Select The Correct Answer.Dan Is Tiling His Rectangular, Concrete Porch With Square, Porcelain Tiles. The Length Of The Porch Is Represented By The Function $l(x) = 4x + 9$, Where $x$ Is The Side Length, In Feet, Of Each Tile. The

Introduction

In this article, we will delve into a mathematical problem that involves tiling a rectangular, concrete porch with square, porcelain tiles. The length of the porch is represented by the function $l(x) = 4x + 9$, where $x$ is the side length, in feet, of each tile. Our goal is to determine the correct answer to this problem, which requires a thorough understanding of mathematical concepts and problem-solving strategies.

Understanding the Problem

The problem states that Dan is tiling his rectangular, concrete porch with square, porcelain tiles. The length of the porch is represented by the function $l(x) = 4x + 9$, where $x$ is the side length, in feet, of each tile. This means that the length of the porch is dependent on the side length of each tile. To find the correct answer, we need to understand how the length of the porch changes as the side length of each tile increases.

Analyzing the Function

The function $l(x) = 4x + 9$ represents the length of the porch in terms of the side length of each tile, $x$. To analyze this function, we can start by finding the domain of the function, which is the set of all possible values of $x$. Since the side length of each tile cannot be negative, the domain of the function is $x \geq 0$.

Next, we can find the range of the function, which is the set of all possible values of $l(x)$. To do this, we can substitute different values of $x$ into the function and find the corresponding values of $l(x)$. For example, if $x = 1$, then $l(x) = 4(1) + 9 = 13$. If $x = 2$, then $l(x) = 4(2) + 9 = 17$. We can continue this process to find the range of the function.

Finding the Correct Answer

To find the correct answer, we need to determine the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile. In other words, we need to find the value of $x$ such that $l(x)$ is a multiple of $x$. To do this, we can use the fact that $l(x) = 4x + 9$ is a linear function, which means that it has a constant rate of change.

Let's assume that the length of the porch is $L$ feet. Then, we can set up the equation $L = 4x + 9$ and solve for $x$. This will give us the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile.

Solving the Equation

To solve the equation $L = 4x + 9$, we can start by subtracting 9 from both sides of the equation, which gives us $L - 9 = 4x$. Next, we can divide both sides of the equation by 4, which gives us $\frac{L - 9}{4} = x$.

This means that the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile is $\frac{L - 9}{4}$.

Conclusion

In this article, we have analyzed the problem of tiling a rectangular, concrete porch with square, porcelain tiles. We have found that the length of the porch is represented by the function $l(x) = 4x + 9$, where $x$ is the side length, in feet, of each tile. We have also determined that the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile is $\frac{L - 9}{4}$.

Final Answer

The final answer to this problem is $\boxed{\frac{L - 9}{4}}$.

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "Calculus" by James Stewart

Additional Resources

• [1] Khan Academy: Algebra and Trigonometry
• [2] MIT OpenCourseWare: Calculus

Mathematical Concepts

• Linear functions
• Domain and range of a function
• Solving linear equations

Problem-Solving Strategies

• Analyzing the function
• Finding the domain and range of the function
• Solving the equation

Real-World Applications

• Tiling a rectangular, concrete porch with square, porcelain tiles
• Finding the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile.
  Q&A: Selecting the Correct Answer - A Mathematical Approach to Tiling a Rectangular Porch =====================================================================================

Introduction

In our previous article, we analyzed the problem of tiling a rectangular, concrete porch with square, porcelain tiles. We found that the length of the porch is represented by the function $l(x) = 4x + 9$, where $x$ is the side length, in feet, of each tile. We also determined that the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile is $\frac{L - 9}{4}$.

In this article, we will answer some of the most frequently asked questions related to this problem.

Q: What is the domain of the function $l(x) = 4x + 9$?

A: The domain of the function $l(x) = 4x + 9$ is $x \geq 0$, since the side length of each tile cannot be negative.

Q: What is the range of the function $l(x) = 4x + 9$?

A: The range of the function $l(x) = 4x + 9$ is all real numbers, since the length of the porch can be any positive value.

Q: How do I find the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile?

A: To find the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile, you can use the equation $L = 4x + 9$ and solve for $x$. This will give you the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile.

Q: What is the final answer to this problem?

A: The final answer to this problem is $\boxed{\frac{L - 9}{4}}$.

Q: What are some real-world applications of this problem?

A: Some real-world applications of this problem include:

• Tiling a rectangular, concrete porch with square, porcelain tiles
• Finding the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile
• Designing a rectangular, concrete porch with a specific length and width

Q: What are some mathematical concepts that are used in this problem?

A: Some mathematical concepts that are used in this problem include:

• Linear functions
• Domain and range of a function
• Solving linear equations

Q: What are some problem-solving strategies that can be used to solve this problem?

A: Some problem-solving strategies that can be used to solve this problem include:

• Analyzing the function
• Finding the domain and range of the function
• Solving the equation

Conclusion

In this article, we have answered some of the most frequently asked questions related to the problem of tiling a rectangular, concrete porch with square, porcelain tiles. We have also provided some real-world applications and mathematical concepts that are used in this problem.

Final Thoughts

The problem of tiling a rectangular, concrete porch with square, porcelain tiles is a classic example of a mathematical problem that requires a thorough understanding of mathematical concepts and problem-solving strategies. By analyzing the function, finding the domain and range of the function, and solving the equation, we can find the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile.

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "Calculus" by James Stewart

Additional Resources

• [1] Khan Academy: Algebra and Trigonometry
• [2] MIT OpenCourseWare: Calculus

Mathematical Concepts

• Linear functions
• Domain and range of a function
• Solving linear equations

Problem-Solving Strategies

• Analyzing the function
• Finding the domain and range of the function
• Solving the equation

Real-World Applications

• Tiling a rectangular, concrete porch with square, porcelain tiles
• Finding the value of $x$ that results in a length of the porch that is a multiple of the side length of each tile
• Designing a rectangular, concrete porch with a specific length and width