Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Let's analyze each of the given tables and determine which one matches the equation [tex]\(c = 3.5 \cdot b\)[/tex] while including only viable solutions. The equation [tex]\(c = 3.5 \cdot b\)[/tex] means that the cost [tex]\(c\)[/tex] is directly proportional to the number of loaves [tex]\(b\)[/tex] with a proportionality constant of 3.5.
### Table 1
[tex]\[ \begin{tabular}{|c|c|} \hline Loaves (b) & Cost $(c)$ \\ \hline -2 & -7 \\ \hline 0 & 0 \\ \hline 2 & 7 \\ \hline 4 & 14 \\ \hline \end{tabular} \][/tex]
Let's check each pair:
- For [tex]\(b = -2\)[/tex], [tex]\(c = 3.5 \times (-2) = -7\)[/tex]. The value matches.
- For [tex]\(b = 0\)[/tex], [tex]\(c = 3.5 \times 0 = 0\)[/tex]. The value matches.
- For [tex]\(b = 2\)[/tex], [tex]\(c = 3.5 \times 2 = 7\)[/tex]. The value matches.
- For [tex]\(b = 4\)[/tex], [tex]\(c = 3.5 \times 4 = 14\)[/tex]. The value matches.
All the values in this table match the equation.
### Table 2
[tex]\[ \begin{tabular}{|c|c|} \hline Loaves $(b)$ & Cost $(c)$ \\ \hline 0 & 0 \\ \hline 0.5 & 1.75 \\ \hline 1 & 3.5 \\ \hline 1.5 & 5.25 \\ \hline \end{tabular} \][/tex]
Let's check each pair:
- For [tex]\(b = 0\)[/tex], [tex]\(c = 3.5 \times 0 = 0\)[/tex]. The value matches.
- For [tex]\(b = 0.5\)[/tex], [tex]\(c = 3.5 \times 0.5 = 1.75\)[/tex]. The value matches.
- For [tex]\(b = 1\)[/tex], [tex]\(c = 3.5 \times 1 = 3.5\)[/tex]. The value matches.
- For [tex]\(b = 1.5\)[/tex], [tex]\(c = 3.5 \times 1.5 = 5.25\)[/tex]. The value matches.
All the values in this table match the equation.
### Table 3
[tex]\[ \begin{tabular}{|c|c|} \hline Loaves $(b)$ & Cost $(c)$ \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{tabular} \][/tex]
Let's check each pair:
- For [tex]\(b = 0\)[/tex], [tex]\(c = 3.5 \times 0 = 0\)[/tex]. The value matches.
- For [tex]\(b = 3\)[/tex], [tex]\(c = 3.5 \times 3 = 10.5\)[/tex]. The value matches.
- For [tex]\(b = 6\)[/tex], [tex]\(c = 3.5 \times 6 = 21\)[/tex]. The value matches.
- For [tex]\(b = 9\)[/tex], [tex]\(c = 3.5 \times 9 = 31.5\)[/tex]. The value matches.
All the values in this table match the equation.
### Conclusion
All three tables (Table 1, Table 2, and Table 3) have values that match the equation [tex]\(c = 3.5 \cdot b\)[/tex]. However, we need to choose the table with only viable solutions. Typically, for such problems, viable solutions refer to non-negative values, as negative values for number of loaves or cost don't make practical sense.
- Table 1 includes a negative value for [tex]\(b\)[/tex] and [tex]\(c\)[/tex] (-2, -7), making it not entirely viable.
- Table 2 includes non-negative values that are fractions and whole numbers of loaves, which are viable.
- Table 3 also includes non-negative values that are whole numbers of loaves, which are viable.
Both Table 2 and Table 3 include only viable solutions. But considering standard practice and the need to align with realistic whole numbers for purchasing loaves of bread, Table 3 is often considered more practical with whole numbers.
Thus, Table 3 is the table of values that matches the equation [tex]\(c = 3.5 \cdot b\)[/tex] and includes only viable solutions.
### Table 1
[tex]\[ \begin{tabular}{|c|c|} \hline Loaves (b) & Cost $(c)$ \\ \hline -2 & -7 \\ \hline 0 & 0 \\ \hline 2 & 7 \\ \hline 4 & 14 \\ \hline \end{tabular} \][/tex]
Let's check each pair:
- For [tex]\(b = -2\)[/tex], [tex]\(c = 3.5 \times (-2) = -7\)[/tex]. The value matches.
- For [tex]\(b = 0\)[/tex], [tex]\(c = 3.5 \times 0 = 0\)[/tex]. The value matches.
- For [tex]\(b = 2\)[/tex], [tex]\(c = 3.5 \times 2 = 7\)[/tex]. The value matches.
- For [tex]\(b = 4\)[/tex], [tex]\(c = 3.5 \times 4 = 14\)[/tex]. The value matches.
All the values in this table match the equation.
### Table 2
[tex]\[ \begin{tabular}{|c|c|} \hline Loaves $(b)$ & Cost $(c)$ \\ \hline 0 & 0 \\ \hline 0.5 & 1.75 \\ \hline 1 & 3.5 \\ \hline 1.5 & 5.25 \\ \hline \end{tabular} \][/tex]
Let's check each pair:
- For [tex]\(b = 0\)[/tex], [tex]\(c = 3.5 \times 0 = 0\)[/tex]. The value matches.
- For [tex]\(b = 0.5\)[/tex], [tex]\(c = 3.5 \times 0.5 = 1.75\)[/tex]. The value matches.
- For [tex]\(b = 1\)[/tex], [tex]\(c = 3.5 \times 1 = 3.5\)[/tex]. The value matches.
- For [tex]\(b = 1.5\)[/tex], [tex]\(c = 3.5 \times 1.5 = 5.25\)[/tex]. The value matches.
All the values in this table match the equation.
### Table 3
[tex]\[ \begin{tabular}{|c|c|} \hline Loaves $(b)$ & Cost $(c)$ \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{tabular} \][/tex]
Let's check each pair:
- For [tex]\(b = 0\)[/tex], [tex]\(c = 3.5 \times 0 = 0\)[/tex]. The value matches.
- For [tex]\(b = 3\)[/tex], [tex]\(c = 3.5 \times 3 = 10.5\)[/tex]. The value matches.
- For [tex]\(b = 6\)[/tex], [tex]\(c = 3.5 \times 6 = 21\)[/tex]. The value matches.
- For [tex]\(b = 9\)[/tex], [tex]\(c = 3.5 \times 9 = 31.5\)[/tex]. The value matches.
All the values in this table match the equation.
### Conclusion
All three tables (Table 1, Table 2, and Table 3) have values that match the equation [tex]\(c = 3.5 \cdot b\)[/tex]. However, we need to choose the table with only viable solutions. Typically, for such problems, viable solutions refer to non-negative values, as negative values for number of loaves or cost don't make practical sense.
- Table 1 includes a negative value for [tex]\(b\)[/tex] and [tex]\(c\)[/tex] (-2, -7), making it not entirely viable.
- Table 2 includes non-negative values that are fractions and whole numbers of loaves, which are viable.
- Table 3 also includes non-negative values that are whole numbers of loaves, which are viable.
Both Table 2 and Table 3 include only viable solutions. But considering standard practice and the need to align with realistic whole numbers for purchasing loaves of bread, Table 3 is often considered more practical with whole numbers.
Thus, Table 3 is the table of values that matches the equation [tex]\(c = 3.5 \cdot b\)[/tex] and includes only viable solutions.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
