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N76 [4]
3 years ago
14

If 3x+2y=12 and -4x+6y=24 what is the value of -x+2y

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
6 0
(1) 3x+2y=12
(2) -4x+6y=24

Solving the system of equations using the method of substitution:
Isolating y in the first equation:
(1) 3x+2y=12→3x+2y-3x=12-3x→2y=12-3x→2y/2=(12-3x)/2→y=(12-3x)/2

Replacing "y" by (12-3x)/2 in the second equation:
(2) -4x+6y=24
y=(12-3x)/2→-4x+6[(12-3x)/2]=24

Solving for x:
-4x+3(12-3x)=24
-4x+36-9x=24
-13x+36=24
-13x+36-36=24-36
-13x=-12
-13x/(-13)=-12/(-13)
x=12/13

Replacing "x" by 12/13 in y=(12-3x)/2
x=12/13→y=[12-3(12/13)]/2
y=(12-36/13)/2
y={[(13)(12)-36]/13}/2
y=[(156-36)/13]/2
y=(120/13)/2
y=(120/13)(1/2)
y=60/13

x=12/13; y=60/13
-x+2y=-12/13+2(60/13)
-x+2y=-12/13+120/13
-x+2y=(-12+120)/13
-x+2y=108/13

Answer: The value of -x+2y is 108/13 
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Sergei says that 10% of a number will always be less than 20% of any other number.
11111nata11111 [884]
That's false.
Let's see an instance:
10% of 300=30
20% of 100=20
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5 0
3 years ago
A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. How
anyanavicka [17]

Answer: 60 gallons of the 20% solution and 120 gallons of the 50% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of 20% solution that should be mixed.

Let y represent the number of gallons of 50% solution that should be mixed.

A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. This means that

0.2x + 0.5y = 0.4×180

0.2x + 0.5y = 72- - - - - - - - - - - -1

Since the total number of gallons is 180, it means that

x + y = 180

Substituting x = 180 - y into equation 1, it becomes

0.2(180 - y) + 0.5y = 72

36 - 0.2y + 0.5y = 72

- 0.2y + 0.5y = 72 - 36

0.3y = 36

y = 36/0.3

y = 120

x = 180 - y = 180 - 120

x = 60

4 0
3 years ago
A circle has a diameter of 12 inches. What is the area of the circle? А 367 inches squared B 247 inches squared C 127 inches squ
Ann [662]

Answer:

113.1

Step-by-step explanation:

A = πr²

A = π (6)²

A = π (36)

A = 113.09 = 113.1

8 0
3 years ago
Which number is rational
Paul [167]

B is rational. B is the correct answer. B is rational.

7 0
3 years ago
Read 2 more answers
Si un triángulo tiene una hipotenusa de 15 cm y un cateto que mide 12 cm, ¿cual es la longitud del otro cateto?
BartSMP [9]

Answer:

   

9cm

Explicación:

El teorema de pitagoras nos dice que la hipotenusa al cuadrado es igual a la suma de los catetos al cuadrado:

c^{2} =a^{2} + b^{2}

Donde c es la hipotenusa y a  y b son los catetos.

Por lo cual, podemos reemplazar c por 15cm y a por 12cm :

15^{2} =12^{2} +b^{2}

Finalmente , debemos resolver la ecuación para b, así que b es igual a :

225=144+b^{2} \\225-144=144+b^{2} -144\\81=b^{2} \\\sqrt{81} =b\\9=b

Por lo tanto, la longitud del otro cateto es 9 cm

3 0
3 years ago
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