In equilateral ∆abc, points m, p, and k belong to ab , bc , and ac respectively and am: mb = bp: pc = ck: ka = 1: 3. prove that ∆mpk is an equilateral triangle.

See explanation

Step-by-step explanation:

In equilateral ∆ABC,

Points M, P, and K belong to AB , BC , and AC respectively and

AM:MB = BP:PC = CK:KA = 1:3.

So,

Triangles AMK, BPM and CKP are all congruent by SAS postulate, so

If triangle MPK is equilateral triangle

for the points! : )

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).