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Temka [501]
3 years ago
5

The sum of three consecutive integers is equal to twice the 2nd number decreased by 14. Write an equation and determine the 3 co

nsecutive integers
Mathematics
2 answers:
adoni [48]3 years ago
4 0

Let lowest integer be x then the second and third are x+1 and x+2.

x + x + 1 + x + 2 = 2(x + 1) - 14

3x + 3 = 2x - 12

x = -12 - 3 = -15

answer is -15, -14 and -13

meriva3 years ago
3 0

Givens

Let the smallest integer = x

The middle integer = x + 1

The largest integer = x + 2

Remark

The first phrase up to is says the sum of ... The key word is sum. So far you have x + x + 1 + x + 2. Simplified this comes to 3x + 3.

Two times the 2nd number is 2*(x + 1) and from that, subtract 14

2(x + 1) - 14

If you break down each phrase as I have done you will soon become very good at doing these types of problems.

So the equation looks like this.

Solution

3x + 3 = 2(x + 1) - 14 Remove the brackets.

3x + 3 = 2x + 2 - 14 Combine the like terms on the right.

3x + 3 = 2x - 12 Subtract 3 from both sides.

3x = 2x - 12 - 3

3x = 2x - 15 Subtract 2x from both sides.

3x - 2x = - 15

x = -15 <<<< Answer for smallest number.

Answer

-15

- 14

-13 Are the three numbers you seek.

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jeka57 [31]

Answer:

<u>Options 1 and 3</u>

Step-by-step explanation:

We should know that, the system of linear equations can be treated as matrices, i.e: we can modify or make any operations provide that we must apply the same operation for all terms of each equation.

Given:  the solution for the following system is (2,9)

Px + Qy = R  ⇒(1)

Tx + Uy = V  ⇒(2)

We will check which system of equation has the same solution.

<u>System A)</u>  Px + Qy = R

                  (P+T)x + (Q+U)y = R+V  ⇒(3)

So, By summing (1) and (2) we will get the equation (3)

So, system A has the same solution (2,9)

<u>System B)</u> Px + Qy = R

                 (P+2T)x + (Q+2U)y = R-2V  ⇒(4)

By multiplying equation (2) by 2 and add with equation (1), we will get:

 (P+2T)x + (Q+2U)y = R+2V

Which is not the same as equation (4)

So, system B has not the same solution (2,9)

<u>System C)</u> (T-P)x + (U-Q)y = V-R  ⇒(5)

                  Tx + Uy = V  

By multiplying equation (1) by -1 and add with equation (2), we will get the equation (5)

So, system C has the same solution of (2,9)

<u>System D)</u> (T-P)x + (Q+U)y = V-R  ⇒(6)

                  Tx + Uy = V  

We cannot get equation (6) by the same operation over equation (1)

Note the coefficient of x and y⇒ (T-P) and (Q+U)

They must be (T+P) and (Q+U) <u>OR </u>(T-P) and (Q-U)

So, system D has not the same solution of (2,9)

<u>System E)</u> (5T-P)x + (5U-Q)y = V-5R ⇒ (6)

                  Tx + Uy = V  

By subtract equation (1) from 5 times equation (2), we will get:

(5T-P)x + (5U-Q)y = 5V-R

Which is not the same as equation (6)

So, system E has not the same solution (2,9)

As a conclusion, the systems which have the same solution are:

<u>Options 1 and 3</u>

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A school dance committee has 14 volunteers. Each dance requires 3 volunteers at the door, 5 volunteers on the floor, and 6 float
siniylev [52]

There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.

Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.

We are required to find the number of ways in which the volunteers can be assigned.

Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.

nC_{r}=n!/r!(n-r)!

Number of ways in which the volunteers can be assigned is equal to the following:

Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.

Number of ways =14C_{12}

=14!/12!(14-12)!

=14!/12!*2!

=14*13/2*1

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Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.

Learn more about combinations at brainly.com/question/11732255

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