The time a projectile spends in the air can be modeled by the equation t² -t – 8 = 0, in which t represents the amount of time traveled, in

Question

The time a projectile spends in the air can be modeled by the equation t² -t – 8 = 0, in which t represents the amount of time traveled, in seconds. Which of the following is equivalent to the equation t² – 2t – 8 = 0?
(t + 4)(t – 2) = 0
t -4)(t – 2) = 0
(t + 4)(t + 2) = 0
(t – 4) (t + 2) = 0

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Isabelle 3 months 2022-02-09T05:41:04+00:00 1 Answer 0 views 0

Answers ( )

    0
    2022-02-09T05:42:24+00:00

    Answer:

    (t – 4)(t + 2) = 0  

    Step-by-step explanation:

    The general formula for a quadratic expression is

    y = ax² + bx + c

    Your expression is

    y = t² – 2t – 8 = 0

    By comparison, we see that

    a = 1; b = -2; c = -8

    1. Find two numbers that multiply to give ac and add to give b.

    In this case, find two numbers that multiply to give -8 and add to give -2.

    It helps to list the factors of  -8.

    They are ±1, ±2, ±4, and ±8

    After a little trial and error, you should find the numbers -4 and +2.

    -4 × 2 = -8, and -4 + 2 = -2)

    2. Rewrite the middle term with those numbers

    t² -4t + 2t – 8 = 0

    3. Factor the first and last pairs of terms separately

    t(t – 4) +2(t – 4) = 0

    4. Separate the common factor

    The common factor is t – 4.

    (t – 4)(t + 2) = 0

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