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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)

Relax

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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