When The Product Of 6 And The Square Of A Number Is Increased By 5 Times The Number, The Result Is 4. Which Equation Represents This Situation?A. $6x^2 + 5x - 4 = 0$B. $6x^2 + 5x + 4 = 0$C. $6^2 X + 5 + X = 4$D. $6 + X^2

Feb 27, 2025 by ADMIN 221 views

When the Product of 6 and the Square of a Number is Increased by 5 Times the Number, the Result is 4: A Mathematical Equation

Understanding the Problem

The problem presents a mathematical scenario where the product of 6 and the square of a number is increased by 5 times the number, resulting in 4. To represent this situation mathematically, we need to translate the given information into an equation. This requires a clear understanding of the problem and the ability to represent it using mathematical notation.

Breaking Down the Problem

Let's break down the problem step by step to understand it better:

The product of 6 and the square of a number is represented as $6x^2$ .
5 times the number is represented as $5x$ .
The result of increasing the product by 5 times the number is 4, which can be represented as $6x^2 + 5x = 4$ .

Representing the Situation Mathematically

To represent the situation mathematically, we need to set up an equation that reflects the given information. The equation should include the product of 6 and the square of the number, the increase by 5 times the number, and the resulting value of 4.

Equation Representation

Based on the breakdown of the problem, the equation that represents the situation is:

6x^2 + 5x = 4

However, this equation is not among the given options. To match the options, we need to rearrange the equation to set it equal to zero. This can be done by subtracting 4 from both sides of the equation:

6x^2 + 5x - 4 = 0

This equation matches option A.

Analyzing the Options

Let's analyze the other options to see why they are incorrect:

Option B: $6x^2 + 5x + 4 = 0$ is incorrect because it adds 4 to the right-hand side of the equation, which is not consistent with the given information.
Option C: $6^2 x + 5 + x = 4$ is incorrect because it incorrectly represents the product of 6 and the square of the number, and also adds 5 to the right-hand side of the equation.
Option D: $6 + x^2$ is incorrect because it does not represent the product of 6 and the square of the number, and also does not include the increase by 5 times the number.

Conclusion

In conclusion, the equation that represents the situation described in the problem is $6x^2 + 5x - 4 = 0$ . This equation accurately reflects the given information and can be used to solve for the value of x.

Key Takeaways

The product of 6 and the square of a number is represented as $6x^2$ .
5 times the number is represented as $5x$ .
The result of increasing the product by 5 times the number is 4, which can be represented as $6x^2 + 5x = 4$ .
The equation that represents the situation is $6x^2 + 5x - 4 = 0$ .

Mathematical Representation

The mathematical representation of the problem can be summarized as follows:

Let x be the number.
The product of 6 and the square of the number is $6x^2$ .
5 times the number is $5x$ .
The result of increasing the product by 5 times the number is 4, which can be represented as $6x^2 + 5x = 4$ .
The equation that represents the situation is $6x^2 + 5x - 4 = 0$ .

Solving the Equation

To solve the equation $6x^2 + 5x - 4 = 0$ , we can use various methods such as factoring, quadratic formula, or graphing. However, the specific method used to solve the equation is not relevant to the problem at hand, which is to identify the correct equation that represents the situation.

Final Answer

The final answer is option A: $6x^2 + 5x - 4 = 0$ .
When the Product of 6 and the Square of a Number is Increased by 5 Times the Number, the Result is 4: A Q&A Article

Q: What is the product of 6 and the square of a number?

A: The product of 6 and the square of a number is represented as $6x^2$ , where x is the number.

Q: How is 5 times the number represented mathematically?

A: 5 times the number is represented as $5x$ .

Q: What is the result of increasing the product by 5 times the number?

A: The result of increasing the product by 5 times the number is 4, which can be represented as $6x^2 + 5x = 4$ .

Q: What is the equation that represents the situation?

A: The equation that represents the situation is $6x^2 + 5x - 4 = 0$ .

Q: Why is the equation $6x^2 + 5x - 4 = 0$ the correct representation of the situation?

A: The equation $6x^2 + 5x - 4 = 0$ is the correct representation of the situation because it accurately reflects the given information. The product of 6 and the square of the number is $6x^2$ , 5 times the number is $5x$ , and the result of increasing the product by 5 times the number is 4.

Q: How can the equation $6x^2 + 5x - 4 = 0$ be solved?

A: The equation $6x^2 + 5x - 4 = 0$ can be solved using various methods such as factoring, quadratic formula, or graphing.

Q: What is the final answer to the problem?

A: The final answer to the problem is option A: $6x^2 + 5x - 4 = 0$ .

Frequently Asked Questions

Q: What is the difference between the product of 6 and the square of a number and 5 times the number? A: The product of 6 and the square of a number is $6x^2$ , while 5 times the number is $5x$ .
Q: How can the equation $6x^2 + 5x - 4 = 0$ be used in real-life situations? A: The equation $6x^2 + 5x - 4 = 0$ can be used to model real-life situations where the product of two quantities is increased by a certain amount.
Q: What is the significance of the number 4 in the equation $6x^2 + 5x - 4 = 0$ ? A: The number 4 in the equation $6x^2 + 5x - 4 = 0$ represents the result of increasing the product by 5 times the number.