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prohojiy [21]
3 years ago
10

HELP PICTURE SHOWNNNN!!!

Mathematics
1 answer:
djyliett [7]3 years ago
5 0
A, B, and F because corresponding angles are angles that are in the same position on both parallel lines.
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Yes , your total savings on gas proportional to the number of beverages you purchases.

As for every beverage purchased , there is a saving of $0.20

If we show by an equation , where savings is s , and number of beverages is b

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s = 0.20 b

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Explain why multiplying two negative<br>numbers results in a positive product using a model.​
Mumz [18]

Answer:

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Travis and Paula went to lunch. Travis ordered a sandwich for $7.50, and Paula ordered a burger for $5.25. After lunch, they lef
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3 years ago
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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
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