Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
### Part A: Situation Description with Area Output in Square Feet
Let's consider a real-world scenario to model the given function [tex]\( f(x) = (x)(2x + 5) \)[/tex].
#### Situation Description
Imagine you have a rectangular garden. The width of this garden is represented by [tex]\( x \)[/tex] feet. The length of this garden, however, is determined by the expression [tex]\( 2x + 5 \)[/tex] feet. This means that the length is always 5 feet more than twice the width.
To find the area of the garden, we use the formula for the area of a rectangle, which is:
[tex]\[ \text{Area} = \text{Width} \times \text{Length} \][/tex]
Given that the width [tex]\( x \)[/tex] and the length [tex]\( 2x + 5 \)[/tex] are defined in feet, the area of the garden can be modeled by the function:
[tex]\[ f(x) = x \cdot (2x + 5) \][/tex]
To summarize, in this situation:
- [tex]\( x \)[/tex] represents the width of the rectangular garden in feet.
- [tex]\( 2x + 5 \)[/tex] represents the length of the garden in feet.
- [tex]\( f(x) = x \cdot (2x + 5) \)[/tex] calculates the area of the garden in square feet.
#### Example Calculations
Let's say the width of the garden ([tex]\( x \)[/tex]) is 3 feet:
1. Calculate the length:
[tex]\[ \text{Length} = 2x + 5 = 2(3) + 5 = 6 + 5 = 11 \text{ feet} \][/tex]
2. Calculate the area using the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = 3 \cdot (2(3) + 5) = 3 \cdot 11 = 33 \text{ square feet} \][/tex]
So, if the width of the garden is 3 feet, the garden's area will be 33 square feet.
### Evaluation of my work
I provided a detailed description of a scenario that fits the given function [tex]\( f(x) = (x)(2x+5) \)[/tex]. By giving a real-world example of a rectangular garden, I effectively demonstrated how the function models the area in square feet. Additionally, I included a specific example calculation to further clarify how the function is applied. I believe my explanation is thorough and should help students grasp the concept and apply the function to similar problems.
Let's consider a real-world scenario to model the given function [tex]\( f(x) = (x)(2x + 5) \)[/tex].
#### Situation Description
Imagine you have a rectangular garden. The width of this garden is represented by [tex]\( x \)[/tex] feet. The length of this garden, however, is determined by the expression [tex]\( 2x + 5 \)[/tex] feet. This means that the length is always 5 feet more than twice the width.
To find the area of the garden, we use the formula for the area of a rectangle, which is:
[tex]\[ \text{Area} = \text{Width} \times \text{Length} \][/tex]
Given that the width [tex]\( x \)[/tex] and the length [tex]\( 2x + 5 \)[/tex] are defined in feet, the area of the garden can be modeled by the function:
[tex]\[ f(x) = x \cdot (2x + 5) \][/tex]
To summarize, in this situation:
- [tex]\( x \)[/tex] represents the width of the rectangular garden in feet.
- [tex]\( 2x + 5 \)[/tex] represents the length of the garden in feet.
- [tex]\( f(x) = x \cdot (2x + 5) \)[/tex] calculates the area of the garden in square feet.
#### Example Calculations
Let's say the width of the garden ([tex]\( x \)[/tex]) is 3 feet:
1. Calculate the length:
[tex]\[ \text{Length} = 2x + 5 = 2(3) + 5 = 6 + 5 = 11 \text{ feet} \][/tex]
2. Calculate the area using the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = 3 \cdot (2(3) + 5) = 3 \cdot 11 = 33 \text{ square feet} \][/tex]
So, if the width of the garden is 3 feet, the garden's area will be 33 square feet.
### Evaluation of my work
I provided a detailed description of a scenario that fits the given function [tex]\( f(x) = (x)(2x+5) \)[/tex]. By giving a real-world example of a rectangular garden, I effectively demonstrated how the function models the area in square feet. Additionally, I included a specific example calculation to further clarify how the function is applied. I believe my explanation is thorough and should help students grasp the concept and apply the function to similar problems.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
