Consider the function p(x) = x^2 + 6x + 5.
what is the average rate of change from x=1 to x=5

The average rate of change is 12.

Step-by-step explanation:

Given

p(x)= x^2+6x+5

The average rate of change in the given interval a ≤ x ≤ b is given by the expression

Rate of change=  (p(b)-p(a))/(b-a)

Here p(b) is the value of function at point b and p(a) is the value of function point a.  

From the question,

a = 1  

and  

b = 5

So,

Rate of change=  (p(5)-p(1))/(5-1)

Now,  

p(5)= (5)^2+6(5)+5

p(5)=25+30+5

p(5)=60

And

p(1)= (1)^2+6(1)+5

p(1)=1+6+5

p(1)=12

Putting in the formula

Rate of change=  (60-12)/(5-1)

=  48/4

=12

how long did the flood last

step-by-step explanation:

then i will answer

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.