select the correct answer from each drop - down menu. an amusement park prices tickets at $55 and sells an…

select the correct answer from each drop - down menu. an amusement park prices tickets at $55 and sells an average of 500 tickets daily. the management finds, over multiple increases in ticket pricing, that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day. management uses the combined function p to model the daily earnings of the amusement part, where x is the number of $2 increases in the price of a ticket. p(x)=-40x² - 100x + 27,500 use the given information to complete the sentences. the constant of the polynomial expression represents the in the price of a ticket. the binomial (500 - 20x) is a factor of the polynomial expression and represents the in the price of a ticket. reset next

select the correct answer from each drop - down menu. an amusement park prices tickets at $55 and sells an average of 500 tickets daily. the management finds, over multiple increases in ticket pricing, that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day. management uses the combined function p to model the daily earnings of the amusement part, where x is the number of $2 increases in the price of a ticket. p(x)=-40x² - 100x + 27,500 use the given information to complete the sentences. the constant of the polynomial expression represents the in the price of a ticket. the binomial (500 - 20x) is a factor of the polynomial expression and represents the in the price of a ticket. reset next

Answer

Answer:

The constant of the polynomial expression represents the initial daily earnings when there are no price - increases. The binomial $(500 - 20x)$ is a factor of the polynomial expression and represents the number of tickets sold after $x$ price - increases.

Explanation:

Step1: Analyze the constant term

The initial situation is when $x = 0$ (no price - increases). The initial ticket price is $$55$ and the initial number of tickets sold is $500$. So the initial daily earnings are $55\times500=27500$, which is the constant term in $P(x)=- 40x^{2}-100x + 27500$.

Step2: Analyze the binomial factor

We know that initially 500 tickets are sold and for each $$2$ increase in price ($x$ represents the number of $$2$ increases), 20 fewer tickets are sold. So the number of tickets sold after $x$ price - increases is given by the expression $500 - 20x$.