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Alex Ar [27]
2 years ago
12

The sum of 4 consecutive odd integers is equal to zero. Write an equation to model the sentence. Solve the equation to find the

numbers. Check your solution.
Mathematics
2 answers:
Xelga [282]2 years ago
6 0

Answer:

  {-3, -1, 1, 3}

Step-by-step explanation:

Sometimes it is convenient to consider the average value of the integers in a "consecutive integer" problem.

<h3>Setup</h3>

We know the average value of 4 consecutive odd integers is the even integer between the middle two. If we call that "n", then the integers of interest are (n-3), (n-1), (n+1), and (n+3). Of course, their sum is 4 times the average value, so is 4n.

  4n = 0 . . . . . . the sum of the 4 consecutive odd integers is 0

<h3>Solution</h3>

Dividing by 4, we find the average value to be ...

  n = 0/4 = 0

Then the 4 integers are ...

  • n -3 = 0 -3 = -3
  • n -1 = 0 -1 = -1
  • n +1 = 0 +1 = 1
  • n +3 = 0 +3 = 3

<h3>Check</h3>

The average is the sum, divided by the number of contributors:

  0 = (-3 +(-1) +1 +3)/4 = 0/4 . . . . . . true

alexira [117]2 years ago
6 0

The equation that models the sentence is : x + (x + 2) + (x + 4) +  (x + 6)  = 0. The numbers are {-3, -1, 1, 3}.

An odd number is a number that cannot be divided into half without any remainders. For example when 7 is divided in half, its value is 3.5. Examples of Positive odd numbers are 1,3, 5, 7. 11 etc. Examples of Negative odd numbers are -1, -3, -5, -7 etc.

<h3>What are Consecutive Odd Numbers?</h3>

Consecutive odd numbers are odd numbers that follow each other. Examples are 1, 3, 5. Consecutive odd numbers increase/decreases by 2.

In order to model the sentence, let x represent the first odd number then

Second odd number = x + 2

Third odd number = x + 4

Fourth odd number = x + 6

The equation is: x + (x + 2) + (x + 4) + (x + 6)  = 0

{ put x = -3 } we get {-3, -1, 1, 3} numbers. Here,

First odd number = -3

Second odd number = -1

Third odd number = 1

Fourth odd number = 3

When we put {-3, -1, 1, 3} values in the above equation then,

such that: (-3) + (-1) + 1 + 3 = 0.

Hence, The equation that models the sentence is : x + (x + 2) + (x + 4) +  (x + 6)  = 0 and the numbers are {-3, -1, 1, 3}.

Learn more about "Consecutive Odd Numbers" from here: brainly.com/question/15453368

#SPJ1

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For a field trip, a highschool want to buy T-shirts and sweatshirts. The expression px + 29y repersents the cost of buying x T-s
marysya [2.9K]

Answer:

The value of p is $12.

Step-by-step explanation:

Given;

c = px + 29y ,,,,,,,,,,,,,,,,,,, (1)

Where;

c = cost of buying x T-shirts and y sweatshirts from the store

p = price of one or each T-shirt = ?

x = number of T-shirts bought

29 = price of one or each sweatshirt

y = number of sweatshirt bought

Based on the above breakdown, if each sweatshirt cost $17 more than a T-shirt, the value of p can be calculated as follows:

29 = p + 17

p = 29 - 17

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Therefore, the value of p is $12.

Additional note:

Note that this is not part of the question but it is just an example to make you understand the question better.

If we assume that 10 T-shirts and 10 sweatshirts are bought from the store, we can use equation (1) above to calculate the cost as follows:

Where;

c = cost of buying x T-shirts and y sweatshirts from the store = ?

p = price of one or each T-shirt = 12

x = number of T-shirts bought = 10

29 = price of one or each sweatshirt

y = number of sweatshirt bought = 10

Substituting the values into equation (1), we have:

c = (12 * 10) + (29 * 10)

c = 120 + 290

c = 410

Therefore, the cost of of buying 10 T-shirts and 10 sweatshirts from the store will be $410.

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