Tawny Wrote An Expression To Represent the Quotient Of 82 And A Number, Decreased By 26. She Then Evaluated The Expression When $n=2$.Which Statements Are True About The Expression And Its Value? Check All That Apply.- The Correct

Introduction

In mathematics, expressions and equations are used to represent relationships between variables and constants. Tawny's expression is a mathematical representation of a specific scenario, and evaluating it at a given value of the variable can provide valuable insights. In this article, we will explore Tawny's expression, its evaluation, and the statements that are true about the expression and its value.

Tawny's Expression

Tawny's expression is given as "the quotient of 82 and a number, decreased by 26." This can be represented mathematically as:

$$\frac{82}{n} - 26$$

where $n$ is the variable representing the unknown number.

Evaluating the Expression

To evaluate the expression, we need to substitute the given value of $n$ into the expression. In this case, $n=2$. Substituting this value into the expression, we get:

$$\frac{82}{2} - 26$$

Simplifying the expression, we get:

$$41 - 26$$

Evaluating the expression further, we get:

$$15$$

True Statements About the Expression and Its Value

Now that we have evaluated the expression, let's examine the statements that are true about the expression and its value.

Statement 1: The expression is a quotient.

• True: The expression is indeed a quotient, as it represents the result of dividing 82 by a number ($n$) and then subtracting 26.

Statement 2: The expression is a linear expression.

• True: The expression is a linear expression, as it consists of a single term (the quotient) and a constant term (-26).

Statement 3: The value of the expression is 15.

• True: As we evaluated earlier, the value of the expression when $n=2$ is indeed 15.

Statement 4: The expression is a polynomial expression.

• False: The expression is not a polynomial expression, as it does not consist of multiple terms with non-negative integer exponents.

Statement 5: The expression is a rational expression.

• True: The expression is a rational expression, as it consists of a quotient of two polynomials (82 and $n$).

Statement 6: The expression is a constant expression.

• False: The expression is not a constant expression, as it contains a variable ($n$) that can take on different values.

Statement 7: The value of the expression is dependent on the value of $n$.

• True: The value of the expression is indeed dependent on the value of $n$, as changing the value of $n$ will result in a different value of the expression.

Statement 8: The expression is a quadratic expression.

• False: The expression is not a quadratic expression, as it does not consist of a quadratic term (i.e., a term with a squared variable).

Statement 9: The expression is a function of $n$.

• True: The expression is indeed a function of $n$, as it represents a relationship between the variable $n$ and a constant value.

Statement 10: The value of the expression is always positive.

• False: The value of the expression is not always positive, as the quotient of 82 and $n$ can be negative if $n$ is negative.

Conclusion

$$$$$$

Introduction

In our previous article, we explored Tawny's expression, a mathematical representation of a specific scenario. We evaluated the expression at a given value of the variable and examined the statements that are true about the expression and its value. In this article, we will provide a Q&A guide to help you better understand Tawny's expression and its properties.

Q: What is Tawny's expression?

A: Tawny's expression is a mathematical representation of the scenario "the quotient of 82 and a number, decreased by 26." It can be represented mathematically as:

$$\frac{82}{n} - 26$$

Q: What is the value of the expression when $n=2$?

A: The value of the expression when $n=2$ is 15. This can be evaluated by substituting $n=2$ into the expression and simplifying:

$$\frac{82}{2} - 26 = 41 - 26 = 15$$

Q: Is the expression a quotient?

A: Yes, the expression is a quotient, as it represents the result of dividing 82 by a number ($n$) and then subtracting 26.

Q: Is the expression a linear expression?

A: Yes, the expression is a linear expression, as it consists of a single term (the quotient) and a constant term (-26).

Q: Is the expression a polynomial expression?

A: No, the expression is not a polynomial expression, as it does not consist of multiple terms with non-negative integer exponents.

Q: Is the expression a rational expression?

A: Yes, the expression is a rational expression, as it consists of a quotient of two polynomials (82 and $n$).

Q: Is the expression a constant expression?

A: No, the expression is not a constant expression, as it contains a variable ($n$) that can take on different values.

Q: Is the value of the expression dependent on the value of $n$?

A: Yes, the value of the expression is indeed dependent on the value of $n$, as changing the value of $n$ will result in a different value of the expression.

Q: Is the expression a function of $n$?

A: Yes, the expression is indeed a function of $n$, as it represents a relationship between the variable $n$ and a constant value.

Q: Is the value of the expression always positive?

A: No, the value of the expression is not always positive, as the quotient of 82 and $n$ can be negative if $n$ is negative.

Q: Can the expression be evaluated for any value of $n$?

A: Yes, the expression can be evaluated for any value of $n$, as it is a well-defined mathematical expression.

Q: What is the domain of the expression?

A: The domain of the expression is all real numbers except for $n=0$, as division by zero is undefined.

Conclusion

In conclusion, Tawny's expression is a mathematical representation of a specific scenario, and evaluating it at a given value of the variable can provide valuable insights. We hope this Q&A guide has helped you better understand Tawny's expression and its properties. If you have any further questions, please don't hesitate to ask.

Additional Resources

• Tawny's Expression: A Mathematical Representation
• Evaluating Expressions: A Guide
• Functions and Their Properties