Calculate the exact value of the algebraic expression 3x^2y - \frac{12y}{x} when the varia… — Armed Services Vocational Aptitude Battery (ASVAB)

Calculate the exact value of the algebraic expression $3x^2y - \frac{12y}{x}$ when the variables are assigned the values $x = -2$ and $y = -5$ .

Cevap: -90

The correct evaluated result is -90.

By accurately substituting the values, correctly squaring the negative number

(-2)^2 = 4

, evaluating the fractional term as

\frac{-60}{-2} = 30

, and completing the final subtraction

-60 - 30

, the expression correctly evaluates to -90.

Substitute the given variable values into the algebraic expression.

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

This sets up the expression with numerical values for evaluation.

Evaluate the exponent applied to the negative base.

(-2)^2 = 4

, making the expression

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

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

Perform the multiplication in the first term.

3(4)(-5) = 12(-5) = -60

Evaluating the first term completely from left to right.

Perform the multiplication and division in the second term (the fraction).

\frac{12(-5)}{-2} = \frac{-60}{-2} = 30

Evaluating the fractional term by first multiplying the numerator, then dividing by the negative denominator.

Subtract the result of the fraction from the first term.

-60 - 30 = -90

The final operation is the subtraction of the two evaluated terms.

Evaluating algebraic expressions using substitution and the order of operations with signed numbers.

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