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Zorluk: OrtaEvaluating Algebraic Expressions

A chemist uses the algebraic formula E=2x2−yzx+y2E = \frac{2x^2 - yz}{x + y^2} to determine the stability index of a synthesized compound. If x=−4x = -4, y=−3y = -3, and z=23z = \frac{2}{3}, what is the value of EE?

  1. A
    −6-6
  2. B
    66
  3. C
    3449\frac{34}{49}
  4. 345\frac{34}{5}Cevap
  5. E
    −3413-\frac{34}{13}

Cevap

345\frac{34}{5}
Substituting x=−4x = -4, y=−3y = -3, and z=23z = \frac{2}{3} into the numerator yields 2(−4)2−(−3)(23)=2(16)−(−2)=32+2=342(-4)^2 - (-3)\left(\frac{2}{3}\right) = 2(16) - (-2) = 32 + 2 = 34. Substituting into the denominator yields −4+(−3)2=−4+9=5-4 + (-3)^2 = -4 + 9 = 5. Thus, the value of the expression is 345\frac{34}{5}.

Adım Adım Çözüm

1
Substitute the given values into the numerator 2x2−yz2x^2 - yz.
2(−4)2−(−3)(23)=2(16)−(−2)=32+2=342(-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(-4)^2 = 16, and multiplying −3-3 by 23\frac{2}{3} gives −2-2, which is then subtracted.
2
Substitute the given values into the denominator x+y2x + y^2.
−4+(−3)2=−4+9=5-4 + (-3)^2 = -4 + 9 = 5
Evaluating the exponent first gives (−3)2=9(-3)^2 = 9, then adding −4-4 gives 55.
3
Divide the numerator by the denominator.
345\frac{34}{5}
Combine the evaluated numerator and denominator to get the final value of the expression.

Anahtar Kavram

Evaluating algebraic expressions involving multiple variables with negative bases and fractional terms using standard order of operations.
Tahmini Süre:1m 15s
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Evaluating Algebraic Expressions

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