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Troyanec [42]
3 years ago
10

the sum of three numbers is 2100. the first number x is equal to the sum of the other two (y and z) which are equal to each othe

r. what are the three numbers x,y and z
Mathematics
1 answer:
max2010maxim [7]3 years ago
7 0
We will have a system of equations, and we are going to solve it by using substitution.
Let's make the equations.
x+y+z=2100
z+y=x
Since y and z are equal, I think it is easier for us to have them as one variable for now. Let the value of z and y be a.
These are the equations now.
x+2a=2100
2a=x
Since the second equation is giving the value of x, let it replace the value of x also in the first equation.
2a+2a=2100
4a=2100
2100÷4= 525
so, x and y equal 525. Let's put this in our original equation.
x+525+525=2100
x+ 1,050= 2,100
x= 1,050
So, x=1,050, y= 525 =z.

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Brienne and 3 friends bought tickets to the movies. They spent a total of $27.00 on the tickets. Which equation represents this
Sindrei [870]
Hello!

The equation that represents this situation is A. 3t = 27.

Explanation:

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3 years ago
On a linear X temperature scale, water freezes at −115.0°X and boils at 325.0°X. On a linear Y temperature scale, water freezes
belka [17]

Answer:

The current temperature on the X scale is 1150 °X.

Step-by-step explanation:

Let is determine first the ratio of change in X linear temperature scale to change in Y linear temperature scale:

r = \frac{\Delta T_{X}}{\Delta T_{Y}}

r = \frac{325\,^{\circ}X-(-115\,^{\circ}X)}{-25\,^{\circ}Y - (-65.00\,^{\circ}Y)}

r = 11\,\frac{^{\circ}X}{^{\circ}Y}

The difference between current temperature in Y linear scale with respect to freezing point is:

\Delta T_{Y} = 50\,^{\circ}Y - (-65\,^{\circ}Y)

\Delta T_{Y} = 115\,^{\circ}Y

The change in X linear scale is:

\Delta T_{X} = r\cdot \Delta T_{Y}

\Delta T_{X} = \left(11\,\frac{^{\circ}X}{^{\circ}Y} \right)\cdot (115\,^{\circ}Y)

\Delta T_{X} = 1265\,^{\circ}X

Lastly, the current temperature on the X scale is:

T_{X} = -115\,^{\circ}X + 1265\,^{\circ}X

T_{X} = 1150\,^{\circ}X

The current temperature on the X scale is 1150 °X.

5 0
3 years ago
2<br> .<br> 2<br> 12n = 42<br> NEED HELP ASAP⬆️
Anni [7]

Answer:

  6  

 —————

 n + 8

Step-by-step explanation:

Step by Step Solution:

More Icon

STEP

1

:

Equation at the end of step 1

 ((12•(n3))-(24•(n2)))       (12n-42)      

 —————————————————————•———————————————————

  (((4•(n2))-22n)+28)  ((6•(n3))+(24•3n2))  

STEP  

2

:

Equation at the end of step

2

:

 ((12•(n3))-(24•(n2)))      (12n-42)      

 —————————————————————•——————————————————

  (((4•(n2))-22n)+28)  ((2•3n3)+(24•3n2))  

STEP

3

:

            12n - 42  

Simplify   ——————————

           6n3 + 48n2

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  12n - 42  =   6 • (2n - 7)  

STEP

5

:

Pulling out like terms

5.1     Pull out like factors :

  6n3 + 48n2  =   6n2 • (n + 8)  

Equation at the end of step

5

:

 ((12•(n3))-(24•(n2)))  (2n-7)  

 —————————————————————•————————

  (((4•(n2))-22n)+28)  n2•(n+8)

STEP  

6

:

Equation at the end of step

6

:

 ((12•(n3))-(24•(n2)))  (2n-7)  

 —————————————————————•————————

    ((22n2-22n)+28)    n2•(n+8)

STEP  

7

:

Equation at the end of step

7

:

 ((12•(n3))-(23•3n2))  (2n-7)  

 ————————————————————•————————

     (4n2-22n+28)     n2•(n+8)

STEP  

8

:

Equation at the end of step

8

:

 ((22•3n3) - (23•3n2))      (2n - 7)  

 ————————————————————— • ————————————

   (4n2 - 22n + 28)      n2 • (n + 8)

STEP

9

:

             12n3 - 24n2  

Simplify   ——————————————

           4n2 - 22n + 28

STEP

10

:

Pulling out like terms

10.1     Pull out like factors :

  12n3 - 24n2  =   12n2 • (n - 2)  

STEP

11

:

Pulling out like terms

11.1     Pull out like factors :

  4n2 - 22n + 28  =   2 • (2n2 - 11n + 14)  

Trying to factor by splitting the middle term

11.2     Factoring  2n2 - 11n + 14  

The first term is,  2n2  its coefficient is  2 .

The middle term is,  -11n  its coefficient is  -11 .

The last term, "the constant", is  +14  

Step-1 : Multiply the coefficient of the first term by the constant   2 • 14 = 28  

Step-2 : Find two factors of  28  whose sum equals the coefficient of the middle term, which is   -11 .

     -28    +    -1    =    -29  

     -14    +    -2    =    -16  

     -7    +    -4    =    -11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -4  

                    2n2 - 7n - 4n - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

                   n • (2n-7)

             Add up the last 2 terms, pulling out common factors :

                   2 • (2n-7)

Step-5 : Add up the four terms of step 4 :

                   (n-2)  •  (2n-7)

            Which is the desired factorization

Canceling Out :

11.3    Cancel out  (n-2)  which appears on both sides of the fraction line.

Equation at the end of step

11

:

   6n2      (2n - 7)  

 —————— • ————————————

 2n - 7   n2 • (n + 8)

STEP

12

:

Canceling Out

12.1    Cancel out  (2n-7)  which appears on both sides of the fraction line.

Canceling Out :

12.2    Canceling out n2 as it appears on both sides of the fraction line

Final result :

   6  

 —————

 n + 8

8 0
3 years ago
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