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3 years ago

Please help! 6th grade decimals

Mathematics

1 answer:

marissa [1.9K]3 years ago

6 0

Answer:

24.6 miles

Step-by-step explanation:

33.1-8.5=24.6

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Show that every perfect square is congruent to 0, 1, or 4 modulo 8

Keith_Richards [23]

You want to prove that

$n^2\equiv k\mod8,k\in\{0,1,4\}$

for (presumably) all integers $n\ge1$ .

Let's consider some sub-cases.

Suppose $n=2\ell-1$ is odd. Then

$n^2=(2\ell-1)^2=4\ell^2-4\ell+1$

If $\ell$ is even, then so is $\ell^2-\ell$ , which means you can write $4\ell^2-4\ell=8m$ for some integer $m$ , and this reduces to $n^2\equiv1\mod8$ .

If $\ell$ is odd, the same thing happens; you get that $\ell^2-\ell$ is still even, so $4\ell^2-4\ell\equiv0\mod8$ and you're left again with $n^2\equiv1\mod8$ .

Now assume $n=2\ell$ is even. Then $n^2=4\ell^2$ . If $\ell=2j$ is even, then you will always be able to write

$n^2=(2\ell)^2=4\ell^2=4(2j)^2=8\times2j^2\equiv0\mod8$

Meanwhile, if $\ell=2j-1$ is odd, then

$n^2=4\ell^2=4(2j-1)^2=16j^2-16j+4\equiv4\mod8$

So you conclude that

$n^2\equiv\begin{cases}0\mod8&\text{for }n\in\{4,8,12,16,\ldots\}\\1\mod8&\text{for }n\in\{1,3,5,7,\ldots\}\\4\mod8&\text{for }n\in\{2,6,10,14,\ldots\}\end{cases}$

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3 years ago

Max worked 13 hours last week at the grocery store and earned $94.25.If he only worked 5 hours this week, how much money did he

Marrrta [24]

ANSWER: $36.25

Explanation: First find the rate. Divide $94.25 by 13 (hours) to get the rate. Now you know that Max earns $7.25 each hour he works. Multiply his hourly rate by 5 (hours) to get how much Max earns in five hours.

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4 years ago

Solve log2 base x + log4 base x + log8 base x = 12 ?

Sauron [17]

Answer:

Step-by-step explanation:

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3 years ago

Your family of 5 went to the Chinese buffet. The cost for each person was $8.95. The sales tax was

vampirchik [111]

Answer:

9.93

Step-by-step explanation:

Just add your tax to your price.

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3 years ago

IF 24.5% OF A LENGTH IS 2 M 45CM .WHAT IS THE LENGTH

stellarik [79]

Answer:

X= 10m

Step-by-step explanation:

Assume that x is the length

(24.5/100)*x = 2.45 m (2m 45cm = 2.45m)

x = (2.45 * 100)/24.5

x = 10m

(hope it will help you can I pls have brainlist (crown) ☺️)

6 0

3 years ago

Please help! 6th grade decimals​

Please help! 6th grade decimals