Textbook Question
Evaluate each exponential expression in Exercises 1–22.
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 17
The formula C=5/9(F-32) expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. In Exercises 17–18, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. 50 °F
Verified step by step guidance1
Identify the given Fahrenheit temperature, which is \(F = 50\) degrees.
Recall the formula that relates Fahrenheit and Celsius temperatures: \(C = \frac{5}{9}(F - 32)\).
Substitute the given Fahrenheit value into the formula: \(C = \frac{5}{9}(50 - 32)\).
Simplify the expression inside the parentheses: calculate \(50 - 32\).
Multiply the result by \(\frac{5}{9}\) to find the Celsius temperature.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Equations
A linear equation represents a straight-line relationship between variables, often in the form y = mx + b. In this problem, the formula C = (5/9)(F - 32) is a linear equation relating Fahrenheit (F) and Celsius (C) temperatures, where the conversion involves scaling and shifting values.
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Temperature Conversion Formula
The temperature conversion formula converts Fahrenheit to Celsius by adjusting for the difference in zero points and scaling the degree size. Specifically, subtracting 32 from Fahrenheit accounts for the offset, and multiplying by 5/9 scales the temperature to the Celsius degree size.
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Substitution in Algebraic Expressions
Substitution involves replacing a variable in an expression with a given value to evaluate it. Here, substituting F = 50 into the formula allows calculation of the corresponding Celsius temperature by performing arithmetic operations on the expression.
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Related Practice
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Textbook Question
Evaluate each exponential expression in Exercises 1–22.