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. $2.5x + 0.6 = 4.9$B. $2.5x - 0.6 = 4.9$C.
Introduction
In mathematics, equations are used to represent relationships between variables. In this article, we will explore a real-world scenario involving the height and width of a window. We will use mathematical equations to determine the width of the window, given its height.
The Problem
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 , the width of the window?
Understanding the Relationship Between Height and Width
Let's break down the given information. The height of the window is 0.6 feet less than 2.5 times its width. This can be represented as:
Height = 2.5 脳 Width - 0.6
We are given that the height of the window is 4.9 feet. We can substitute this value into the equation:
4.9 = 2.5 脳 Width - 0.6
Solving for Width
To solve for the width, we need to isolate the variable Width. We can do this by adding 0.6 to both sides of the equation:
4.9 + 0.6 = 2.5 脳 Width
This simplifies to:
5.5 = 2.5 脳 Width
Next, we can divide both sides of the equation by 2.5 to solve for Width:
Width = 5.5 梅 2.5
Width = 2.2
Writing the Equation
Now that we have solved for Width, we can write the equation that represents the relationship between the height and width of the window:
2.5 脳 Width - 0.6 = 4.9
This equation can be rewritten as:
2.5x - 0.6 = 4.9
where x represents the width of the window.
Conclusion
In this article, we used mathematical equations to determine the width of a window, given its height. We started with a real-world scenario and used algebraic manipulations to isolate the variable Width. The resulting 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 2.5x - 0.6 = 4.9 is a linear equation, which means it can be represented graphically as a straight line. The slope of the line represents the coefficient of x, which is 2.5 in this case. The y-intercept represents the constant term, which is -0.6 in this case.
Answer
The correct equation is:
2.5x - 0.6 = 4.9
This equation can be used to determine the width of the window, given its height.
Comparison of Options
Let's compare the given options:
A. 2.5x + 0.6 = 4.9
This equation is incorrect because it adds 0.6 to the left-hand side, rather than subtracting it.
B. 2.5x - 0.6 = 4.9
This equation is correct because it subtracts 0.6 from the left-hand side, as required by the problem.
C. 2.5x + 0.6 = 4.9
This equation is incorrect because it adds 0.6 to the left-hand side, rather than subtracting it.
Final Answer
The correct equation is:
2.5x - 0.6 = 4.9
This equation can be used to determine the width of the window, given its height.
Introduction
In our previous article, we explored a real-world scenario involving the height and width of a window. We used mathematical equations to determine the width of the window, given its height. In this article, we will answer some frequently asked questions related to the topic.
Q&A
Q: What is the relationship between the height and width of the window?
A: The height of the window is 0.6 feet less than 2.5 times its width. This can be represented as:
Height = 2.5 脳 Width - 0.6
Q: How do I determine the width of the window, given its height?
A: To determine the width of the window, you can use the equation:
2.5x - 0.6 = 4.9
where x represents the width of the window.
Q: What if the height of the window is not 4.9 feet? How do I adjust the equation?
A: If the height of the window is not 4.9 feet, you can simply substitute the given height into the equation:
2.5x - 0.6 = Height
For example, if the height of the window is 5.5 feet, the equation would be:
2.5x - 0.6 = 5.5
Q: Can I use this equation to determine the height of the window, given its width?
A: Yes, you can use the equation to determine the height of the window, given its width. Simply rearrange the equation to isolate the height:
Height = 2.5x - 0.6
Q: What if I want to find the width of the window, but I don't know the height?
A: In that case, you will need to use a different equation or approach. The equation we derived assumes that the height of the window is known.
Q: Can I use this equation to determine the width of multiple windows?
A: Yes, you can use this equation to determine the width of multiple windows, as long as you know the height of each window.
Q: What if the width of the window is not a whole number? How do I handle that?
A: If the width of the window is not a whole number, you can simply use the decimal value. For example, if the width of the window is 2.2 feet, you can use that value in the equation.
Conclusion
In this article, we answered some frequently asked questions related to the topic of the height and width of a window. We provided equations and explanations to help you determine the width of the window, given its height.
Discussion
The equation 2.5x - 0.6 = Height is a linear equation, which means it can be represented graphically as a straight line. The slope of the line represents the coefficient of x, which is 2.5 in this case. The y-intercept represents the constant term, which is -0.6 in this case.
Final Answer
The correct equation to determine the width of the window, given its height, is:
2.5x - 0.6 = Height
This equation can be used to determine the width of the window, given its height.