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anonymous

  • one year ago

Based on the graph below, what are the solutions to the equation f(x) = g(x)?

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  1. anonymous
    • one year ago
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    x = -3, 0.8, 4 x = -1.9, 0.8, 4.1 x = -2, 2, 3 x = -2.5, 0.8, 3 Those are the options and then the graph is attached

  2. Michele_Laino
    • one year ago
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    from your graph we have three intersection points

  3. anonymous
    • one year ago
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    Yes, I get it, however none of the answers match and I'm really confused because I thought it just was where the two lines connect in those 3 points but that doesn't match any of my options

  4. Michele_Laino
    • one year ago
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    I think that we can choose the first option

  5. Michele_Laino
    • one year ago
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    it is the one closest to the right result

  6. anonymous
    • one year ago
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    yeah, I really hope your right haha thanks

  7. Michele_Laino
    • one year ago
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    :)

  8. anonymous
    • one year ago
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    Wait do you have time to help me with another one?

  9. Michele_Laino
    • one year ago
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    yes!

  10. anonymous
    • one year ago
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    THANK YOU

  11. anonymous
    • one year ago
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    Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 2 to x = 5 represent? (4 points) The water travels an average distance of 4 feet from 2 seconds to 5 seconds. The water travels an average distance of 1 foot from 2 seconds to 5 seconds. The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

  12. Michele_Laino
    • one year ago
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    we have to compute the average rate, using this formula: \[\Large r = \frac{{f\left( 5 \right) - f\left( 2 \right)}}{{5 - 2}}\]

  13. Michele_Laino
    • one year ago
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    where: \[\Large \begin{gathered} f\left( 5 \right) = - {5^2} + 6 \cdot 5 + 6 = ... \hfill \\ f\left( 2 \right) = - {2^2} + 6 \cdot 2 + 6 = ... \hfill \\ \end{gathered} \]

  14. anonymous
    • one year ago
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    f(5) = 11 f(2) = 14

  15. Michele_Laino
    • one year ago
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    ok! so after a substitution, we get: \[\Large r = \frac{{f\left( 5 \right) - f\left( 2 \right)}}{{5 - 2}} = \frac{{11 - 14}}{{5 - 2}} = ...\]

  16. anonymous
    • one year ago
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    -4 ---- 3

  17. Michele_Laino
    • one year ago
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    11-14=-3

  18. anonymous
    • one year ago
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    whoops hehe sorry

  19. Michele_Laino
    • one year ago
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    :) so r= -1, right?

  20. anonymous
    • one year ago
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    yeah

  21. Michele_Laino
    • one year ago
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    now since f(5)= 11 and f(2) = 14, we can say that going from 2 seconds to 5 seconds water is falling down

  22. anonymous
    • one year ago
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    at 3 feet per second?

  23. anonymous
    • one year ago
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    sorry 1 foot per second

  24. Michele_Laino
    • one year ago
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    so, what is the right option?

  25. anonymous
    • one year ago
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    4 or 2

  26. anonymous
    • one year ago
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    4

  27. Michele_Laino
    • one year ago
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    please keep in mind that water is falling down with a rate equal to 1 (if we neglect the minus sign)

  28. Michele_Laino
    • one year ago
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    correct!

  29. anonymous
    • one year ago
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    Thank you so much, you are really helpful!

  30. Michele_Laino
    • one year ago
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    :) :)

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