The length of the segment ad is 28 cm. the distance between the midpoints of segments ab and cd is 16 cm. find the length of the segment bc .

Given=

length of the segment AD is 28 cm

distance between the midpoints of segments AB and CD is 16 cm

find out length of BC

To proof

AD = 28 cm

let the midpoint of the AB is E.

let the midpoint of the CD is F.

E & F are the midpoints i.e these points divide AB & CD in two equal parts.

Let BC = z

Let AE = EB = x     ( E is midpoint)

Let CF = FD = y      (F is midpoint)

the equation becomes

2x + 2y + z = 28

x + y + z = 16

mulitipy above equation by 2

we  get

2x + 2y + 2z = 32

thus solving the equations

2x + 2y + 2z = 32

2x + 2y + z = 28

we get

z = 4 cm

i.e BC = 4 cm

Hence proved

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."

a. is correct