Evaluate -3.25 - 7.5z for $z = -4$.

Question

02-11-2026
Mathematics

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Evaluate -3.25 - 7.5z for $z = -4$.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-02T01:09:23-05:00

Substitute $z = -4$ into $-3.25 \cdot 75z$ to get $-3.25 \cdot 75 \cdot (-4) = 975$.
Simplify the expression $-3.25 \cdot (2.7 \cdot 5) - 4$ by first calculating $2.7 \cdot 5 = 13.5$.
Multiply $-3.25 \cdot 13.5 = -43.875$.
Subtract $4$ to obtain $-43.875 - 4 = -47.875$.
The final results are $\boxed{975}$ and $\boxed{-47.875}$.

Explanation

Analysis of the Expressions

The objective is to evaluate two arithmetic expressions based on provided values and standard order of operations.

The first expression is $-3.25 \cdot 75z$ given $z = -4$.
The second expression is $-3.25 \cdot (2.7 \cdot 5) - 4$.

These evaluations rely on fundamental arithmetic rules: multiplication of real numbers, handling negative signs, and respecting the order of operations (parentheses first, followed by multiplication/division, and then addition/subtraction).

Evaluating the First Expression

To evaluate $-3.25 \cdot 75z$ with $z = -4$:

Substitute the value of $z$ into the expression: $-3.25 \cdot 75 \cdot (-4)$.
Apply the associative property of multiplication: $(-3.25 \cdot 75) \cdot (-4)$ or $-3.25 \cdot (75 \cdot -4)$.
Using the second approach, multiply $75$ by $-4$, which is $-300$.
Now, multiply the result by $-3.25$: $-3.25 \cdot (-300) = 975$.

Thus, the value of the first expression is $975$.

Evaluating the Second Expression

To evaluate $-3.25 \cdot (2.7 \cdot 5) - 4$:

According to the order of operations, perform the calculation inside the parentheses first: $2.7 \cdot 5 = 13.5$.
Substitute this back into the expression: $-3.25 \cdot 13.5 - 4$.
Perform the multiplication: $-3.25 \cdot 13.5 = -43.875$.
Subtract $4$ from the result: $-43.875 - 4 = -47.875$.

Thus, the value of the second expression is $-47.875$.

Examples

Mathematical operations like these are fundamental in financial management and budget analysis. For instance, if a company's profit is expressed as $-3.25 \cdot 75 \cdot z$ (where $z$ represents the number of units shifted from a target), calculating the outcome helps in financial forecasting. Similarly, expressions like $-3.25 \cdot (2.7 \cdot 5) - 4$ could represent the calculation of total cost or revenue fluctuations over a period, ensuring that small variations are correctly accounted for before final reporting. Precise arithmetic evaluation is essential in these scenarios to avoid significant errors in decision-making.