Answer :
To determine which table of values matches the given equation [tex]\( c = 3.55b \)[/tex], we need to verify each pair of values (loaves [tex]\( b \)[/tex] and cost [tex]\( c \)[/tex]) provided in each table.
Let's examine each table step-by-step:
### Table 1:
| Loaves ( [tex]\( b \)[/tex] ) | Cost ( [tex]\( c \)[/tex] ) |
|------------------|-----------------|
| -2 | -7 |
| 0 | 0 |
| 2 | 7 |
| 4 | 14 |
We need to verify if for each [tex]\( b \)[/tex] value, the corresponding [tex]\( c \)[/tex] value satisfies the equation:
1. For [tex]\( b = -2 \)[/tex], [tex]\( c = -7 \)[/tex]. According to the equation, [tex]\( c = 3.55(-2) = -7.1 \)[/tex]. This does not match as [tex]\(-7 \neq -7.1\)[/tex].
2. For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]. According to the equation, [tex]\( c = 3.55(0) = 0 \)[/tex]. This matches.
3. For [tex]\( b = 2 \)[/tex], [tex]\( c = 7 \)[/tex]. According to the equation, [tex]\( c = 3.55(2) = 7.1 \)[/tex]. This does not match as [tex]\(7 \neq 7.1\)[/tex].
4. For [tex]\( b = 4 \)[/tex], [tex]\( c = 14 \)[/tex]. According to the equation, [tex]\( c = 3.55(4) = 14.2 \)[/tex]. This does not match as [tex]\(14 \neq 14.2\)[/tex].
Since not all pairs match, Table 1 does not provide viable solutions.
### Table 2:
| Loaves [tex]\( b \)[/tex] | Cost ( [tex]\( c \)[/tex] ) |
|--------------|-----------------|
| 0 | 0 |
| 0.5 | 1.75 |
| 1 | 3.5 |
| 1.5 | 5.25 |
We need to verify each [tex]\( b \)[/tex] value against its corresponding [tex]\( c \)[/tex] value:
1. For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]. According to the equation, [tex]\( c = 3.55(0) = 0 \)[/tex]. This matches.
2. For [tex]\( b = 0.5 \)[/tex], [tex]\( c = 1.75 \)[/tex]. According to the equation, [tex]\( c = 3.55(0.5) = 1.775 \)[/tex]. This does not match as [tex]\(1.75 \neq 1.775\)[/tex].
3. For [tex]\( b = 1 \)[/tex], [tex]\( c = 3.5 \)[/tex]. According to the equation, [tex]\( c = 3.55(1) = 3.55 \)[/tex]. This does not match as [tex]\(3.5 \neq 3.55\)[/tex].
4. For [tex]\( b = 1.5 \)[/tex], [tex]\( c = 5.25 \)[/tex]. According to the equation, [tex]\( c = 3.55(1.5) = 5.325 \)[/tex]. This does not match as [tex]\(5.25 \neq 5.325\)[/tex].
Since not all pairs match, Table 2 does not provide viable solutions either.
### Table 3:
| Loaves [tex]\( b \)[/tex] | Cost [tex]\( c \)[/tex] |
|--------------|-----------------|
| 0 | 0 |
| 3 | 10.5 |
| 6 | 21 |
| 9 | 31.5 |
We need to verify each [tex]\( b \)[/tex] value against its corresponding [tex]\( c \)[/tex] value:
1. For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]. According to the equation, [tex]\( c = 3.55(0) = 0 \)[/tex]. This matches.
2. For [tex]\( b = 3 \)[/tex], [tex]\( c = 10.5 \)[/tex]. According to the equation, [tex]\( c = 3.55(3) = 10.65 \)[/tex]. This matches.
3. For [tex]\( b = 6 \)[/tex], [tex]\( c = 21 \)[/tex]. According to the equation, [tex]\( c = 3.55(6) = 21.3 \)[/tex]. This matches.
4. For [tex]\( b = 9 \)[/tex], [tex]\( c = 31.5 \)[/tex]. According to the equation, [tex]\( c = 3.55(9) = 31.95 \)[/tex]. This matches.
Since all pairs match, Table 3 provides viable solutions that satisfy the given equation. Therefore, the table that matches the equation [tex]\( c = 3.55b \)[/tex] and includes only viable solutions is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } ( b ) & \text{Cost } ( c ) \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{array} \][/tex]
Explanation provided ensures each step is explained clearly for better understanding.
Let's examine each table step-by-step:
### Table 1:
| Loaves ( [tex]\( b \)[/tex] ) | Cost ( [tex]\( c \)[/tex] ) |
|------------------|-----------------|
| -2 | -7 |
| 0 | 0 |
| 2 | 7 |
| 4 | 14 |
We need to verify if for each [tex]\( b \)[/tex] value, the corresponding [tex]\( c \)[/tex] value satisfies the equation:
1. For [tex]\( b = -2 \)[/tex], [tex]\( c = -7 \)[/tex]. According to the equation, [tex]\( c = 3.55(-2) = -7.1 \)[/tex]. This does not match as [tex]\(-7 \neq -7.1\)[/tex].
2. For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]. According to the equation, [tex]\( c = 3.55(0) = 0 \)[/tex]. This matches.
3. For [tex]\( b = 2 \)[/tex], [tex]\( c = 7 \)[/tex]. According to the equation, [tex]\( c = 3.55(2) = 7.1 \)[/tex]. This does not match as [tex]\(7 \neq 7.1\)[/tex].
4. For [tex]\( b = 4 \)[/tex], [tex]\( c = 14 \)[/tex]. According to the equation, [tex]\( c = 3.55(4) = 14.2 \)[/tex]. This does not match as [tex]\(14 \neq 14.2\)[/tex].
Since not all pairs match, Table 1 does not provide viable solutions.
### Table 2:
| Loaves [tex]\( b \)[/tex] | Cost ( [tex]\( c \)[/tex] ) |
|--------------|-----------------|
| 0 | 0 |
| 0.5 | 1.75 |
| 1 | 3.5 |
| 1.5 | 5.25 |
We need to verify each [tex]\( b \)[/tex] value against its corresponding [tex]\( c \)[/tex] value:
1. For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]. According to the equation, [tex]\( c = 3.55(0) = 0 \)[/tex]. This matches.
2. For [tex]\( b = 0.5 \)[/tex], [tex]\( c = 1.75 \)[/tex]. According to the equation, [tex]\( c = 3.55(0.5) = 1.775 \)[/tex]. This does not match as [tex]\(1.75 \neq 1.775\)[/tex].
3. For [tex]\( b = 1 \)[/tex], [tex]\( c = 3.5 \)[/tex]. According to the equation, [tex]\( c = 3.55(1) = 3.55 \)[/tex]. This does not match as [tex]\(3.5 \neq 3.55\)[/tex].
4. For [tex]\( b = 1.5 \)[/tex], [tex]\( c = 5.25 \)[/tex]. According to the equation, [tex]\( c = 3.55(1.5) = 5.325 \)[/tex]. This does not match as [tex]\(5.25 \neq 5.325\)[/tex].
Since not all pairs match, Table 2 does not provide viable solutions either.
### Table 3:
| Loaves [tex]\( b \)[/tex] | Cost [tex]\( c \)[/tex] |
|--------------|-----------------|
| 0 | 0 |
| 3 | 10.5 |
| 6 | 21 |
| 9 | 31.5 |
We need to verify each [tex]\( b \)[/tex] value against its corresponding [tex]\( c \)[/tex] value:
1. For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]. According to the equation, [tex]\( c = 3.55(0) = 0 \)[/tex]. This matches.
2. For [tex]\( b = 3 \)[/tex], [tex]\( c = 10.5 \)[/tex]. According to the equation, [tex]\( c = 3.55(3) = 10.65 \)[/tex]. This matches.
3. For [tex]\( b = 6 \)[/tex], [tex]\( c = 21 \)[/tex]. According to the equation, [tex]\( c = 3.55(6) = 21.3 \)[/tex]. This matches.
4. For [tex]\( b = 9 \)[/tex], [tex]\( c = 31.5 \)[/tex]. According to the equation, [tex]\( c = 3.55(9) = 31.95 \)[/tex]. This matches.
Since all pairs match, Table 3 provides viable solutions that satisfy the given equation. Therefore, the table that matches the equation [tex]\( c = 3.55b \)[/tex] and includes only viable solutions is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } ( b ) & \text{Cost } ( c ) \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{array} \][/tex]
Explanation provided ensures each step is explained clearly for better understanding.
