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anastassius [24]
3 years ago
14

The function f(t) = 4t^2 − 8t + 6 shows the height from the ground f(t), in meters, of a roller coaster car at different times t

. Write f(t) in the vertex form a(x − h)^2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
A - f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground
B - f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 1 meter from the ground
Mathematics
1 answer:
andreev551 [17]3 years ago
3 0

Answer:

C - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 2 meters from the ground.

Step-by-step explanation:

Here we're asked to rewrite the given equation f(t) = 4t^2 − 8t + 6 in the form f(t) = a(t - h)^2 + k (which is known as the "vertex form of the equation of a parabola.")  Here (h, k) is the vertex and a is a scale factor.

Let's begin by factoring 4 out of all three terms:

f(t) = 4 [ t^2 - 2t + 6/4 ]

Next, we must "complete the square" of t^2 - 2t + 6/4; in other words, we must re-write this expression in the form (t - h)^2 + k.

(To be continued)

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fiasKO [112]

Answer:

15

Step-by-step explanation:

6 0
3 years ago
An object is moving at a speed of 3 kilometers per hour. Express this speed in feet per
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Answer:

590,551.2

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6 0
3 years ago
If 5y = 6x + 16 and 9x = 7y-20, what is the value of 3x - 2y?
Law Incorporation [45]

The value of 3x-2y is -4. From the equation 5y=6x=16 and 9x=7y-20 the values of (x,y) is (4,8).

Step-by-step explanation:

        The given equations are,

                 5y=6x+16.......................(1)

                 9x=7y-20......................(2)

                3x-2y...............................(3)

Step:1

    Modify the equations (1) and (2) in (x+y=constant) format,

                6x-5y=-16.....................(4)

                9x-7y=-20....................(5)

Step:2

     Equation (4) is multiplied by 7     ( ∵ 7×Eqn(4))

                42x-35y=-112..............(6)

Step:3

     Equation (5) is multiplied by 5     (∵ 5×Eqn(5))

               45x-35y=-100.............(7)

Step:4

    Subtracting Equation (6) and (7)

               42x-35y=-112

              45x-35y=-100

    ( - )

     (42x-45x)+(35y-35y)=(100-112)

     (-3x)+(0)=(-12)

    x=4

Step:5

    Substitute X value in Equation (1),

             5y=6x+16...................(1)

     where, x=4,

             5y= (6×4)+16

             5y=40

            y= 8

Step: 6

      Check for solution, substitute x and y values in equation (2).

                9x=7y-20.......................(2)

               (9×4)=(7×8)-20

              36=36

Step:7

      From given, 3x-2y

      where, X=4 and y=8

              3x-2y = (3×4)-(2×8)

                        = 12-16

            3x-2y = -4

Result:

      The value for 3x-2y is -4. The values of (x,y) are (4,8).

   

5 0
3 years ago
Read 2 more answers
Sam went to a pizza place with 2 friends. They ordered a large mushroom pizza for $12.60 and a garden salad for $3.30. They also
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Answer:

$4.45

Step-by-step explanation:

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6 0
3 years ago
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Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....
Alekssandra [29.7K]

Answer:

<u>b(n) = -11 + (n-1)*8</u>

<u></u>

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

<u><em>b(1)</em></u><em>   -11</em>         + 8 =   -3

<u><em>b(2)</em></u><em>   -3</em>          + 8 =    5

<u><em>b(3)</em></u>   <em> 5 </em>         + 8 =   13

<u><em>b(4)</em></u><em> </em> <em>13</em>

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

<u>b(n) = -11 + (n-1)*8</u>

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   <u><em>YES</em></u>

5 0
2 years ago
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