Answered

IDNLearn.com is designed to help you find the answers you need quickly and easily. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

Select the correct answer from each drop-down menu.

An amusement park prices tickets at \[tex]$55 and sells an average of 500 tickets daily. The management finds that a \$[/tex]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 [tex]\( P(x) \)[/tex] to model the daily earnings of the amusement park, where [tex]\( x \)[/tex] is the number of \[tex]$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 $[/tex]\square[tex]$ in the price of a ticket.
The binomial \((500 - 20x)\) is a factor of the polynomial expression and represents the $[/tex]\square$ in the price of a ticket.

Sagot :

GinnyAnsweridn
Let's break down the question step by step:

1. We start with the polynomial expression [tex]\( P(x) = -40x^2 - 100x + 27,500 \)[/tex] which models the daily earnings of the amusement park. In this expression:
- [tex]\( x \)[/tex] represents the number of [tex]\( \$2 \)[/tex] increases in the price of a ticket.

2. Understanding the terms in the polynomial:
- The constant term is [tex]\( 27,500 \)[/tex]. This term represents the initial daily earnings before any price increase.
- The binomial expression [tex]\( (500-20x) \)[/tex] is mentioned as a factor of the polynomial. Let's interpret this:
- [tex]\( 500 \)[/tex] stands for the average number of tickets sold when no price increase is applied.
- [tex]\( 20x \)[/tex] accounts for the decrease in the number of tickets sold when the price of a ticket increases.

Given these observations, we can fill out the sentences as follows:
1. The constant of the polynomial expression represents the initial daily earnings in the price of a ticket.
2. The binomial [tex]\((500 - 20x)\)[/tex] is a factor of the polynomial expression and represents the number of tickets sold based on the new price in the price of a ticket.

Therefore, the correct answers should be:

"The constant of the polynomial expression represents the initial daily earnings in the price of [tex]\( a \)[/tex] ticket."
"The binomial [tex]\((500 - 20x)\)[/tex] is a factor of the polynomial expression and represents the number of tickets sold based on the new price in the price of [tex]\( a \)[/tex] ticket."
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.