In ΔPQR, \text{m}\angle P = (4x-14)^{\circ}m∠P=(4x−14) ∘
, \text{m}\angle Q = (5x+6)^{\circ}m∠Q=(5x+6)
∘
, and \text{m}\angle R = (x-2)^{\circ}m∠R=(x−2)
∘
. Find \text{m}\angle R. m∠R.

52

Step-by-step explanation:

4x+8 = 5x-3 by the Vertical Angles Theorem that states the vertical angles are congruent.  

Subtract 4x from both sides and get:

8=1x -3

Add 3 to both sides:

11= 1x

if x =11, plug that in to angle A.  

4x+ 8 becomes 4(11)+8 =

44+ 8=

  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).