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Svetlanka [38]
3 years ago
14

Find x, y and ab and how to check if the answer is right ​

Mathematics
1 answer:
iris [78.8K]3 years ago
4 0

Answer:

  x = 2, y = -2, AB = 142

Step-by-step explanation:

The fact that X is the midpoint gives you two relations:

  AX = XB

  AX + XB = AB

Since you have two unknowns, this number of equations is sufficient to find their values. Substituting the given expressions in the above equations, you have ...

  • 8(3x+5) -3(y-7) -22x = 5x +y +23 -4(x-12)
  • 8(3x+5) -3(y-7) -22x + 5x +y +23 -4(x-12) = 2x -5y +128

Simplifying the first of these can make simplifying the second one easier.

  24x +40 -3y +21 -22x = 5x +y +23 -4x +48

  2x -3y +61 = x +y +71 . . . . . . we can use this simplification

  x -4y = 10 . . . . . . . . . . . . . . . . subtract x+y+61

Now, we can simplify the second equation to ...

  2x -3y +61 +x +y +71 = 2x -5y +128

  3x -2y +132 = 2x -5y +128 . . . . . simplify the left side

  x +3y = -4 . . . . . . . . . . . . . . . add -2x+5y-132

Then the two equations we need to solve are ...

  • x -4y = 10
  • x +3y = -4

Subtracting the second from the first, we get

  -7y = 14

  y = -2

Substituting into the first of these simplified equations, we get

  x -4(-2) = 10 . . . . substitute for y

  x +8 = 10 . . . . . . .evaluate

  x = 2 . . . . . . . . . .subtract 8

So, the solution is (x, y) = (2, -2).

Now, the values of AX and XB are ...

  AX = 2x -3y +61 = 2·2 -3(-2) +61 = 71

  XB = x+y+71 = 2 +(-2) +71 = 71 . . . . . . . . matches AX, a good sign

  AB = 2x -5y +128 = 2·2 -5(-2) +128 = 142 . . . . = AX+XB, another good sign

The desired values are x = 2, y = -2, AB = 142.

_____

You check the answer by filling the values into the expressions given in the problem statement and seeing if you get consistent results. Here, we used the simplified expressions, rather than the original expressions, so if we did the simplification wrong, we may have the wrong answer. It is always best to use the original equations. (A machine solver working with the original equations confirms our result, so "confidence is high.")

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zlopas [31]

Answer:

(0, -2), (1, -3), (2, -2) y (3, 7) son pares ordenados de f(x) = x^{3}-2\cdot x^{2}-2.

Step-by-step explanation:

Un par ordenado es un elemento de la forma (x,f(x)), donde x es un elemento del dominio de la función, mientras f(x) es la imagen de la función evaluada en x. Entonces, un par ordenado que está contenido en la citada función debe satisfacer la siguiente condición:

La imagen de la función existe para un elemento dado del dominio. Esto es:

x \rightarrow f(x)

Dado que f(x) es una función polinómica, existe una imagen para todo elemento x. Ahora, se eligen elementos arbitrarios del dominio para determinar sus imágenes respectivas:

x = 0

f(0) = 0^{3}-2\cdot (0)^{2}-2

f(0) = -2

(0, -2) es un par ordenado de f(x) = x^{3}-2\cdot x^{2}-2.

x = 1

f(1) = 1^{3}-2\cdot (1)^{2}-2

f(1) = -3

(1, -3) es un par ordenado de f(x) = x^{3}-2\cdot x^{2}-2.

x = 2

f(2) = 2^{3}-2\cdot (2)^{2}-2

f(2) = -2

(2, -2) es un par ordenado de f(x) = x^{3}-2\cdot x^{2}-2.

x = 3

f(3) = 3^{3}-2\cdot (3)^{2}-2

f(3) = 7

(3, 7) es un par ordenado de f(x) = x^{3}-2\cdot x^{2}-2.

(0, -2), (1, -3), (2, -2) y (3, 7) son pares ordenados de f(x) = x^{3}-2\cdot x^{2}-2.

6 0
2 years ago
A manufacturing company produces engines for light aircraft . The graph shows the number of engine produced each year since the
photoshop1234 [79]

Answer:

y=13x+32

149 engines in 9th year

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

From a look at the photo and the data plot can be represented by the function, so we can pick 2 points in our given graph

  • (x1, y1) = (2,60)
  • (x2, y2) = (5,99)

The standard form of a linear equation is:

y = mx + b where:

  • m is the slope
  • b is the y-intercept

We know the slope of the function can be found as following:

m = \frac{y2 - y1}{x2 - x1}  so in this situation we have:

<=> m=\frac{99-60}{5-2}=\frac{39}{3}=13

=> y = 13x + b (1)

Because the line goes through point  (2,60) so we substitute it into (1):

60 = 13*2 + b

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=> y = 13x + 34

Now we will substitute x=9 to find the engines produced by company in 9th year as:

y=13(9)+32\\y=117+32=149

Hence, the company will produce 149 engines in 9th year

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oksano4ka [1.4K]

Answer:

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(y−y1)=m(x−x1)

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(x1,y1)(x2,y2)

(-4 , 1) (-2 , 3)

Solve for the slope

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(y−3)=2(x−(−2)) Plug in known values.

y−3=2(x+2) Simplify signs

y−3=2x+4 Use Distributive property

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answer (y = −5x+7 ) Simplify

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Answer:16×16×16

Step-by-step explanaution:

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