Evaluate [tex]\frac{2 x^2-5 y}{3 x-y}[/tex] when [tex]x=2[/tex] and [tex]y=-4[/tex].
A. 10
B. 4
C. 8
D. 14
Answer (2)
Substitute x = 2 and y = − 4 into the expression 2 x 2 − 5 y .
Calculate 2 ( 2 ) 2 − 5 ( − 4 ) .
Simplify the expression: 2 ( 4 ) + 20 = 8 + 20 = 28 .
The final answer is 28 .
Explanation
Understanding the Problem We are asked to evaluate the expression 2 x 2 − 5 y when x = 2 and y = − 4 . We will substitute these values into the expression and simplify.
Substitution First, substitute x = 2 and y = − 4 into the expression: 2 x 2 − 5 y = 2 ( 2 ) 2 − 5 ( − 4 )
Simplification Next, we simplify the expression: 2 ( 2 ) 2 − 5 ( − 4 ) = 2 ( 4 ) − ( − 20 ) = 8 + 20 = 28 So, the value of the expression 2 x 2 − 5 y when x = 2 and y = − 4 is 28.
Evaluating the second expression Now, let's evaluate the expression 3 x − y when x = 2 and y = − 4 :
3 x − y = 3 ( 2 ) − ( − 4 ) = 6 + 4 = 10 So, the value of the expression 3 x − y when x = 2 and y = − 4 is 10.
Final Answer The problem asks us to evaluate 2 x 2 − 5 y when x = 2 and y = − 4 . We found that 2 x 2 − 5 y = 28 and 3 x − y = 10 . The question is poorly formatted, but we are looking for the value of the first expression.
Examples
In physics, this type of calculation could represent the potential energy of an object. For example, the term 2 x 2 might relate to kinetic energy based on velocity x , while − 5 y could represent potential energy related to height y . Evaluating the expression helps determine the total energy of the system at a specific state.
After substituting x = 2 and y = − 4 into the expression 3 x − y 2 x 2 − 5 y , we simplify to find the result is 2.8 .
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