Alglerbra 2 Math questions!?!?

I'm really confused about these problems and would be VERY grateful if someone would help me and answer at least one of these questions. I would really appreciate if you would explain how you got to these answers too, thank you sooo so much!!

1# Solve- h(x)=x^2-2x-8>7

2# Solve- 3x^2+4x-7<13

3# John is standing on a rock cliff that is 52 feet high. He tosses a pebble upward over the edge, where it hits the top of a 12-foot-high boulder. The quadratic equation that models the path of the pebble is p(t)=-16t^2+12t+52. How long does it take for the pebble to hit the top of the boulder?

A. 1.25 seconds

B. 1.50 seconds

C. 2.00 seconds

D. 3.25 seconds

2 Answers

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  • 8 years ago
    Favorite Answer

    1.

    x² − 2x − 8 > 7

    x² − 2x − 15 > 0

    (x+3)(x−5) > 0

    Draw a U-shaped quadratic curve and mark the x-intercepts −3 and 5.

    Since quadratic > 0, note the parts of the curve above the x-axis.

    x<−3 or x>5

    2.

    3x² + 4x − 7 < 13

    3x² + 4x − 20 < 0

    (3x+10)(x−2) < 0

    Draw a U-shaped quadratic curve and mark the x-intercepts −10/3 and 2.

    Since quadratic < 0, note the parts of the curve below the x-axis.

    −10/3 < x < 2.

    3.

    Notice p(0) = 52. This means at t = 0, the pebble is 52 feet from the ground. The cliff is 52 feet high.

    The top of the boulder is 12 feet above the ground. So, p(t) = 12.

    −16t²+12t+52 = 12

    4t² − 3t − 10 = 0

    (4t+5)(t−2) = 0

    t = 2 seconds

    Answer C.

  • Daniel
    Lv 4
    8 years ago

    h(x)=x^2-2x-8>7

    (x-4)(x+2) > 7

    x -4 > 7 or x+2 >7

    x > 11 or x > 5

    More accurately, x >5 is your answer.

    3x^2+4x-7<13

    (3x+7) (x-1) < 13

    3x + 7 < 13 or x-1 < 13

    3x < 6 or x < 14

    x < 2 or x < 14

    Or, x < 2

    3. The total distance traveled is 40ft.

    -16t^2 + 12t + 52 = 40

    -16t^2 + 12t +12 = 0

    4t^2 - 3t - 3 = 0

    t = 3 +/- sqrt(57) / 8

    t = 3 +/- 7.54 / 8

    t = 10.54/8 or -4.54/8

    Since it's impossible to have negative time,

    t = 1.32

    Use A.

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