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3 years ago

14

A multiple of 9 with the tens digit that is more than the units digit

1 answer:

Colt1911 [192]3 years ago

7 0

Answer:

81, tens place is 8 ,unit's pkace is 1, so 8>1, that satisfies.

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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

Identify the coefficients in the expression below.<br><br> -6x+5y+4x+9

Montano1993 [528]

Answer:

3 coefficients in this expression are: -2x, 5y and 9 (natural number)

Step-by-step explanation:

-6x + 5y + 4x + 9

= -6x + 4x + 5y + 9

= -2x + 5y + 9

3 coefficients in this expression are: -2x, 5y and 9 (natural number)

Hope this help you :3

5 0

3 years ago

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a college student would like to invest the prices of sandwiches offered near the campus a sample of 50 shops that's so sandwiche

fredd [130]

Answer:

the answer is A

Step-by-step explanation:

because the graph is skewed to the left

3 0

3 years ago

Write the expressions "Four times the difference of a number and 1 is equal to six times the sum of the number and three. Find t

DochEvi [55]

Answer:

4(x - 1) = 6(x + 3)

x = -11

Step-by-step explanation:

x represents “the number” so we would substitute this with a variable.

(I hope this helps! Have a great day AND STAN BTS)

8 0

3 years ago

Whats 2 plus 2 x 5 free 100 points

faltersainse [42]

Answer:

12

Step-by-step explanation:

2+2*5

2*5=10

10+2=12

7 0

3 years ago

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