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Evaluating when and
To evaluate a variable expression involving negative numbers and multiple variables, substitute the given values, using parentheses to preserve the operations and signs, and simplify using the order of operations.
For example, to evaluate when and :
- Substitute: Replace with and with . Use parentheses to clearly indicate multiplication and negative bases: .
- Simplify exponents: Evaluate and . The expression becomes .
- Multiply: Perform all multiplications from left to right: , , 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.
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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 data analyst is updating a risk assessment model based on the mathematical expression . The model requires inputting a market volatility factor for and an economic downturn indicator for . If the current volatility factor is 2 and the downturn indicator is -1, the analyst must first document the exact substitution step for a compliance audit. Recalling the rules for evaluating expressions, which of the following correctly shows how to substitute these values while preserving all operations and signs?
A logistics assistant at a regional warehouse uses the formula to calculate a 'Priority Storage Fee,' where represents the pallet weight in tons and represents the climate-control factor. For a specific shipment where and , arrange the following steps in the correct procedural order to evaluate the total fee.
A financial analyst uses the mathematical model to determine the risk-adjusted return of a specialized investment. In this model, represents the asset's beta and represents the market's volatility index. If the analyst inputs a beta () of 2 and a volatility index () of -1, the resulting risk-adjusted return is ____.
An operations manager uses the formula to determine the 'Operational Risk Score' for a project. In this scenario, the complexity factor is and the safety variance is . Match each component of the evaluation process to its correctly simplified value.
A Warehouse Supervisor uses the formula to calculate a storage priority score. If the supervisor needs to evaluate this formula for a weight factor of and a perishability factor of , true or false: the correct way to show the substitution for the term $3y^2{}3(-1)^2$ to ensure the negative value is squared correctly.
Documentation of Variable Substitution