What is the numerical value of the algebraic expression -5x^2 + \frac{12y}{x} - y^2 when e… — Armed Services Vocational Aptitude Battery (ASVAB)

What is the numerical value of the algebraic expression $-5x^2 + \frac{12y}{x} - y^2$ when evaluated for $x = -2$ and $y = -3$ ?

The correct numerical value of the expression is -11.

Substituting

x = -2

and

y = -3

gives

-5(-2)^2 + \frac{12(-3)}{-2} - (-3)^2

. Evaluating the exponents first results in

-5(4) + \frac{-36}{-2} - 9

. Multiplying and dividing yields

-20 + 18 - 9

. Finally, adding and subtracting gives the correct value of

-11

Substitute the given numeric values into the algebraic expression using parentheses.

-5(-2)^2 + \frac{12(-3)}{-2} - (-3)^2

Using parentheses during substitution prevents sign errors, especially when variables have negative values.

Evaluate the terms with exponents.

-5(4) + \frac{12(-3)}{-2} - (9)

According to the order of operations (PEMDAS), exponents must be evaluated before multiplication and division.

Perform the multiplication and division operations.

-20 + \frac{-36}{-2} - 9 \Rightarrow -20 + 18 - 9

Multiplication and division are processed from left to right before addition and subtraction.

Complete the evaluation by performing addition and subtraction from left to right.

-20 + 18 - 9 = -2 - 9 = -11

Addition and subtraction are the final steps in the order of operations.

Evaluating algebraic expressions requires careful substitution of values using parentheses and strict adherence to the order of operations (PEMDAS).

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