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Sagot :
To analyze the given statements, we will refer to the data provided in the table and the given equations for the heights of Plant 1 and Plant 2 over the weeks.
### Given Data
The table indicates the heights (in inches) of Plant 1 and Plant 2 over a series of weeks.
| Week (w) | Plant 1 (h1) | Plant 2 (h2) |
|------------|--------------|--------------|
| 0 | 2.5 | 2.5 |
| 1 | 2.9 | 2.7 |
| 2 | 3.1 | 2.9 |
| 3 | 3.5 | 3.1 |
| 4 | 3.9 | 3.3 |
### Provided Equations
- For Plant 1: [tex]\(h_1 = 2.5 + 0.4w\)[/tex]
- For Plant 2: [tex]\(h_2 = 2.5 + 0.2w\)[/tex]
### Statements to Verify
1. The table shows a partial representation of the equations.
- To verify if the table is a partial representation of the given equations, we need to check if the height values given in the table match the values calculated using the equations across the weeks specified.
Calculated Heights for Plant 1:
- Week 0: [tex]\(2.5 + 0.4 \times 0 = 2.5\)[/tex]
- Week 1: [tex]\(2.5 + 0.4 \times 1 = 2.9\)[/tex]
- Week 2: [tex]\(2.5 + 0.4 \times 2 = 3.3\)[/tex]
- Week 3: [tex]\(2.5 + 0.4 \times 3 = 3.7\)[/tex]
- Week 4: [tex]\(2.5 + 0.4 \times 4 = 4.1\)[/tex]
Calculated Heights for Plant 2:
- Week 0: [tex]\(2.5 + 0.2 \times 0 = 2.5\)[/tex]
- Week 1: [tex]\(2.5 + 0.2 \times 1 = 2.7\)[/tex]
- Week 2: [tex]\(2.5 + 0.2 \times 2 = 2.9\)[/tex]
- Week 3: [tex]\(2.5 + 0.2 \times 3 = 3.1\)[/tex]
- Week 4: [tex]\(2.5 + 0.2 \times 4 = 3.3\)[/tex]
Comparing these heights with the table:
- Plant 1 heights calculated vs. table: [tex]\([2.5, 2.9, 3.3, 3.7, 4.1] \neq [2.5, 2.9, 3.1, 3.5, 3.9]\)[/tex]
- Plant 2 heights calculated vs. table: [tex]\([2.5, 2.7, 2.9, 3.1, 3.3] = [2.5, 2.7, 2.9, 3.1, 3.3]\)[/tex]
Since one of the heights does not fully match, the statement "The table shows a partial representation of the equations" is False.
2. (2, 3.1) is an ordered pair from the table.
- We need to check if the pair [tex]\((w = 2, h = 3.1)\)[/tex] exists in the table.
- For Plant 1 (Week 2, Height 3.1) exists in the table.
Therefore, this statement is True.
3. Plant 1 grew faster than Plant 2.
- Growth rate for Plant 1: [tex]\(0.4\)[/tex] inches per week.
- Growth rate for Plant 2: [tex]\(0.2\)[/tex] inches per week.
Since [tex]\(0.4 > 0.2\)[/tex], this statement is True.
4. Both plants died at week 4.
- The table indicates heights for both plants at week 4.
- Plant 1 at Week 4: [tex]\(3.9\)[/tex]
- Plant 2 at Week 4: [tex]\(3.3\)[/tex]
Neither plant has a height of [tex]\(0.0\)[/tex], indicating they are both alive.
Therefore, this statement is False.
### Conclusion
Based on the analysis, the supported statements are:
- (2, 3.1) is an ordered pair from the table.
- Plant 1 grew faster than Plant 2.
The final results are:
- The table shows a partial representation of the equations - False
- (2, 3.1) is an ordered pair from the table - True
- Plant 1 grew faster than Plant 2 - True
- Both plants died at week 4 - False
### Given Data
The table indicates the heights (in inches) of Plant 1 and Plant 2 over a series of weeks.
| Week (w) | Plant 1 (h1) | Plant 2 (h2) |
|------------|--------------|--------------|
| 0 | 2.5 | 2.5 |
| 1 | 2.9 | 2.7 |
| 2 | 3.1 | 2.9 |
| 3 | 3.5 | 3.1 |
| 4 | 3.9 | 3.3 |
### Provided Equations
- For Plant 1: [tex]\(h_1 = 2.5 + 0.4w\)[/tex]
- For Plant 2: [tex]\(h_2 = 2.5 + 0.2w\)[/tex]
### Statements to Verify
1. The table shows a partial representation of the equations.
- To verify if the table is a partial representation of the given equations, we need to check if the height values given in the table match the values calculated using the equations across the weeks specified.
Calculated Heights for Plant 1:
- Week 0: [tex]\(2.5 + 0.4 \times 0 = 2.5\)[/tex]
- Week 1: [tex]\(2.5 + 0.4 \times 1 = 2.9\)[/tex]
- Week 2: [tex]\(2.5 + 0.4 \times 2 = 3.3\)[/tex]
- Week 3: [tex]\(2.5 + 0.4 \times 3 = 3.7\)[/tex]
- Week 4: [tex]\(2.5 + 0.4 \times 4 = 4.1\)[/tex]
Calculated Heights for Plant 2:
- Week 0: [tex]\(2.5 + 0.2 \times 0 = 2.5\)[/tex]
- Week 1: [tex]\(2.5 + 0.2 \times 1 = 2.7\)[/tex]
- Week 2: [tex]\(2.5 + 0.2 \times 2 = 2.9\)[/tex]
- Week 3: [tex]\(2.5 + 0.2 \times 3 = 3.1\)[/tex]
- Week 4: [tex]\(2.5 + 0.2 \times 4 = 3.3\)[/tex]
Comparing these heights with the table:
- Plant 1 heights calculated vs. table: [tex]\([2.5, 2.9, 3.3, 3.7, 4.1] \neq [2.5, 2.9, 3.1, 3.5, 3.9]\)[/tex]
- Plant 2 heights calculated vs. table: [tex]\([2.5, 2.7, 2.9, 3.1, 3.3] = [2.5, 2.7, 2.9, 3.1, 3.3]\)[/tex]
Since one of the heights does not fully match, the statement "The table shows a partial representation of the equations" is False.
2. (2, 3.1) is an ordered pair from the table.
- We need to check if the pair [tex]\((w = 2, h = 3.1)\)[/tex] exists in the table.
- For Plant 1 (Week 2, Height 3.1) exists in the table.
Therefore, this statement is True.
3. Plant 1 grew faster than Plant 2.
- Growth rate for Plant 1: [tex]\(0.4\)[/tex] inches per week.
- Growth rate for Plant 2: [tex]\(0.2\)[/tex] inches per week.
Since [tex]\(0.4 > 0.2\)[/tex], this statement is True.
4. Both plants died at week 4.
- The table indicates heights for both plants at week 4.
- Plant 1 at Week 4: [tex]\(3.9\)[/tex]
- Plant 2 at Week 4: [tex]\(3.3\)[/tex]
Neither plant has a height of [tex]\(0.0\)[/tex], indicating they are both alive.
Therefore, this statement is False.
### Conclusion
Based on the analysis, the supported statements are:
- (2, 3.1) is an ordered pair from the table.
- Plant 1 grew faster than Plant 2.
The final results are:
- The table shows a partial representation of the equations - False
- (2, 3.1) is an ordered pair from the table - True
- Plant 1 grew faster than Plant 2 - True
- Both plants died at week 4 - False
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