Given the function g(x) = -x^2+ 2x + 8, determine the average rate of change of
the function over the interval -3 < x < 2.

3

Step-by-step explanation:

The average rate of change of g(x) in the closed interval [ a, b ] is

Here [ a, b ] = [ - 3, 2 ], thus

g(b) = g(2) = - 2² + 2(2) + 8 = - 4 + 4 + 8 = 8

g(a) = g(- 3) = - (- 3)² + 2(- 3) + 8 = - 9 - 6 + 8 = - 7

average rate of change = = = 3

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.