If x = -3, y = -\frac{1}{2}, and z = 4, what is the numerical value of the algebraic expre… — ACT

If $x = -3$ , $y = -\frac{1}{2}$ , and $z = 4$ , what is the numerical value of the algebraic expression $\frac{x^2 - 4y^2}{x + yz}$ ?

Answer: -1.6

The numerical value of the expression is

-1.6

Substituting

x = -3

y = -\frac{1}{2}

, and

z = 4

into

\frac{x^2 - 4y^2}{x + yz}

gives a numerator of

(-3)^2 - 4\left(-\frac{1}{2}\right)^2 = 9 - 4\left(\frac{1}{4}\right) = 8

and a denominator of

-3 + \left(-\frac{1}{2}\right)(4) = -3 - 2 = -5

. Evaluating

\frac{8}{-5}

yields

-1.6

Evaluate the numerator

x^2 - 4y^2

Squaring

-3

gives

9

, and squaring

-\frac{1}{2}

gives

\frac{1}{4}

. Thus,

9 - 4\left(\frac{1}{4}\right) = 9 - 1 = 8

Evaluate the denominator

x + yz

-5

Multiplying

-\frac{1}{2}

4

gives

-2

. Adding

-3 + (-2)

yields

-5

Compute the final fraction quotient

-1.6

Dividing the numerator

8

by the denominator

-5

yields

-1.6

Evaluating algebraic expressions using order of operations with negative bases and fractional values.

Estimated Time:1m 30s

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