A chemist uses the algebraic formula E = \frac{2x^2 - yz}{x + y^2} to determine the stabil… — ACT

A chemist uses the algebraic formula $E = \frac{2x^2 - yz}{x + y^2}$ to determine the stability index of a synthesized compound. If $x = -4$ , $y = -3$ , and $z = \frac{2}{3}$ , what is the value of $E$ ?

A
$-6$
B
$6$
C
$\frac{34}{49}$
$\frac{34}{5}$ Answer
E
$-\frac{34}{13}$

Answer

\frac{34}{5}

Substituting

x = -4

y = -3

, and

z = \frac{2}{3}

into the numerator yields

2(-4)^2 - (-3)\left(\frac{2}{3}\right) = 2(16) - (-2) = 32 + 2 = 34

. Substituting into the denominator yields

-4 + (-3)^2 = -4 + 9 = 5

. Thus, the value of the expression is

\frac{34}{5}

Step-by-Step Solution

Substitute the given values into the numerator

2x^2 - yz

2(-4)^2 - (-3)\left(\frac{2}{3}\right) = 2(16) - (-2) = 32 + 2 = 34

Squaring a negative number yields a positive result

(-4)^2 = 16

, and multiplying

-3

\frac{2}{3}

gives

-2

, which is then subtracted.

Substitute the given values into the denominator

x + y^2

-4 + (-3)^2 = -4 + 9 = 5

Evaluating the exponent first gives

(-3)^2 = 9

, then adding

-4

gives

5

Divide the numerator by the denominator.

\frac{34}{5}

Combine the evaluated numerator and denominator to get the final value of the expression.

Key Concept

Evaluating algebraic expressions involving multiple variables with negative bases and fractional terms using standard order of operations.

Estimated Time:1m 15s

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