The Height Of A Window Is 0.6 Feet Less Than 2.5 Times Its Width. If The Height Of The Window Is 4.9 Feet, Which Equation Can Be Used To Determine $x$, The Width Of The Window?A. $2.5x + 0.8 = 4.9$B. $2.5x - 0.6 = 4.9$C.

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Understanding the Relationship Between Height and Width

In this article, we will explore the relationship between the height and width of a window, and how to use mathematical equations to determine the width of the window given its height. We will use the given information to create an equation that can be used to solve for the width of the window.

The Given Information

The height of the window is 4.9 feet, and it is 0.6 feet less than 2.5 times its width. We can use this information to create an equation that relates the height and width of the window.

Creating the Equation

Let's start by using the given information to create an equation. We know that the height of the window is 4.9 feet, and it is 0.6 feet less than 2.5 times its width. We can write this as:

Height = 2.5 × Width - 0.6

We can substitute the given value for the height into this equation:

4.9 = 2.5 × Width - 0.6

Solving for the Width

Now that we have the equation, we can solve for the width of the window. To do this, we need to isolate the width term on one side of the equation. We can do this by adding 0.6 to both sides of the equation:

4.9 + 0.6 = 2.5 × Width

This simplifies to:

5.5 = 2.5 × Width

Next, we can divide both sides of the equation by 2.5 to solve for the width:

Width = 5.5 ÷ 2.5

Width = 2.2

The Final Equation

So, the equation that can be used to determine the width of the window is:

2.5x - 0.6 = 4.9

This equation can be used to solve for the width of the window given its height.

Conclusion

In this article, we used the given information to create an equation that relates the height and width of a window. We then solved for the width of the window using this equation. The final equation is:

2.5x - 0.6 = 4.9

This equation can be used to determine the width of the window given its height.

Discussion

The equation we derived in this article can be used to solve for the width of a window given its height. This is a simple example of how mathematical equations can be used to model real-world problems.

Mathematical Concepts

This article uses the following mathematical concepts:

  • Equations: An equation is a statement that two mathematical expressions are equal.
  • Variables: A variable is a value that can change.
  • Constants: A constant is a value that does not change.
  • Algebraic manipulation: Algebraic manipulation is the process of using mathematical operations to simplify or solve an equation.

Real-World Applications

This article has real-world applications in the following areas:

  • Architecture: Architects use mathematical equations to design buildings and windows.
  • Engineering: Engineers use mathematical equations to design and build structures.
  • Science: Scientists use mathematical equations to model and analyze data.

Conclusion

In conclusion, this article used the given information to create an equation that relates the height and width of a window. We then solved for the width of the window using this equation. The final equation is:

2.5x - 0.6 = 4.9

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to the height of a window and how to use mathematical equations to determine the width of the window.

Q: What is the relationship between the height and width of a window?

A: The height of a window is 0.6 feet less than 2.5 times its width.

Q: How can we use mathematical equations to determine the width of the window?

A: We can use the equation:

2.5x - 0.6 = 4.9

to determine the width of the window. This equation can be solved for x, which represents the width of the window.

Q: What is the value of x in the equation 2.5x - 0.6 = 4.9?

A: To solve for x, we need to isolate the x term on one side of the equation. We can do this by adding 0.6 to both sides of the equation:

2.5x = 4.9 + 0.6

This simplifies to:

2.5x = 5.5

Next, we can divide both sides of the equation by 2.5 to solve for x:

x = 5.5 ÷ 2.5

x = 2.2

Q: What is the width of the window if its height is 4.9 feet?

A: Using the equation 2.5x - 0.6 = 4.9, we can solve for x, which represents the width of the window. We have already determined that x = 2.2.

Q: Can we use this equation to determine the width of a window with a different height?

A: Yes, we can use this equation to determine the width of a window with a different height. We just need to substitute the new height value into the equation and solve for x.

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

A: This equation has real-world applications in the following areas:

  • Architecture: Architects use mathematical equations to design buildings and windows.
  • Engineering: Engineers use mathematical equations to design and build structures.
  • Science: Scientists use mathematical equations to model and analyze data.

Q: What mathematical concepts are used in this equation?

A: This equation uses the following mathematical concepts:

  • Equations: An equation is a statement that two mathematical expressions are equal.
  • Variables: A variable is a value that can change.
  • Constants: A constant is a value that does not change.
  • Algebraic manipulation: Algebraic manipulation is the process of using mathematical operations to simplify or solve an equation.

Conclusion

In conclusion, this article answers some frequently asked questions related to the height of a window and how to use mathematical equations to determine the width of the window. We have also discussed some real-world applications of this equation and the mathematical concepts used in it.

Additional Resources

For more information on mathematical equations and their applications, please refer to the following resources:

  • Mathematics textbooks: There are many mathematics textbooks available that cover the topics of equations, variables, and algebraic manipulation.
  • Online resources: There are many online resources available that provide information and examples on mathematical equations and their applications.
  • Mathematical software: There are many mathematical software packages available that can be used to solve and manipulate mathematical equations.

Final Thoughts

In conclusion, mathematical equations are a powerful tool for modeling and analyzing real-world problems. By understanding and using these equations, we can gain a deeper understanding of the world around us and make more informed decisions.