Points B, D, and Fare midpoints of the sides of angle ACE. EC = 39 and DF = 18. Find AC

9
78
39
36

Line AC = 36

Step-by-step explanation: The first and most important clue is the fact that points B, D and F are midpoints of the triangle ACE. What this tells us is that point B divides line AC into two equal sides. Likewise points D and F. If point D divides line EC into two equal sides, then line ED equals

39/2 = 19.5

Also, triangle FED is similar to triangle AEC. Since ED is half of EC, and FE is half of AE. Therefore in triangles FED and AEC,

FD/ED = AC/EC

18/19.5 = AC/39

By cross multiplication we now have

(18 x 39)/19.5 = AC

702/19.5 = AC

36 = AC

Therefore line AC = 36

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."