The table lists selected values of Sam's walking speed, in kilometers per hour (km/h), and his corresponding pulse, in beats per minute (bpm). There is a linear relationship between Sam's speed, x, and his pulse, f(x).
Which of the following equations describes f(x)?

9514 1404 393

  (C) f(x) = 5x +57

Step-by-step explanation:

Heart rate increases as speed increases, so only equations with a positive x-coefficient are of interest. It is pretty easy to see that ...

  f(x) = x+57

doesn't give ...

  f(4) = 77

However, the other reasonable choice is ...

  f(x) = 5x +57

which does give f(4) = 77.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

sorry, i can't understand your question. will later if you describe more clearly!

: )