To calculate the hourly revenue from the buffet after [tex]x[/tex] $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner's desired revenue.

Type the correct answer in each box. Use numerals instead of words.

[tex] x^2 + \square x + \square \geq \square [/tex]



Answer :

Certainly! Let's go through this step by step:

1. Understanding the Variables and Terms:
- We are tasked with calculating the hourly revenue from the buffet after certain price increases.
- The price paid by each customer after [tex]$x$[/tex] increments is derived from the initial price increment.
- The average number of customers per hour is affected by these price increments (though this relationship isn't explicitly provided in the given answer).

2. Identifying the Coefficients:
- Given the inequality in standard form, we need three coefficients: [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
- From the given answer, we have:
- [tex]\( a = 0 \)[/tex]
- [tex]\( b = 1 \)[/tex]
- [tex]\( c = 0 \)[/tex]

3. Form the Inequality in Standard Form:
- The standard form of the quadratic inequality is [tex]\(ax^2 + bx + c \geq \text{desired revenue}\)[/tex].
- Substituting in the coefficients, we have:
- [tex]\(0x^2 + 1x + 0 \geq \text{desired revenue}\)[/tex]

4. Composing the Final Answer:
- The inequality simplifies to: [tex]\(0x^2 + 1x + 0 \geq \text{desired revenue}\)[/tex]
- Or more simply: [tex]\(x \geq \text{desired revenue}\)[/tex]

So, the correctly formatted inequality is:

[tex]\[ 0x^2 + 1x + 0 \geq \text{desired revenue} \][/tex]