https://file.aiquickdraw.com/mathbot/file/1725586634097penu8ecl.jpg

It seems the image contains a math-related question. I will extract the content for analysis and provide a detailed solution. Let me process that.

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The visible content contains questions related to a demand and price function scenario. Here's what I can decipher from the image:

1. **General context**:
   - You are given two demand equations: $ q = -2p + 75 $ and $ q = -5p + 60 $, where $ q $ represents the number of items demanded and $ p $ is the price in dollars.
   - The task seems to involve analyzing both equations and answering several questions.

2. **Question breakdown**:
   - **(a)**: Which equation in the demand equation has a more negative slope?
     - Answer selected: Equation 2 is correct, as it has a slope of $ -5 $ compared to $ -2 $ in Equation 1, indicating a steeper negative slope.
   
   - **(b)**: How many items are demanded when $ p = 15 $ in Equation 1 and Equation 2?
     - The number of items can be calculated by substituting $ p = 15 $ into both equations:
       - For $ q = -2p + 75 $: 
         \[
         q = -2(15) + 75 = 45
         \]
       - For $ q = -5p + 60 $: 
         \[
         q = -5(15) + 60 = -15
         \]
     - It looks like the answers are meant to be written down based on this substitution.
   
   - **(c)**: What price will lead to zero demand in Equation 1?
     - Set $ q = 0 $ in Equation 1 and solve for $ p $:
       \[
       0 = -2p + 75 \implies 2p = 75 \implies p = 37.5
       \]
     - This means at a price of $ p = 37.5 $, the demand will be zero in Equation 1.
   
   - **(d)**: Predict how many items are demanded if the price is $10 in Equation 1 and Equation 2.
     - Substituting $ p = 10 $ into both equations:
       - For Equation 1: 
         \[
         q = -2(10) + 75 = 55
         \]
       - For Equation 2: 
         \[
         q = -5(10) + 60 = 10
         \]

Would you like more details on any part of this problem? Let me know if you'd like further clarifications!

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Here are 5 related questions:

1. What does the slope represent in a demand equation, and how does it affect the demand?
2. What real-world factors could influence a demand function to have a steeper slope?
3. If the price decreases from $15 to $10, how does the demand change for both equations?
4. How would you calculate the price elasticity of demand for each equation?
5. Can you graph both demand equations on the same coordinate plane and compare their behavior visually?

**Tip**: Understanding how to manipulate and interpret linear equations can be very useful in economics and business-related scenarios.

You are given two demand equations q = -2p + 75 and q = -5p + 60. Solve for demand at different price points and determine when demand equals zero.

Analyze and solve linear demand equations: q = -2p + 75 and q = -5p + 60. This exercise involves calculating demand at various prices, predicting zero demand, and interpreting economic implications. Ideal for students in Grades 9-11 studying algebra and economics.

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