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)=-40x^{2}-100x + 27,500. use the given information to complete the sentences. the constant of the polynomial expression represents the drop - down in the price of a ticket. the binomial (500 - 20x) is a factor of the polynomial expression and represents the drop - down in the price of a ticket.

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)=-40x^{2}-100x + 27,500. use the given information to complete the sentences. the constant of the polynomial expression represents the drop - down in the price of a ticket. the binomial (500 - 20x) is a factor of the polynomial expression and represents the drop - down in the price of a ticket.

Answer

Explanation:

Step1: Analyze the constant term

The constant term in the profit - function $P(x)=-40x^{2}-100x + 27500$ is 27500. When $x = 0$ (i.e., no price - increases), the daily earnings are calculated by substituting $x = 0$ into the function. The initial price of a ticket is $55$ and the initial number of tickets sold is 500. So the initial daily earnings are $55\times500=27500$. So the constant represents the initial daily earnings.

Step2: Analyze the binomial factor

The binomial $(500 - 20x)$ represents the number of tickets sold. Initially, 500 tickets are sold, and for each $x$ (where $x$ is the number of $2 price - increases), 20 fewer tickets are sold.

Answer:

The constant of the polynomial expression represents the initial daily earnings in the price of a ticket. The binomial $(500 - 20x)$ is a factor of the polynomial expression and represents the number of tickets sold in the price of a ticket.