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Chapter 1: Problem 39

Evaluate each expression using the values provided. \(20+r^{2}-s,\) for \(r=5\) and \(s=10\)

Short Answer

Expert verified
35

Step by step solution

01

- Substitute the values

First, substitute the given values of the variables into the expression. The expression is: \(20+r^{2}-s\) Given: \(r=5\) and \(s=10\) Substitute these values into the expression to get: \(20+5^{2}-10\)
02

- Evaluate the exponent

Next, evaluate the exponent part of the expression. \(5^{2}=25\) So the expression now becomes: \(20+25-10\)
03

- Perform the addition and subtraction

Finally, perform the addition and subtraction operations. \(20+25=45\) Then, subtract 10 from 45: \(45-10=35\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

substitution
Substitution is a core concept in algebra where you replace variables in an expression with their given values. In the provided exercise, you start with the expression: \(20 + r^{2} - s\). Given the values \(r = 5\) and \(s = 10\), substitution involves replacing \(r\) with 5 and \(s\) with 10.
This step transforms the expression into: \(20 + 5^{2} - 10\).
Understanding substitution well is crucial because it is the first step in solving many algebraic problems. It sets the stage for further simplification and evaluation.
exponents
Exponents represent repeated multiplication of the same number. In the equation from the step-by-step solution, we see an exponent in \(5^{2}\).
The exponent 2 tells us to multiply the base, which is 5, by itself: \(5 \times 5 = 25\).
This changes the expression from \(20 + 5^{2} - 10\) to \(20 + 25 - 10\).
Recognizing and evaluating exponents correctly is key to simplifying expressions accurately. Always perform operations with exponents before moving on to addition or subtraction.
addition and subtraction
After handling substitution and evaluating exponents, the next step is performing any addition or subtraction. For the transformed expression \(20 + 25 - 10\), you start with addition:
  • First, add 20 and 25 to get 45: \(20 + 25 = 45\)
  • Next, subtract 10 from 45: \(45 - 10 = 35\)
Following the order of operations鈥攐ften remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)鈥攅nsures accurate results. First perform any operations inside parentheses, evaluate exponents, then handle multiplication/division, and finally, address addition/subtraction. This consistency provides clarity and precision in solving mathematical expressions.

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