Reyna runs a textile company that manufactures t-shirts. the profit, p, made by the company is modeled by the function p=s2+9s-142, where s is the number of t-shirts sold. how many t-shirts should be sold to earn a profit of more than $2,000?
s < 42
s > 42
s > 51
s < 51

The profit, p, made by the company is modeled by the function

→→ p=s²+9 s-142, where s is the number of T-shirts sold.

We want profit on T shirt sold should be more than $ 2,000.So,the profit equation can be written as,

⇒s²+9 s-142>2000

→We will neglect, s+51> or <0,because number of T-shirts sold can't be negative.

Or,→→there is second way, mark points, 42 and -51 on the number line, and substitute , number greater than 42 on the profit Inequality,which is s²+9 s-2142>0, which gives ,s>42.

Option B: s >42

  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).