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3 years ago

5

Which table of ordered pairs represents a proportional relationship

1 answer:

Citrus2011 [14]3 years ago

5 0

You are right on the answer

You might be interested in

Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

Molodets [167]

Notice that

$(n+1)^4-n^4=4n^3+6n^2+4n+1$

so that

$\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

We have

$\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)$

$\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1$

so that

$\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

You might already know that

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

so from these formulas we get

$\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n$

$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

3 years ago

ASAP HELP FOR QUESTION 4 ASAP

galina1969 [7]

Answer:

convert 17 meters into feet and then write it down to teh nearest 10thof a foot

Step-by-step explanation:

6 0

3 years ago

If EG = 28 and F is the midpoint of<br> segment EG, the length of EF =<br> E<br> F.<br> G

valina [46]

If line segment EF is 28 and F is halfway through the line, then segment EF will be half of 28. So segment EF=14

8 0

2 years ago

Help me please ill give u Brainly

Mamont248 [21]

Answer:

The answer is 2.6. You get this by adding up all the numbers (0,1,2,3,7) and then dividing by the amount of numbers there are (5). The equation would be 0+1+2+3+7=13/5= 2.6

Hope this helps.

5 0

3 years ago

What is the answer and please show work

zhuklara [117]

#26 right?

35x + 140 = 1050
-140 -140

<u>35</u>x = <u> 910
</u>35 35

x = 26 weeks

7 0

3 years ago