Select the correct answer.
Evaluate the following expression when [tex]x=-5[/tex] and [tex]y=25[/tex].
[tex]\frac{5|x|-y^3}{x}[/tex]
A. 3,120
B. -630
C. 620
D. -3,130
Answer (2)
Substitute the given values x = − 5 and y = 25 into the expression x 5∣ x ∣ − y 3 .
Evaluate the absolute value: ∣ − 5∣ = 5 .
Calculate the powers and multiplication: 5 × 5 = 25 and 2 5 3 = 15625 .
Simplify the expression to find the final answer: − 5 25 − 15625 = − 5 − 15600 = 3120 . The final answer is 3120 .
Explanation
Understanding the Problem We are given the expression x 5∣ x ∣ − y 3 and the values x = − 5 and y = 25 . Our goal is to evaluate the expression by substituting the given values.
Substituting the Values First, we substitute x = − 5 and y = 25 into the expression: − 5 5∣ − 5∣ − 2 5 3
Evaluating Absolute Value Next, we evaluate the absolute value of x , which is ∣ − 5∣ = 5 . So the expression becomes: − 5 5 ( 5 ) − 2 5 3
Calculating Powers and Multiplication Now, we calculate 5 ( 5 ) = 25 and 2 5 3 = 15625 . The expression is now: − 5 25 − 15625
Performing Subtraction Then, we calculate 25 − 15625 = − 15600 . The expression is now: − 5 − 15600
Performing Division Finally, we divide − 15600 by − 5 : − 5 − 15600 = 3120
Final Answer Therefore, the value of the expression is 3120 .
Examples
Evaluating algebraic expressions is a fundamental skill in mathematics and has numerous real-world applications. For instance, in physics, you might use such expressions to calculate the force acting on an object given its mass and acceleration. In finance, you could evaluate expressions to determine the return on an investment based on various factors like interest rates and time. In computer science, similar evaluations are used in algorithms to process data and make decisions. Understanding how to substitute values into expressions and simplify them is crucial for solving practical problems in these fields.
After substituting x = − 5 and y = 25 into the expression x 5∣ x ∣ − y 3 , we find the value evaluates to 3120 . This corresponds to option A. Thus, the correct answer is A. 3,120 .
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