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You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y=-x²
+7x+1 and the path of the dogis modeled by y = 2x + 5, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?

A: Yes, they intersect at the coordinates (1,7) and (4, 13)

B: Yes, they intersect at the coordinates (1,9) and (2, 9)

C: Yes, they intersect at the coordinates (2, 11) and (3, 11)

D: No, the paths do not cross

Respuesta :

facundo3141592

the intersection points are (1, 7) and (4, 13), So the correct option is A.

Will the dog catch the frisbee?

To see that, we need to see when the two equations:

y = -x²+7x+1

y = 2x + 5

Can be solved simultaneously for a point (x, y). So we need to solve a system of equations.

y = -x²+7x+1

y = 2x + 5

We can rewrite:

-x²+7x+1 = y =  2x + 5

Then we can solve this for x:

-x²+7x+1 =  2x + 5

x² - 5x + 4 = 0

This is just a quadratic equation, the solutions are:

[tex]x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*(1)*(4)} }{2} \\\\x = \frac{5 \pm 3 }{2}[/tex]

So we have two values of x:

  • x = (5 + 3)/2 = 4
  • x = (5 - 3)/2 = 1

The correspondent values of y are:

y = 2*(4) + 5 = 13

y = 2*(1) + 5 = 7

Then the intersection points are (1, 7) and (4, 13)

Then the correct option is A. The dog will catch the frisbee.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

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