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An amusement park prices tickets at [tex]$\$[/tex] 55[tex]$ and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing, that a $[/tex]\[tex]$ 2$[/tex] 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 [tex]$P$[/tex] to model the daily earnings of the amusement park, where [tex]$x$[/tex] is the number of [tex]$\$[/tex] 2[tex]$ increases in the price of a ticket.
\[ P(x) = -40 x^2 - 100 x + 27,500 \]

Use the given information to complete the sentences.

The constant of the polynomial expression represents the ticket. $[/tex]\square[tex]$ in the price of a

The binomial $[/tex](500-20x)[tex]$ is a factor of the polynomial expression and represents the the price of a ticket. $[/tex]\square$ in

Sagot :

GinnyAnswer
Given the situation, let's break down the various components of the problem and answer the given statements.

The amusement park has an initial ticket price of \[tex]$55 and sells 500 tickets daily. When the price is increased by \$[/tex]2, 20 fewer tickets are sold for each increase. The polynomial expression provided by the management, [tex]\( P(x) = -40x^2 - 100x + 27,500 \)[/tex], models the daily earnings where [tex]\( x \)[/tex] is the number of \[tex]$2 increases. The polynomial \( P(x) \) represents the daily earnings. 1. The constant of the polynomial: The constant term of the polynomial \( P(x) \) is \( 27,500 \). This represents the daily earnings when there are no price increases, that is when \( x = 0 \). If no price increases (\$[/tex]2) were made, the earnings would be constant at \[tex]$27,500. 2. The binomial factor: The binomial factor \( (500 - 20x) \) is derived from the total number of tickets sold after \( x \) increases. Initially, the park sells 500 tickets per day. For each \( x \) increase (where the price is increased by \$[/tex]2), 20 fewer tickets are sold. So, this binomial factor represents the number of tickets sold at different price levels.

Now filling in the blanks:

The constant of the polynomial expression represents the ticket earnings in the price of a facility.

The binomial [tex]\( (500 - 20x) \)[/tex] is a factor of the polynomial expression and represents the number in tickets sold.

So, the complete sentences are:

- The constant of the polynomial expression represents the ticket earnings.
- The binomial [tex]\( (500 - 20x) \)[/tex] is a factor of the polynomial expression and represents the number of tickets sold.
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