Answer the following questions accurately

Question

The linear function m = 50 - 9d represents the amount of m (in dollars) of your money you have left after buying d DVDs

a. Interpret the terms and coefficient in the equation 
b. Find the domain of the function. Is the domain discrete or continuous?

GPT-4o mini · Answer

Sure! Let's break down the linear function $ m = 50 - 9d $ step by step.

a. Interpret the terms and coefficient in the equation

m: This represents the amount of money (in dollars) you have left after purchasing DVDs.
d: This is the number of DVDs you have bought.
50: This is the initial amount of money you have (in dollars) before purchasing any DVDs.
-9: This is the coefficient of $ d $, representing the cost of each DVD. Specifically, it indicates that each DVD costs $9. As you buy more DVDs (increase $ d $), your remaining money decreases by $9 for each additional DVD purchased.

b. Find the domain of the function. Is the domain discrete or continuous?

The domain of the function represents the valid values of $ d $ (the number of DVDs bought). In this context:

$ d $ cannot be negative because you cannot buy a negative number of DVDs.
The maximum number of DVDs you can buy occurs when $ m $ reaches zero (i.e., you spend all your money). To find the maximum $ d $, we can set $ m = 0 $ and solve for $ d $:

\[ 0 = 50 - 9d \ 9d = 50 \ d = \frac{50}{9} \approx 5.56 \]

Since you cannot buy a fraction of a DVD, the maximum whole number of DVDs you can buy is 5.

Thus, the domain of $ d $ in the context of this equation is:

\[ d \in {0, 1, 2, 3, 4, 5} \]

This shows that the values of $ d $ can only take on whole numbers from 0 to 5.

Is the domain discrete or continuous?

The domain is discrete because $ d $ can only take integer values (whole numbers) rather than every possible real number in the interval.

Answer

Simplify to just the answer, please.

GPT-4o mini · Answer

a. **Interpretation**: - **m**: Money left (in dollars). - **d**: Number of DVDs bought. - **50**: Initial money (in dollars). - **-9**: Cost per DVD (in dollars). b. **Domain**: $ d \in \{0, 1, 2, 3, 4, 5\} $ (discrete).

Answer

Now if I were the graph it, what would be the points

GPT-4o mini · Answer

To graph the function $ m = 50 - 9d $, you can find the points by substituting values for $ d $ (from 0 to 5) into the equation: 1. $ d = 0 $: $ m = 50 - 9(0) = 50 $ → Point: $ (0, 50) $ 2. $ d = 1 $: $ m = 50 - 9(1) = 41 $ → Point: $ (1, 41) $ 3. $ d = 2 $: $ m = 50 - 9(2) = 32 $ → Point: $ (2, 32) $ 4. $ d = 3 $: $ m = 50 - 9(3) = 23 $ → Point: $ (3, 23) $ 5. $ d = 4 $: $ m = 50 - 9(4) = 14 $ → Point: $ (4, 14) $ 6. $ d = 5 $: $ m = 50 - 9(5) = 5 $ → Point: $ (5, 5) $ ### Points: - $ (0, 50) $ - $ (1, 41) $ - $ (2, 32) $ - $ (3, 23) $ - $ (4, 14) $ - $ (5, 5) $

Answer

No, the points of the function using the domain

GPT-4o mini · Answer

Apologies for the oversight. Here are the points of the function $ m = 50 - 9d $ based on the discrete domain $ d \in \{0, 1, 2, 3, 4, 5\} $: - For $ d = 0 $: $ m = 50 - 9(0) = 50 $ → Point: $ (0, 50) $ - For $ d = 1 $: $ m = 50 - 9(1) = 41 $ → Point: $ (1, 41) $ - For $ d = 2 $: $ m = 50 - 9(2) = 32 $ → Point: $ (2, 32) $ - For $ d = 3 $: $ m = 50 - 9(3) = 23 $ → Point: $ (3, 23) $ - For $ d = 4 $: $ m = 50 - 9(4) = 14 $ → Point: $ (4, 14) $ - For $ d = 5 $: $ m = 50 - 9(5) = 5 $ → Point: $ (5, 5) $ ### Points based on the domain: - $ (0, 50) $ - $ (1, 41) $ - $ (2, 32) $ - $ (3, 23) $ - $ (4, 14) $ - $ (5, 5) $

Answer

My grid is only 10x10. Graph the fiction using its domain.

GPT-4o mini · Answer

Since the grid is only 10x10, we will only plot the points within that grid and limit our consideration to the maximum $m$ value that fits within the constraints of the grid.

Given the points based on the original domain $ d \in {0, 1, 2, 3, 4, 5} $:

$ (0, 50) $ - This point is outside the 10x10 grid.
$ (1, 41) $ - This point is also outside the grid.
$ (2, 32) $ - This point is outside the grid.
$ (3, 23) $ - This point is outside the grid.
$ (4, 14) $ - This point is outside the grid.
$ (5, 5) $ - This point is within the grid.

Points on a 10x10 Grid:

Since all points except $ (5, 5) $ are outside the 10x10 grid range, the only point you can plot is:

$ (5, 5) $

Summary:

The only point to graph on a 10x10 grid is $ (5, 5) $.