Given that B, D and F are midpoints, find the length of segment DA.

The length of segment DA is 15 units

Step-by-step explanation:

Let us use this rule to solve the question

In Δ AEC

∵ D is the midpoint of EC

∴ AD is a median

∵ B is the midpoint of AC

∴ EB is a median

∵ F is the midpoint of AE

∴ CF is a median

→ The three medians intersected at a point inside the triangle,

   let us called it M

∵ AD ∩ EB ∩ CF at M

∴ M is the point of intersection of the medians of Δ AEC

→ By using the rule above

∴ AD = 3 MD

∵ MD = 5

∴ AD = 3(5)

∴ AD = 15 units

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.