Which of the following is a solution to the system shown below? y = 3x 2 - 8x - 2 and 2x - y = 5 (1, 3) (1/3,-13/3) (-1/3,13/3) (17/6, 0)

Option B

Step-by-step explanation:

We have to find the solution to the system of equations

y = 3x² - 8x - 2 ----------------(1)

2x - y = 5

y = 2x - 5 -----------------(2)

Now equate the equations (1) and (2) for the values of y.

3x² - 8x - 2 = 2x - 5

3x² - 8x - 2x - 2 + 5 = 0

3x² - 10x + 3 = 0

3x² - 9x - x + 3 = 0

3x ( x-3 ) - 1 ( x-3 ) = 0

( 3x - 1 ) ( x-3 ) = 0

x = and 3

Now we put x =   and 3 in equation (2)

y = 2 × - 5

= =

and y = 3 × 2 - 5

         = 6 - 5

        = 1

So solutions are , and ( 3, 1 )

Option B is the answer.

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f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50