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Step-by-step explanation:

The sum of top and bottom bases is twice the midsegment.

  (c² +6) +(c² +2) = 2(4c)

  2c² -8c +8 = 0 . . . . . . . . . subtract 8c

  2(c -2)² = 0 . . . . . . . . factor

  c = 2 . . . . . . the value that makes the binomial be zero

The value of c is 2; the segment lengths (top-down) are 10, 8, 6.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.