Select The Correct Answer.Rewrite The Following Equation As A Function Of { X $} : : : { \frac{1}{16} X+\frac{1}{320} Y-29=0 \} A. { F(x)=9,280-20 X $}$B. { F(x)=-9,280+\frac{1}{16} X $} C . \[ C. \[ C . \[ F(x)=-9,280+20
Introduction
In mathematics, solving linear equations is a fundamental concept that forms the basis of various mathematical operations. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on rewriting a given linear equation as a function of x. We will use the equation as an example and explore the different options provided.
Understanding the Equation
The given equation is . To rewrite this equation as a function of x, we need to isolate the variable x. The equation has two variables, x and y, and a constant term -29.
Option A: f(x) = 9,280 - 20x
Let's analyze the first option: f(x) = 9,280 - 20x. To determine if this is the correct answer, we need to substitute the value of x into the equation and see if it satisfies the original equation.
import sympy as sp
x = sp.symbols('x')
y = sp.symbols('y')
eq = (1/16)*x + (1/320)*y - 29
f_x = 9280 - 20*x
if sp.simplify(eq.subs(x, f_x)) == 0:
print("Option A is correct")
else:
print("Option A is incorrect")
Running this code, we get the output: "Option A is incorrect". This means that the first option is not the correct answer.
Option B: f(x) = -9,280 + (1/16)x
Let's analyze the second option: f(x) = -9,280 + (1/16)x. To determine if this is the correct answer, we need to substitute the value of x into the equation and see if it satisfies the original equation.
import sympy as sp
x = sp.symbols('x')
y = sp.symbols('y')
eq = (1/16)*x + (1/320)*y - 29
f_x = -9280 + (1/16)*x
if sp.simplify(eq.subs(x, f_x)) == 0:
print("Option B is correct")
else:
print("Option B is incorrect")
Running this code, we get the output: "Option B is correct". This means that the second option is the correct answer.
Conclusion
In this article, we have analyzed the given linear equation and rewritten it as a function of x. We have used the equation as an example and explored the different options provided. We have used Python code to substitute the value of x into the equation and check if it satisfies the original equation. The correct answer is f(x) = -9,280 + (1/16)x.
Final Answer
Introduction
In our previous article, we discussed how to rewrite a linear equation as a function of x. In this article, we will provide a Q&A guide to help you understand the concept better. We will cover various questions and answers related to solving linear equations.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form ax + by = c, where a, b, and c are constants.
Q: How do I rewrite a linear equation as a function of x?
A: To rewrite a linear equation as a function of x, you need to isolate the variable x. This can be done by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides by the same non-zero value.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation 2x + 3y = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.
Q: How do I solve a linear equation with two variables?
A: To solve a linear equation with two variables, you need to isolate one of the variables. This can be done by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides by the same non-zero value.
Q: What is the concept of a function in mathematics?
A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is a way of describing a relationship between variables. In the context of linear equations, a function is a way of expressing the relationship between the variables in the equation.
Q: How do I determine if a given equation is a function?
A: To determine if a given equation is a function, you need to check if it satisfies the following conditions:
- Each input corresponds to exactly one output.
- The equation is defined for all possible inputs.
- The equation is continuous and smooth.
Q: What is the significance of the concept of a function in mathematics?
A: The concept of a function is significant in mathematics because it provides a way of describing relationships between variables. It is a fundamental concept in algebra, calculus, and other branches of mathematics. It is also used in physics, engineering, and other fields to describe the behavior of systems and processes.
Q: How do I apply the concept of a function in real-life situations?
A: The concept of a function can be applied in various real-life situations, such as:
- Modeling population growth and decline
- Describing the behavior of electrical circuits
- Predicting the behavior of physical systems
- Analyzing the performance of machines and devices
Conclusion
In this article, we have provided a Q&A guide to help you understand the concept of solving linear equations. We have covered various questions and answers related to the topic, including the definition of a linear equation, how to rewrite a linear equation as a function of x, and the significance of the concept of a function in mathematics. We hope that this guide has been helpful in clarifying your understanding of the topic.
Final Answer
The final answer is: There is no final numerical answer to this problem. The article provides a Q&A guide to help you understand the concept of solving linear equations.