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The path of two bumper cars can be represented by the functions x + y = –5 and y = x2 – x – 6. At which locations will the bumper cars hit one another? (–1, –4) and (1, –6) (–2, 0) and (2, –4) (–2, 0) and (1, –6) (–1, –4) and (2, –4)

Respuesta :

Equaling the equations, it is found that the cars hit each other at: (-1,-4) and (1,-6).

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For the first car, we have that:

[tex]x + y = -5[/tex]

Thus:

[tex]y_1 = -5 - x[/tex]

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For the second car:

[tex]y_2 = x^2 - x - 6[/tex]

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They meet at the the values of x for which:

[tex]y_1 = y_2[/tex]

Thus:

[tex]-5 - x = x^2 - x - 6[/tex]

[tex]x^2 - 1 = 0[/tex]

[tex]x^2 = 1[/tex]

[tex]x = \pm \sqrt{1}[/tex]

[tex]x = \pm 1[/tex]

  • When [tex]x = 1[/tex], they meet at [tex]y = -5 - 1 = -6[/tex]
  • When [tex]x = -1[/tex], they meet at [tex]y = -5 - (-1) = -5 + 1 = -4[/tex]

Thus (-1,-4) and (1,-6).

A similar problem is given at https://brainly.com/question/13308311

Aviatzi

Answer:

(–1, –4) and (1, –6)

Step-by-step explanation:

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