Select The Correct Answer.What Is The Value Of The Expression When $f=-4, G=5$, And $h=\frac{3}{4}$?Expression: $-8h - 2(5 + F^3) + 7g^2$Options: A. 287 B. 51 C. 31 D. 299

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Introduction

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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 explore the process of evaluating algebraic expressions, with a focus on the given expression: $-8h - 2(5 + f^3) + 7g^2$. We will substitute the given values of $f$, $g$, and $h$ into the expression and simplify it to find the final value.

Understanding the Expression

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The given expression is: $-8h - 2(5 + f^3) + 7g^2$. This expression involves several operations, including multiplication, addition, and exponentiation. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
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.

Substituting Values

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We are given the values of $f$, $g$, and $h$ as follows:

• $f = -4$
• $g = 5$
• $h = \frac{3}{4}$

We will substitute these values into the expression and simplify it step by step.

Evaluating the Expression

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Step 1: Evaluate the expressions inside the parentheses

The expression inside the parentheses is: $5 + f^3$. We will substitute the value of $f$ into this expression:

$5 + (-4)^3 = 5 + (-64) = -59$

Step 2: Evaluate the exponential expression

The exponential expression is: $f^3$. We will substitute the value of $f$ into this expression:

$(-4)^3 = -64$

Step 3: Evaluate the multiplication and division operations

The expression involves several multiplication and division operations. We will evaluate these operations from left to right:

• $-8h = -8 \times \frac{3}{4} = -6$
• $-2(5 + f^3) = -2 \times (-59) = 118$
• $7g^2 = 7 \times 5^2 = 7 \times 25 = 175$

Step 4: Evaluate the addition and subtraction operations

Finally, we will evaluate the addition and subtraction operations from left to right:

$-6 + 118 + 175 = 287$

Conclusion

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In this article, we evaluated the given algebraic expression: $-8h - 2(5 + f^3) + 7g^2$. We substituted the given values of $f$, $g$, and $h$ into the expression and simplified it step by step. The final value of the expression is: 287.

Discussion

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The given expression involves several operations, including multiplication, addition, and exponentiation. To evaluate this expression, we need to follow the order of operations (PEMDAS). We also need to be careful when substituting values into the expression and simplifying it step by step.

Final Answer

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The final answer is: A. 287

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Introduction

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In our previous article, we explored the process of evaluating algebraic expressions, with a focus on the given expression: $-8h - 2(5 + f^3) + 7g^2$. We substituted the given values of $f$, $g$, and $h$ into the expression and simplified it step by step. In this article, we will answer some frequently asked questions about evaluating algebraic expressions.

Q&A

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Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate the expressions inside the parentheses.
• Exponents: Evaluate any exponential expressions.
• 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 expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside the parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between an expression and an equation?

A: An expression is a group of numbers, variables, and mathematical operations that are combined to form a value. An equation is a statement that says two expressions are equal. For example, the expression $2x + 3$ is a group of numbers and variables, while the equation $2x + 3 = 5$ is a statement that says the expression $2x + 3$ is equal to the value $5$.

Q: How do I simplify an expression?

A: To simplify an expression, combine like terms and eliminate any unnecessary operations. For example, the expression $2x + 3 + 2x$ can be simplified by combining the like terms $2x$ and $2x$ to get $4x + 3$.

Q: What is the value of the expression when $f = 2, g = 3$, and $h = \frac{1}{2}$?

A: To evaluate this expression, we need to substitute the given values of $f$, $g$, and $h$ into the expression and simplify it step by step. The expression is: $-8h - 2(5 + f^3) + 7g^2$. We will substitute the values of $f$, $g$, and $h$ into this expression and simplify it as follows:

• $-8h = -8 \times \frac{1}{2} = -4$
• $-2(5 + f^3) = -2 \times (5 + 2^3) = -2 \times (5 + 8) = -2 \times 13 = -26$
• $7g^2 = 7 \times 3^2 = 7 \times 9 = 63$

Finally, we will evaluate the addition and subtraction operations from left to right:

$-4 + (-26) + 63 = 33$

The final value of the expression is: 33.

Conclusion

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In this article, we answered some frequently asked questions about evaluating algebraic expressions. We discussed the order of operations (PEMDAS), how to evaluate expressions with multiple operations, and how to simplify expressions. We also evaluated an expression with given values of $f$, $g$, and $h$.

Final Answer

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The final answer is: 33