Respuesta :

Answer:

x

Step-by-step explanation:

We need to solve this equation by graphing. We need to find what roots will make our equation equal zero. This is the same as drawing a line

[tex]y = 0[/tex]

and see what points intercepts both graphs.

According to the graph above, one root are between 0 and 0.5 and the other are between 4 and 4.5.

We can find it actual value by solving it

[tex] - 1 + \frac{9}{2} x - {x}^{2} = 0[/tex]

[tex] - {x}^{2} + \frac{9}{2} x - 1 = 0[/tex]

Apply Quadratic Formula, we get

[tex] \frac{9 + \sqrt{65} }{4} [/tex]

and

[tex] \frac{9 - \sqrt{65} }{4} [/tex]

Which gives us approximately

x=4.27 and 0.23

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sqdancefan

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Answer:

  see attached

Step-by-step explanation:

You have a graph of the function ...

  y = 3 +4x -x^2

You want to find solutions to the equation ...

  0 = -1 +9/2x -x^2

This second equation can be made equivalent to ...

  3 +4x -x^2 = p

for some suitable function p.

We can find that function using the relation ...

  (3 +4x -x^2) -p = 0 = -1 +9/2x -x^2

Solving for p, we get ...

  (3 +4x -x^2) -(-1 +9/2x -x^2) = p

  3 +4x -x^2 +1 -9/2x +x^2 = p . . . . . . . eliminate parentheses

  4 -1/2x = p . . . . . . . . . . . . . . . . . . simplify

The line we want is ...

  p = -1/2x +4 . . . . . . . line with y-intercept 4 and slope -1/2

Where this line crosses the graph you have, the x-coordinates are the solutions of the equation -1 +9/2x -x^2 = 0.

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