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inessss [21]
3 years ago
14

Let the smallest of 4 consecutive odd numbers be 2 n + 1 , where n is an integer. Show, using algebra, that the sum of any 4 con

secutive odd numbers is always a multiple of 8. Give your answer as an expression that makes explicit that it is a multiple of 8.
Mathematics
1 answer:
andrey2020 [161]3 years ago
7 0

Answer:

Expression is 8(n+2)

Step-by-step explanation:

smallest of 4 consecutive odd numbers =2n + 1

consecutive odd integers are found by adding 2 to the any given odd numbers

Thus, 2nd consecutive odd integers  = 2n + 1 + 2 = 2n + 3

3rd consecutive odd integers  = 2n + 3 + 2 = 2n + 5

2nd consecutive odd integers  = 2n + 5 + 2 = 2n + 7

Thus, 4 consecutive odd integers are

2n + 1 ,2n + 3,2n + 5,2n + 7

sum of these numbers are = 2n + 1 +2n + 3 + 2n + 5+2n + 7 = 8n+16

sum of these numbers are = 8(n+2)

Thus, we see that the sum of numbers are 8(n+2)

As, 8 is common for n+2, whatever is value of n, the number will be multiple of 8 .

thus expression is 8(n+2)

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3 years ago
56 points for whoever answers correctly !
vladimir2022 [97]

We need to use what we know about rectangles to get:

1)

  • Total length = 2*W + 8ft
  • Total width = W + 8ft

2) area = 2*W^2 + 24ft*W + 64ft^2

<h3>Working with rectangles:</h3>

We know that rectangles are defined by two measures, width W and length L.

Here we do know that the length of the pool is twice the width, and the width is W, then the length of the pool is:

L = 2*W

And we also have a sidewalk of 4ft all around the pool, now we want to get:

1) The total length and the total width.

This will be equal to the length/width of the pool <u>plus twice the width of the sidewalk</u> (we add it twice because is in both ends) then we have:

  • Total length = L + 2*4ft = 2*W + 8ft
  • Total width = W + 2*4ft = W + 8ft

2) Now we want to get an expression for the total area of the pool.

Remember that for a rectangle the area is just the product between the width and the length, so to get the area of the pool with the sidewalk we just take:

area = (total length)*(total width)

area = (2*W + 8ft)*(W + 8ft) = 2*W^2 + 3*W*8ft + 64ft^2

area = 2*W^2 + 24ft*W + 64ft^2

This is the equation that gives the total area as a function of W, the width of the pool.

If you want to learn more about rectangles, you can read:

brainly.com/question/17297081

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