra-53 [7]

Answer:

thirty-eight

Step-by-step explanation:

31+7= answer

5 0
3 years ago
Read 2 more answers
If f(x) = 6x +5 and g(x) = 2x – 7 find (fºg)(x)
adell [148]

Answer:

f(g(x)) = 12x - 37

Step-by-step explanation:

Step 1: Define

f(x) = 6x + 5

g(x) = 2x - 7

Step 2: Find f(g(x))

f(g(x)) = 6(2x - 7) + 5

f(g(x)) = 12x - 42 + 5

f(g(x)) = 12x - 37

7 0
3 years ago
Given that (8,7) is on the graph of f(x), find the corresponding point for the function f(x)+4
ozzi

Answer:

( 8,11)

Step-by-step explanation:

When x = 8 the output is 7

The new function

f(x) +4

when x = 8

The output is f(8) +4= 7+4 = 11

( 8,11)

7 0
3 years ago
Read 2 more answers
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