Unfortunately, I am unable to view images or graphics that you might be referencing in your questions. However, I can help you with each question based on the descriptions and information provided.
Question 1
To determine how many tables would be needed for 16 people using the provided seating arrangements:
- 1 table seats 4 people (4 people/table)
- 2 tables seat 6 people each (6 people/table)
- 3 tables seat 8 people each (8 people/table)
You may notice a pattern:
- The first group: 1 table → 4 people
- The second group: 2 tables → 6 people (totaling 12)
- The third group: 3 tables → 8 people (totaling 24)
The pattern indicates that with additional tables, the seating can accommodate 4, 12, and 24 people respectively. The increase in people per table can be checked by looking at the arrangement of people and tables: If you follow the increments from 4 to 6 to 8 people across 1, 2, and 3 tables, let's find the next figure (16). From the earlier deduced pattern:
- 1 table = 4 people
- 2 tables = 12 people (2 tables with 6 = 12)
- If we introduce one more:
To seat 16 people, we can use 4 people per table, so:
- 16 people would require 4 tables (4 people per table).
Thus, the answer is 4 tables.
Question 2
Using the table values given: | Time (Minutes) | Distance (Feet) | |---------------------|------------------| | 1 | 75 | | 2 | 150 | | 3 | 225 | | 4 | 300 |
The relationship here shows that for each minute (x), the distance (y) increases by 75 feet. The distance can be represented linearly in the form y = mx + b, where m is the slope (rate of change):
- The slope (m) = 75 feet/minute and b is the initial distance when x = 0, which is 0 feet.
Therefore, the formula can be written as: y = 75x.
Question 3
To determine whether the graph accurately depicts the formula y = 32x + 6, you would check if:
- The y-intercept would be (0, 6)
- The slope is 32, meaning for every 1 unit increase in x, y should increase by 32.
Without the image, it's hard to confirm, but you can enter 1 for yes if the graph matches these parameters, or 2 for no if it does not.
Question 4
Without the image to reference, I can't provide the next point specifically, but if the use of a linear equation is followed, you would use the slope and the last known point to find the next.
If, for example, the last known point is (x, y), the next point's x value would be x + 1 while the y value would follow the increase dictated by the slope.
Question 5
The rate of change of a graph could be derived from the slope of the linear representation. If, for instance, the equation was in the form of y = mx + b, 'm' would provide you the rate of change directly.
In the context of Question 2 where the relationship was established as y = 75x, the rate of change would be 75 feet per minute.
If you could provide me additional context or specifics without needing to view images, I can help you further!
1 answer