Which measure is equivlent to 126 in.? A. 3yd B.3.5 yd C.10.5 yd D31.5 yd

Mathematics

2 answers:

forsale [732]3 years ago

7 0

B.
126/12 =10.5 (12 inches in a foot)
10.5 /3 = 3.5 (3 feet in a yard)

tester [92]3 years ago

5 0

Answer:

Step-by-step explanation:

1 yard = 3 feet = 36 in,

126 in / 36 in = 3.5 yards,

Therefore, the answer is B.

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What number divided by -4 equals -3?

worty [1.4K]

12 divided by -4 equals-3 .

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3 years ago

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,

$37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6$