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3 years ago

Simplify this expression 6w+4+8w-1

Mathematics

2 answers:

FrozenT [24]3 years ago

6 0

Answer:

14w + 3

Step-by-step explanation:

6w + 4 + 8w -1 (Given)

14w + 3 (combine like terms)

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den301095 [7]3 years ago

5 0

Answer:

14w+3

Step-by-step explanation:

6w+4+8w-1

(6w+8w)+(4-1)

14w+3

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Find an equation of the line that satisfies the given conditions. through (9, 7); perpendicular to the line y = 5

cluponka [151]

The answer would defintley be 69 if you want the right answer.

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3 years ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

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1 year ago

Which number should each side of the equation 3/4 = 9 be multiplied by to produce the equivalent equation of x = 12?

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You need to multiply both sides of the equation by the reciprocal of 3/4. The reciprocal is 4/3 and 4/3 multiplied by 9 = 12. So x = 12 because a number times the reciprocal is one.

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3 years ago

Read 2 more answers

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sergij07 [2.7K]

Answer:

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Step-by-step explanation:

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3 years ago

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