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jasenka [17]
3 years ago
12

HELP NEEDED! 10 POINTS! What is the measure of angle FXO?

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
5 0

Answer:

44°

Step-by-step explanation:

< FXO = ½× 88° = 44°

______

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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
at a discount grocery store, jessica paid $0.72 for an 8-ounce bottle of spring water. What is the cost of the spring water per
topjm [15]
8/0.72 = 0.09
Per ounce cost $0.09
This gonna help you
7 0
3 years ago
Read 2 more answers
Solve the following equation show your work 3{-x + (2x + 1)} = x - 1
Reika [66]

Answer:

x = -2

Step-by-step explanation:

For this problem, we must simply solve for x.  To do this, we will need equation operations, and the use of the distributive property.

Let's work this line by line until we have the value for x:

3{-x + (2x + 1)} = x - 1

3*-x + 3*(2x + 1) = x - 1

-3x + 6x + 3 = x - 1

3x + 3 = x - 1

2x = -4

x = -2

Now we can check our answer for x by plugging back into the original equation and see if the left hand side is equal to the right hand side:

3{-x + (2x + 1)} = x - 1

3{-(-2) + (2(-2) + 1)} ?= (-2) - 1

3{2 + (-4 + 1)} ?= -3

3{2 + (-3)} ?= -3

3{-1} ?= -3

-3 == -3

Thus, we have found the solution for x to be equivalent to negative 2.

Cheers.

4 0
3 years ago
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Please help me for 50 points
lidiya [134]

Answer:

why why why humm why why why why

4 0
3 years ago
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Find the mean 3,4,4,2,5,7,2
stich3 [128]
Thats 3.85714285714 because if you add the numbers and divide by the numbers they are it’ll be 3.85714285714
7 0
3 years ago
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