What Is The Value Of The Expression When $n=3$?$\frac{6(n^2+2)}{n}$A. 16 B. 22 C. 30 D. 66

Introduction

In mathematics, expressions are a fundamental concept that helps us represent complex ideas in a concise and organized manner. When we are given an expression and asked to find its value for a specific variable, we need to substitute the given value into the expression and simplify it to obtain the final result. In this article, we will explore the value of the expression $\frac{6(n^2+2)}{n}$ when $n=3$.

Understanding the Expression

The given expression is $\frac{6(n^2+2)}{n}$. To find its value when $n=3$, we need to substitute $n=3$ into the expression and simplify it. Let's break down the expression into smaller parts to understand it better.

The expression consists of three main parts:

1. The numerator: $6(n^2+2)$
2. The denominator: $n$
3. The fraction: $\frac{6(n^2+2)}{n}$

Substituting n=3 into the Expression

Now that we have a clear understanding of the expression, let's substitute $n=3$ into it.

$\frac{6(n^2+2)}{n}$

Substituting $n=3$ into the expression, we get:

$\frac{6((3)^2+2)}{3}$

Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expression inside the parentheses.
2. Exponents: Evaluate any exponents (such as squaring a number).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Let's simplify the expression step by step:

1. Evaluate the expression inside the parentheses:

$(3)^2 = 9$

So, the expression becomes:

$\frac{6(9+2)}{3}$

2. Add 9 and 2:

$9+2 = 11$

So, the expression becomes:

$\frac{6(11)}{3}$

3. Multiply 6 and 11:

$6(11) = 66$

So, the expression becomes:

$\frac{66}{3}$

4. Divide 66 by 3:

$\frac{66}{3} = 22$

Conclusion

Therefore, the value of the expression when $n=3$ is $\boxed{22}$.

Final Answer

The final answer is $\boxed{22}$.

Discussion

The expression $\frac{6(n^2+2)}{n}$ is a simple algebraic expression that can be simplified using basic algebraic operations. When we substitute $n=3$ into the expression, we get a value of 22. This problem requires the application of basic algebraic concepts, such as substitution and simplification, to obtain the final result.

Related Problems

If you are interested in exploring more problems like this, here are a few related problems:

• Find the value of the expression $\frac{4(x^2-3)}{x}$ when $x=2$.
• Simplify the expression $\frac{3(y^2+5)}{y}$ and find its value when $y=4$.
• Find the value of the expression $\frac{2(z^2-2)}{z}$ when $z=3$.

These problems require the application of basic algebraic concepts, such as substitution and simplification, to obtain the final result.

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Introduction

In our previous article, we explored the value of the expression $\frac{6(n^2+2)}{n}$ when $n=3$. We also discussed the importance of understanding algebraic expressions and how to simplify them using basic algebraic operations. In this article, we will answer some frequently asked questions (FAQs) about the expression $\frac{6(n^2+2)}{n}$.

Q&A

Q1: What is the value of the expression $\frac{6(n^2+2)}{n}$ when $n=0$?

A1: The expression $\frac{6(n^2+2)}{n}$ is undefined when $n=0$ because division by zero is not allowed in mathematics.

Q2: Can I simplify the expression $\frac{6(n^2+2)}{n}$ using algebraic manipulations?

A2: Yes, you can simplify the expression $\frac{6(n^2+2)}{n}$ using algebraic manipulations. To simplify the expression, you can start by factoring the numerator and then canceling out any common factors between the numerator and the denominator.

Q3: What is the value of the expression $\frac{6(n^2+2)}{n}$ when $n=1$?

A3: To find the value of the expression $\frac{6(n^2+2)}{n}$ when $n=1$, you can substitute $n=1$ into the expression and simplify it. The expression becomes $\frac{6(1^2+2)}{1}$, which simplifies to $\frac{6(3)}{1} = 18$.

Q4: Can I use the expression $\frac{6(n^2+2)}{n}$ to model real-world problems?

A4: Yes, you can use the expression $\frac{6(n^2+2)}{n}$ to model real-world problems. For example, you can use the expression to model the cost of producing a certain number of items, where the cost is proportional to the number of items produced.

Q5: How can I graph the expression $\frac{6(n^2+2)}{n}$?

A5: To graph the expression $\frac{6(n^2+2)}{n}$, you can use a graphing calculator or a computer algebra system. You can also use algebraic manipulations to rewrite the expression in a form that is easier to graph.

Q6: What is the domain of the expression $\frac{6(n^2+2)}{n}$?

A6: The domain of the expression $\frac{6(n^2+2)}{n}$ is all real numbers except $n=0$, because division by zero is not allowed in mathematics.

Q7: Can I use the expression $\frac{6(n^2+2)}{n}$ to solve equations?

A7: Yes, you can use the expression $\frac{6(n^2+2)}{n}$ to solve equations. For example, you can use the expression to solve the equation $\frac{6(n^2+2)}{n} = 18$.

Q8: How can I use the expression $\frac{6(n^2+2)}{n}$ to model population growth?

A8: You can use the expression $\frac{6(n^2+2)}{n}$ to model population growth by assuming that the population grows at a rate proportional to the current population.

Q9: What is the range of the expression $\frac{6(n^2+2)}{n}$?

A9: The range of the expression $\frac{6(n^2+2)}{n}$ is all real numbers except 0, because the expression is always positive.

Q10: Can I use the expression $\frac{6(n^2+2)}{n}$ to model financial problems?

A10: Yes, you can use the expression $\frac{6(n^2+2)}{n}$ to model financial problems. For example, you can use the expression to model the cost of borrowing money at a certain interest rate.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) about the expression $\frac{6(n^2+2)}{n}$. We have discussed the importance of understanding algebraic expressions and how to simplify them using basic algebraic operations. We have also provided examples of how to use the expression to model real-world problems and how to graph the expression.

Final Answer

The final answer is $\boxed{22}$.

Discussion

The expression $\frac{6(n^2+2)}{n}$ is a simple algebraic expression that can be simplified using basic algebraic operations. When we substitute $n=3$ into the expression, we get a value of 22. This problem requires the application of basic algebraic concepts, such as substitution and simplification, to obtain the final result.

Related Problems

If you are interested in exploring more problems like this, here are a few related problems:

• Find the value of the expression $\frac{4(x^2-3)}{x}$ when $x=2$.
• Simplify the expression $\frac{3(y^2+5)}{y}$ and find its value when $y=4$.
• Find the value of the expression $\frac{2(z^2-2)}{z}$ when $z=3$.

These problems require the application of basic algebraic concepts, such as substitution and simplification, to obtain the final result.