Evaluate The Expression $2x^2 - Y^1 + 3x^0$ For $x = 4$ And \$y = 7$[/tex\].A. 28 B. 60 C. 97 D. 15
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students and professionals alike. In this article, we will evaluate the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$. We will break down the expression into smaller parts, apply the order of operations, and calculate the final result.
Understanding the Expression
The given expression is $2x^2 - y^1 + 3x^0$. Let's analyze each part of the expression:
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2x^2$: This is a quadratic term, where $x$ is raised to the power of 2 and multiplied by 2.
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-y^1$: This is a linear term, where $y$ is raised to the power of 1 and multiplied by -1.
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3x^0$: This is a constant term, where $x$ is raised to the power of 0 and multiplied by 3.
Applying the Order of Operations
The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Evaluating the Expression
Now that we have analyzed the expression and applied the order of operations, let's evaluate it step by step:
- Substitute $x = 4$ and $y = 7$ into the expression:
- Evaluate the exponents:
- Multiply 2 and 16:
- Subtract 7 from 32:
- Add 3 to 25:
Conclusion
In conclusion, the final result of evaluating the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$ is $28$. This result can be verified by plugging in the values of $x$ and $y$ into the expression and following the order of operations.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an algebraic expression?
A: To evaluate an algebraic expression, follow these steps:
- Substitute any given values into the expression.
- Evaluate any exponents.
- Multiply and divide from left to right.
- Add and subtract from left to right.
Q: What is the final result of evaluating the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$?
A: The final result of evaluating the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$ is $28$.
References
Further Reading
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Introduction
Evaluating algebraic expressions is a crucial skill for students and professionals alike. In our previous article, we evaluated the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$. In this article, we will answer some frequently asked questions about evaluating algebraic expressions.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an algebraic expression?
A: To evaluate an algebraic expression, follow these steps:
- Substitute any given values into the expression.
- Evaluate any exponents.
- Multiply and divide from left to right.
- Add and subtract from left to right.
Q: What is the difference between an algebraic expression and an equation?
A: An algebraic expression is a mathematical statement that contains variables and constants, but does not contain an equal sign. An equation, on the other hand, is a mathematical statement that contains an equal sign and is used to solve for a variable.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, follow these steps:
- Combine like terms.
- Eliminate any unnecessary parentheses.
- Rewrite the expression in a simpler form.
Q: What is the final result of evaluating the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$?
A: The final result of evaluating the expression $2x^2 - y^1 + 3x^0$ for $x = 4$ and $y = 7$ is $28$.
Q: How do I evaluate an expression with multiple variables?
A: To evaluate an expression with multiple variables, follow these steps:
- Substitute the given values into the expression.
- Evaluate any exponents.
- Multiply and divide from left to right.
- Add and subtract from left to right.
Q: What is the difference between a variable and a constant?
A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.
Q: How do I evaluate an expression with a negative exponent?
A: To evaluate an expression with a negative exponent, follow these steps:
- Rewrite the expression with a positive exponent.
- Evaluate the expression.
Q: What is the final result of evaluating the expression $x^{-2} + 3x^0$ for $x = 4$?
A: The final result of evaluating the expression $x^{-2} + 3x^0$ for $x = 4$ is $\frac{1}{16} + 3$.
Conclusion
In conclusion, evaluating algebraic expressions is a crucial skill for students and professionals alike. By following the order of operations and simplifying expressions, we can evaluate complex expressions and solve for variables. We hope this Q&A guide has been helpful in answering your questions about evaluating algebraic expressions.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an algebraic expression?
A: To evaluate an algebraic expression, follow these steps:
- Substitute any given values into the expression.
- Evaluate any exponents.
- Multiply and divide from left to right.
- Add and subtract from left to right.