Ask a New Question
Menu

Andre and Kara are collecting food for the food pantry in their neighborhood. For every person they ask to donate, they receive an average of 13 items. Create a table and graph an arithmetic sequence to model this scenario. What would be the most appropriate label for the y-axis?

Responses

neighborhood population

food pantry

number of people asked to donate

number of items donated

7 answers

To model the scenario where Andre and Kara collect food for the food pantry, we can create an arithmetic sequence based on the number of people they ask to donate and the corresponding number of items received. Since they receive an average of 13 items for every person asked, the sequence will increase by 13 with each additional person.

Table

| Number of People Asked to Donate (x) | Number of Items Donated (y) | |---------------------------------------|------------------------------| | 0 | 0 | | 1 | 13 | | 2 | 26 | | 3 | 39 | | 4 | 52 | | 5 | 65 |

Graph

To represent the data in a graph, the x-axis would be "Number of People Asked to Donate" and the y-axis would be "Number of Items Donated."

Most Appropriate Label for the Y-Axis

The most appropriate label for the y-axis in this scenario would be "number of items donated." This clearly conveys the quantity of items collected as they ask more people to donate.

Summary

  • X-axis: Number of People Asked to Donate
  • Y-axis: Number of Items Donated
  • Y-axis Label: "number of items donated"

You may plot the points from the table on a graph to visually represent the linear relationship, which would show a straight line increasing at a constant rate.

To show that arithmetic sequence formulas have the same structure as linear functions, choose the linear function equation that has the same structure as the arithmetic sequence an=6+(n−1)⋅8

Responses

y=8x−2

y=6x+8

y=8x+6

y=2x−8

To determine the linear function that has the same structure as the arithmetic sequence formula \( a_n = 6 + (n-1) \cdot 8 \), we can rewrite this arithmetic sequence formula into a more recognizable form and then identify which of the given options matches that structure.

Step 1: Rewrite the Arithmetic Sequence Formula

Starting with:

\[ a_n = 6 + (n - 1) \cdot 8 \]

Simplifying, we distribute the 8:

\[ a_n = 6 + 8n - 8 \]

Combining like terms:

\[ a_n = 8n - 2 \]

This is the equivalent linear expression.

Step 2: Compare with Given Options

Now we can compare this result, \( a_n = 8n - 2 \), with the provided linear function options:

  1. \( y = 8x - 2 \)
  2. \( y = 6x + 8 \)
  3. \( y = 8x + 6 \)
  4. \( y = 2x - 8 \)

The correct choice is:

\( y = 8x - 2 \)

Conclusion

The linear function equation that has the same structure as the arithmetic sequence \( a_n = 6 + (n-1) \cdot 8 \) is \( y = 8x - 2 \).

Use the table to answer the question.

x y
2 a
4 b
Use the arithmetic sequence formula an=−8+(n−1)⋅2 to find the missing values in the table.

Responses

a=−15

a=−6

a=−10

a=−12

To find the missing values in the table, we'll use the given arithmetic sequence formula:

\[ a_n = -8 + (n - 1) \cdot 2 \]

Calculate \(a\) (when \(x = 2\))

  1. Substitute \(n = 2\) into the formula: \[ a_2 = -8 + (2 - 1) \cdot 2 \] Simplifying this gives: \[ a_2 = -8 + 1 \cdot 2 \] \[ a_2 = -8 + 2 = -6 \]

So, \( a = -6 \).

Calculate \(b\) (when \(x = 4\))

  1. Substitute \(n = 4\) into the formula: \[ a_4 = -8 + (4 - 1) \cdot 2 \] Simplifying this gives: \[ a_4 = -8 + 3 \cdot 2 \] \[ a_4 = -8 + 6 = -2 \]

So, \( b = -2 \).

Summary

  • The values for the table are:
    • \( a = -6 \)
    • \( b = -2 \)

Response to Your Question

The correct answer for \( a \) is \( a = -6 \).

Alex and Jesse are baking holiday muffins. On day one, they baked five muffins, on day two, they baked 11 muffins, and on day three, they baked 17 muffins. What is the slope for this arithmetic sequence?
Responses:
1

6

−1

−6

To find the slope of the arithmetic sequence in which Alex and Jesse baked muffins, we can observe how many muffins were baked each day:

  • Day 1: 5 muffins
  • Day 2: 11 muffins
  • Day 3: 17 muffins

Step 1: Calculate the differences between the terms

From Day 1 to Day 2:

  • \( 11 - 5 = 6 \)

From Day 2 to Day 3:

  • \( 17 - 11 = 6 \)

In both cases, the difference is consistent at 6 muffins.

Step 2: Identify the slope

In an arithmetic sequence, the common difference represents the slope. Thus, the slope is:

6

Conclusion

The correct response for the slope of this arithmetic sequence is 6.