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galina1969 [7]
3 years ago
8

What is the value of x in the equation 8(4-x)=7x+2

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
3 0

Answer:

x=15

Step-by-step explanation:

8(4-x)=7x+2

Distribute

32 - 8x = 7x+2

Add 8x to each side

32 - 8x+8x = 7x+8x+2

32 = 15x+2

Subtract 2 from each side

32-2 = 15x +2-2

30 = 15x

Divide by 15

30/15 = 15x/15

2 = x

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3 years ago
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kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.


Recall the formula for the sum of consecutive positive integers,

\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2

Now,

1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224

numbers, and their sum is

\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of 1+9\times2=19.

So, the sum of the first 1234 terms in the sequence is 2419.

8 0
2 years ago
Who wants to do an algebra 1 assignment for me? I will email you the pdf
andrew11 [14]

Answer:

No

Step-by-step explanation:

People arent on brainly to do others work, they are here to help, NOT DO YOUR WORK

Resepect us more please. We stay on here just to help people. We take time out of our days to help people. So please dont make them do your work. They are here to help not be your personal servant.

Have a wonderful day! :)

4 0
2 years ago
Read 2 more answers
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