Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Each day that a library book is kept past its due date, a [tex]$\$[/tex]0.30[tex]$ fee is charged at midnight. Which ordered pair is a viable solution if $[/tex]x[tex]$ represents the number of days that a library book is late and $[/tex]y[tex]$ represents the total fee?

A. $[/tex](-3, -0.90)[tex]$
B. $[/tex](-2.5, -0.75)[tex]$
C. $[/tex](4.5, 1.35)[tex]$
D. $[/tex](8, 2.40)$


Sagot :

To determine which ordered pair [tex]\((x, y)\)[/tex] is a viable solution, we need to check if the given fee per day and the total fee match. Here, [tex]\(x\)[/tex] represents the number of days a book is late and [tex]\(y\)[/tex] represents the total fee. The daily fee is \$0.30.

Let's evaluate each ordered pair:

1. For [tex]\((-3, -0.90)\)[/tex]:
[tex]\[ \text{Total fee} = 0.30 \times (-3) = -0.90 \][/tex]
The calculated total fee is [tex]\(-0.90\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((-3, -0.90)\)[/tex] is a viable solution.

2. For [tex]\((-2.5, -0.75)\)[/tex]:
[tex]\[ \text{Total fee} = 0.30 \times (-2.5) = -0.75 \][/tex]
The calculated total fee is [tex]\(-0.75\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((-2.5, -0.75)\)[/tex] is a viable solution.

3. For [tex]\((4.5, 1.35)\)[/tex]:
[tex]\[ \text{Total fee} = 0.30 \times 4.5 = 1.35 \][/tex]
The calculated total fee is [tex]\(1.35\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((4.5, 1.35)\)[/tex] is a viable solution.

4. For [tex]\((8, 2.40)\)[/tex]:
[tex]\[ \text{Total fee} = 0.30 \times 8 = 2.40 \][/tex]
The calculated total fee is [tex]\(2.40\)[/tex], which matches the given [tex]\(y\)[/tex] value in the ordered pair. Therefore, [tex]\((8, 2.40)\)[/tex] is a viable solution.

Based on the calculations, the viable solutions are:

- [tex]\((-2.5, -0.75)\)[/tex]
- [tex]\((8, 2.40)\)[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.