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Evaluating when and
Evaluate the multi-variable expression when and by substituting the values and simplifying according to the order of operations:
- Substitute: Replace with and with , using parentheses: .
- Simplify exponents: Evaluate and . The expression becomes .
- Multiply: Calculate each product: , , and . The expression becomes .
- Subtract: The subtraction becomes . The expression becomes .
- Add: .
The final evaluated result is .
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Algebra
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When a financial analyst is asked to 'evaluate' a revenue expression for a specific number of sales, which two steps must they perform according to the mathematical definition of evaluation?
In a professional setting, formulas are often used to calculate key performance indicators (KPIs) and other business metrics. Match each mathematical term to the specific action it describes within the process of finding the value of a formula.
A logistics coordinator is using the expression 15w + 10 to calculate the shipping fee for a package, where 'w' is the weight in pounds. To 'evaluate' this expression for a 5-pound package, arrange the steps of the process in the correct order according to the mathematical definition of evaluation.
The Two Steps of Evaluating an Expression
In a professional business application, the process of 'evaluating' an algebraic expression is considered complete once a specific number has been substituted for the variable, regardless of whether the resulting numerical expression has been simplified.
In a logistics department, a coordinator uses the expression 15w + 10 to calculate shipping costs, where 'w' is the weight of a package. When the coordinator replaces the variable 'w' with the number 5 to find the cost of a specific shipment, they are performing the first step of evaluation, which is known as ________.
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A pharmacy technician is using an algebraic expression to calculate the correct medication dosage for a patient. After substituting the patient's weight for the variable in the expression, which specific set of rules must the technician use to simplify the result?
In a corporate finance department, a data analyst is assigned to 'evaluate' a cost-projection formula using a set of provided figures. According to the mathematical definition of evaluation, which of the following best describes the final result the analyst should obtain?
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Learn After
A structural engineer uses the formula to determine the load-bearing limit of a steel bracket during a stress test. If the horizontal stress () is measured at -2 units and the vertical pressure () is measured at 3 units, what is the calculated load-bearing limit for this component?
A manufacturing quality control supervisor uses the expression to calculate a component's durability index, where represents the flexibility variance and represents the hardness factor. For a specific component where and , arrange the following steps of the evaluation process in the correct mathematical order.
A production analyst at a manufacturing plant uses the formula to calculate a machine's efficiency index. For a specific shift, the downtime variance () is and the output load factor () is $3$. Match each component of the efficiency formula with its correctly evaluated numerical value.
In a manufacturing quality control test, a technician uses the expression to determine a material's stress index. If the flexibility variance () is and the hardness factor () is $3{}4(-2)^2 - (-2)(3) + 5(3)^2$.
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