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Evaluating when and
Evaluate the expression by substituting and :
- Substitute: Replace with and with to obtain .
- Add inside the parentheses: Compute (different signs — subtract the smaller absolute value from the larger: , and take the positive sign since has the larger absolute value). The expression becomes .
- Simplify the exponent: Compute .
The final result is . This example illustrates how to evaluate a two-variable expression that involves both integer addition (with mixed signs) and exponentiation: the parentheses force the addition to be completed before the squaring.
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Ch.1 Foundations - Elementary Algebra @ OpenStax
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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 warehouse manager uses the formula (x + y)^2 to calculate the total storage units needed for seasonal inventory, where x is the current stock level adjustment and y is the incoming shipment. If x = -18 and y = 24, arrange the following steps in the correct order to evaluate the formula.
A logistics coordinator uses the formula (x + y)^2 to determine the total square footage of a storage zone. If the adjustment for existing inventory (x) is -18 and the incoming shipment factor (y) is 24, what is the final calculated value?
A quality control engineer uses the formula (x + y)^2 to calculate a stability index. If the measured variance (x) is -18 and the correction factor (y) is 24, the value that is squared in the final step of the evaluation is 6.
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A logistics coordinator uses the formula to calculate the 'Stability Coefficient' for a shipping container. In this formula, represents a weight adjustment factor and represents the base weight of the cargo. Given an adjustment factor of and a base weight of , match each part of the evaluation process with its correct numerical value or representation.
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In a logistics management system, a 'Zone Efficiency Index' is calculated using the formula . If the inventory adjustment factor () is and the shipment volume factor () is $24$, the resulting Zone Efficiency Index is ____.
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An environmental consultant uses the formula to calculate a site's 'Soil Stability Index.' If the site has a moisture adjustment () of and a compaction factor () of $24$, which expression correctly represents the initial substitution of these values into the formula?
A logistics coordinator is using the formula to calculate a 'Stability Index.' Given an adjustment factor and a base weight , which mathematical rule correctly identifies the sign of the sum performed during the evaluation?