IDNLearn.com provides a seamless experience for finding and sharing answers. Join our Q&A platform to access reliable and detailed answers from experts in various fields.
Sagot :
To determine which table shows the viable solutions for the total number of pages Selma has read after [tex]\( x \)[/tex] minutes, given her pace of reading and initial pages read, we need to confirm that the equation [tex]\( y = 75 + 2x \)[/tex] holds true for all the given data points in each table. Here we start with the initial pages read as 75, and she reads at a rate of 2 pages per minute.
### Analyzing Each Table
Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline 2 & 79 \\ \hline 14 & 101 \\ \hline 39 & 153 \\ \hline 55 & 185 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = 2, y = 79 \)[/tex]
[tex]\[ y = 75 + 2(2) = 75 + 4 = 79 \quad \text{(Correct)} \][/tex]
2. [tex]\( x = 14, y = 101 \)[/tex]
[tex]\[ y = 75 + 2(14) = 75 + 28 = 103 \quad \text{(Incorrect)} \][/tex]
3. [tex]\( x = 39, y = 153 \)[/tex]
[tex]\[ y = 75 + 2(39) = 75 + 78 = 153 \quad \text{(Correct)} \][/tex]
4. [tex]\( x = 55, y = 185 \)[/tex]
[tex]\[ y = 75 + 2(55) = 75 + 110 = 185 \quad \text{(Correct)} \][/tex]
Since the second entry does not match, Table 1 is not valid.
Table 2:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline -16 & 43 \\ \hline 6 & 87 \\ \hline 27 & 129 \\ \hline 52 & 179 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = -16, y = 43 \)[/tex]
[tex]\[ y = 75 + 2(-16) = 75 - 32 = 43 \quad \text{(Correct)} \][/tex]
2. [tex]\( x = 6, y = 87 \)[/tex]
[tex]\[ y = 75 + 2(6) = 75 + 12 = 87 \quad \text{(Correct)} \][/tex]
3. [tex]\( x = 27, y = 129 \)[/tex]
[tex]\[ y = 75 + 2(27) = 75 + 54 = 129 \quad \text{(Correct)} \][/tex]
4. [tex]\( x = 52, y = 179 \)[/tex]
[tex]\[ y = 75 + 2(52) = 75 + 104 = 179 \quad \text{(Correct)} \][/tex]
All entries match, Table 2 is valid.
Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline 0 & 0 \\ \hline 19 & 113 \\ \hline 32 & 139 \\ \hline 47 & 169 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = 0, y = 0 \)[/tex]
[tex]\[ y = 75 + 2(0) = 75 + 0 = 75 \quad \text{(Incorrect)} \][/tex]
2. [tex]\( x = 19, y = 113 \)[/tex]
[tex]\[ y = 75 + 2(19) = 75 + 38 = 113 \quad \text{(Correct)} \][/tex]
3. [tex]\( x = 32, y = 139 \)[/tex]
[tex]\[ y = 75 + 2(32) = 75 + 64 = 139 \quad \text{(Correct)} \][/tex]
4. [tex]\( x = 47, y = 169 \)[/tex]
[tex]\[ y = 75 + 2(47) = 75 + 94 = 169 \quad \text{(Correct)} \][/tex]
Since the first entry does not match, Table 3 is not valid.
Table 4:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline 0 & 75 \\ \hline 11 & 97 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = 0, y = 75 \)[/tex]
[tex]\[ y = 75 + 2(0) = 75 + 0 = 75 \quad \text{(Correct)} \][/tex]
2. [tex]\( x = 11, y = 97 \)[/tex]
[tex]\[ y = 75 + 2(11) = 75 + 22 = 97 \quad \text{(Correct)} \][/tex]
All entries match, Table 4 is valid.
### Conclusion
The viable tables that show the total number of pages Selma has read after [tex]\( x \)[/tex] minutes are Table 2 and Table 4.
### Analyzing Each Table
Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline 2 & 79 \\ \hline 14 & 101 \\ \hline 39 & 153 \\ \hline 55 & 185 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = 2, y = 79 \)[/tex]
[tex]\[ y = 75 + 2(2) = 75 + 4 = 79 \quad \text{(Correct)} \][/tex]
2. [tex]\( x = 14, y = 101 \)[/tex]
[tex]\[ y = 75 + 2(14) = 75 + 28 = 103 \quad \text{(Incorrect)} \][/tex]
3. [tex]\( x = 39, y = 153 \)[/tex]
[tex]\[ y = 75 + 2(39) = 75 + 78 = 153 \quad \text{(Correct)} \][/tex]
4. [tex]\( x = 55, y = 185 \)[/tex]
[tex]\[ y = 75 + 2(55) = 75 + 110 = 185 \quad \text{(Correct)} \][/tex]
Since the second entry does not match, Table 1 is not valid.
Table 2:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline -16 & 43 \\ \hline 6 & 87 \\ \hline 27 & 129 \\ \hline 52 & 179 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = -16, y = 43 \)[/tex]
[tex]\[ y = 75 + 2(-16) = 75 - 32 = 43 \quad \text{(Correct)} \][/tex]
2. [tex]\( x = 6, y = 87 \)[/tex]
[tex]\[ y = 75 + 2(6) = 75 + 12 = 87 \quad \text{(Correct)} \][/tex]
3. [tex]\( x = 27, y = 129 \)[/tex]
[tex]\[ y = 75 + 2(27) = 75 + 54 = 129 \quad \text{(Correct)} \][/tex]
4. [tex]\( x = 52, y = 179 \)[/tex]
[tex]\[ y = 75 + 2(52) = 75 + 104 = 179 \quad \text{(Correct)} \][/tex]
All entries match, Table 2 is valid.
Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline 0 & 0 \\ \hline 19 & 113 \\ \hline 32 & 139 \\ \hline 47 & 169 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = 0, y = 0 \)[/tex]
[tex]\[ y = 75 + 2(0) = 75 + 0 = 75 \quad \text{(Incorrect)} \][/tex]
2. [tex]\( x = 19, y = 113 \)[/tex]
[tex]\[ y = 75 + 2(19) = 75 + 38 = 113 \quad \text{(Correct)} \][/tex]
3. [tex]\( x = 32, y = 139 \)[/tex]
[tex]\[ y = 75 + 2(32) = 75 + 64 = 139 \quad \text{(Correct)} \][/tex]
4. [tex]\( x = 47, y = 169 \)[/tex]
[tex]\[ y = 75 + 2(47) = 75 + 94 = 169 \quad \text{(Correct)} \][/tex]
Since the first entry does not match, Table 3 is not valid.
Table 4:
[tex]\[ \begin{array}{|c|c|} \hline \text{Minutes of Reading }( x ) & \text{Total Pages Read }( y ) \\ \hline 0 & 75 \\ \hline 11 & 97 \\ \hline \end{array} \][/tex]
For each entry, check if [tex]\( y = 75 + 2x \)[/tex]:
1. [tex]\( x = 0, y = 75 \)[/tex]
[tex]\[ y = 75 + 2(0) = 75 + 0 = 75 \quad \text{(Correct)} \][/tex]
2. [tex]\( x = 11, y = 97 \)[/tex]
[tex]\[ y = 75 + 2(11) = 75 + 22 = 97 \quad \text{(Correct)} \][/tex]
All entries match, Table 4 is valid.
### Conclusion
The viable tables that show the total number of pages Selma has read after [tex]\( x \)[/tex] minutes are Table 2 and Table 4.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.
