Textbook Question
Simplify and write the result in standard form. √-108
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Ch. 1 - Equations and Inequalities
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 2, Problem 33
For an international telephone call, a telephone company charges \$0.43 for the first minute, \$0.32 for each additional minute, and a \$2.10 service charge. If the cost of a call is \$5.73, how long did the person talk?
Verified step by step guidance1
Define the variable for the total time of the call in minutes. Let \(t\) represent the total number of minutes talked.
Write an expression for the total cost of the call. The cost consists of three parts: the first minute at \$0.43, the additional minutes at \$0.32 each, and a fixed service charge of \$2.10. So, the cost can be expressed as: \(0.43 + 0.32(t - 1) + 2.10\).
Set up an equation by equating the total cost expression to the given cost of \$5.73: \(0.43 + 0.32(t - 1) + 2.10 = 5.73\).
Simplify the equation by combining like terms and isolating the variable term: first combine \(0.43\) and \(2.10\), then subtract this sum from both sides to isolate \(0.32(t - 1)\).
Solve for \(t\) by dividing both sides by \(0.32\) and then adding 1 to find the total number of minutes talked.
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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 relationship between variables with a constant rate of change. In this problem, the total cost depends linearly on the number of minutes talked, allowing us to set up an equation to solve for the unknown time.
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Piecewise Cost Structure
The cost is divided into different parts: a fixed service charge, a fixed rate for the first minute, and a different rate for additional minutes. Understanding how to separate and combine these parts is essential to model the total cost accurately.
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Solving for an Unknown Variable
After forming the equation based on the cost structure, solving for the unknown variable (the total time talked) involves isolating the variable using algebraic operations. This step finds the exact duration of the call.
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Related Practice
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In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 8x - 11 ≤ 3x - 13
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