Intermediate Algebra
Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
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A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
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In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Textbook Question
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Chapter 4.3, Problem 159E

The manufacturer of a water bottle spends $5 to build each bottle and sells them for $10. The manufacturer also has fixed costs each month of $6500.
(a) Find the cost function C when x bottles are manufactured.
(b) Find the revenue function R when x bottles are sold.
(c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid.
(d) Find the break-even point. Interpret what the break-even point means.

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Chapter 4 Solutions

Intermediate Algebra

Ch. 4.1 - Determine whether the ordered pair is a solution...Ch. 4.1 - Determine whether the ordered pair is a solution...Ch. 4.1 - Solve the system by graphing: {x3y=3x+y=5 .Ch. 4.1 - Solve the system by graphing: {x+y=13x+2y=12 .Ch. 4.1 - Solve the system by graphing: {x+y=12x+y=10 .Ch. 4.1 - Solve the system by graphing: {2x+y=6x+y=1 .Ch. 4.1 - Solve the system by graphing: {y=14x+2x+4y=8 .Ch. 4.1 - Solve the system by graphing: {y=3x16x2y=6 .Ch. 4.1 - Solve the system by graphing: {y=3x66x+2y=12 .Ch. 4.1 - Solve the system by graphing: {y=12x42x4y=16 .
Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - Solve the system by substitution: {2x+y=11x+3y=9 .Ch. 4.1 - Solve the system by substitution: {2x+y=14x+3y=3 .Ch. 4.1 - Solve the system by substitution: {x4y=43x+4y=0 .Ch. 4.1 - Solve the system by substitution: {4xy=02x3y=5 .Ch. 4.1 - Solve the system by elimination: {3x+y=52x3y=7 .Ch. 4.1 - Solve the system by elimination: {4x+y=52x2y=2 .Ch. 4.1 - Solve the system by elimination: {3x4y=95x+3y=14 .Ch. 4.1 - Solve the system by elimination: {7x+8y=43x5y=27 .Ch. 4.1 - Solve the system by elimination: {13x12y=134xy=52...Ch. 4.1 - Solve the system by elimination:...Ch. 4.1 - Solve the system by elimination: {5x3y=15y=5+53x .Ch. 4.1 - Solve the system by elimination: {x+2y=6y=12x+3 .Ch. 4.1 - For each system of linear equations decide whether...Ch. 4.1 - For each system of linear equations decide whether...Ch. 4.1 - In the following exercises, determine if the...Ch. 4.1 - In the following exercises, determine if the...Ch. 4.1 - In the following exercises, determine if the...Ch. 4.1 - In the following exercises, determine if the...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - In the following exercises, solve the following...Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - Without graphing, determine the number of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - In the following exercises, solve the systems of...Ch. 4.1 - 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Solve the system of equations {x+y=10xy=6 (a) by...Ch. 4.2 - The sum of two numbers is 10. One number is 4 less...Ch. 4.2 - The sum of two numbers is 6 . One number is 10...Ch. 4.2 - Geraldine has been offered positions by two...Ch. 4.2 - Kenneth currently sells suits for company A at a...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - The measure of one of the small angles of a right...Ch. 4.2 - The measure of one of the small angles of a right...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - Translate to a system of equations and then solve:...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - 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In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - In the following exercises, translate to a system...Ch. 4.2 - Write an application problem similar to Example...Ch. 4.2 - Write a uniform motion problem similar to Example...Ch. 4.3 - Translate to a system of equations and solve: The...Ch. 4.3 - Translate to a system of equations and solve: The...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve: Leon...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - Translate to a system of equations and solve:...Ch. 4.3 - The manufacturer of a weight training bench spends...Ch. 4.3 - The manufacturer of a weight training bench spends...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - In the following exercises, translate to a system...Ch. 4.3 - 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The manufacturer of an energy drink spends $1.20...Ch. 4.3 - The manufacturer of a water bottle spends $5 to...Ch. 4.3 - Take a handful of two types of coins, and write a...Ch. 4.3 - In Example 4.28, we used elimination to solve the...Ch. 4.4 - Determine whether the ordered triple is a solution...Ch. 4.4 - Determine whether the ordered triple is a solution...Ch. 4.4 - Solve the system by elimination:...Ch. 4.4 - Solve the system by elimination:...Ch. 4.4 - Solve: {3x4z=12y+3z=22x+3y=6 .Ch. 4.4 - Solve: {4x3z=53y+2z=73x+4y=6 .Ch. 4.4 - Solve the system of equations:...Ch. 4.4 - Solve the system of equations:...Ch. 4.4 - Solve the system by equations:...Ch. 4.4 - Solve the system by equations:...Ch. 4.4 - The community college fine arts department sold...Ch. 4.4 - The community college soccer team sold three kinds...Ch. 4.4 - In the following exercises, determine whether the...Ch. 4.4 - In the following exercises, determine whether the...Ch. 4.4 - In the following exercises, determine whether the...Ch. 4.4 - In the following exercises, determine whether the...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the system of...Ch. 4.4 - In the following exercises, solve the given...Ch. 4.4 - In the following exercises, solve the given...Ch. 4.4 - In the following exercises, solve the given...Ch. 4.4 - In the following exercises, solve the given...Ch. 4.4 - In your own words explain the steps to solve a...Ch. 4.4 - How can you tell when a system of three linear...Ch. 4.5 - Write each system of linear equations as an...Ch. 4.5 - Write each system of linear equations as an...Ch. 4.5 - Write the system of equations that corresponds to...Ch. 4.5 - Write the system of equations that corresponds to...Ch. 4.5 - Perform the indicated operations on the augmented...Ch. 4.5 - Perform the indicated operations on the augmented...Ch. 4.5 - Perform the needed row operation that will get the...Ch. 4.5 - Perform the needed row operation that will get the...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - Solve the system of equations using a matrix:...Ch. 4.5 - In the following exercises, write each system of...Ch. 4.5 - In the following exercises, write each system of...Ch. 4.5 - In the following exercises, write each system of...Ch. 4.5 - In the following exercises, write each system of...Ch. 4.5 - Write the system of equations that that...Ch. 4.5 - Write the system of equations that that...Ch. 4.5 - Write the system of equations that that...Ch. 4.5 - Write the system of equations that that...Ch. 4.5 - In the following exercises, perform the indicated...Ch. 4.5 - In the following exercises, perform the indicated...Ch. 4.5 - In the following exercises, perform the indicated...Ch. 4.5 - In the following exercises, perform the indicated...Ch. 4.5 - In the following exercises, perform the indicated...Ch. 4.5 - In the following exercises, perform the indicated...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - In the following exercises, solve each system of...Ch. 4.5 - 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For the determinant |210301123| , find and then...Ch. 4.6 - Evaluate the determinant |324012231| , by...Ch. 4.6 - Evaluate the determinant |322214103| , by...Ch. 4.6 - Evaluate the determinant |213034343| by expanding...Ch. 4.6 - Evaluate the determinant |213122440| by expanding...Ch. 4.6 - Solve using Cramer’s rule: {3x+y=32x+3y=6 .Ch. 4.6 - Solve using Cramer’s rule: {x+y=22x+y=4 .Ch. 4.6 - Solve the system of equations using Cramer’s Rule:...Ch. 4.6 - Solve the system of equations using Cramer’s Rule:...Ch. 4.6 - Solve the system of equations using Cramer’s rule:...Ch. 4.6 - Solve the system of equations using Cramer’s rule:...Ch. 4.6 - Determine whether the points (3,2),(5,3), and...Ch. 4.6 - Determine whether the points (4,1),(6,2) and (2,4)...Ch. 4.6 - In the following exercises, evaluate the...Ch. 4.6 - In the following exercises, evaluate the...Ch. 4.6 - In the following exercises, evaluate the...Ch. 4.6 - In the following exercises, evaluate the...Ch. 4.6 - In the following exercises, find and then evaluate...Ch. 4.6 - 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In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, solve each system of...Ch. 4.6 - In the following exercises, determine whether the...Ch. 4.6 - In the following exercises, determine whether the...Ch. 4.6 - In the following exercises, determine whether the...Ch. 4.6 - In the following exercises, determine whether the...Ch. 4.6 - Explain the difference between a square matrix and...Ch. 4.6 - Explain what is meant by the minor of an entry in...Ch. 4.6 - Explain how to decide which row or column you will...Ch. 4.6 - Explain the steps for solving a system of...Ch. 4.7 - Determine whether the ordered pair is a solution...Ch. 4.7 - Determine whether the ordered pair is a solution...Ch. 4.7 - Solve the system by graphing: {y3x+2yx1 .Ch. 4.7 - Solve the system by graphing: {y 1 2x+3y3x4 .Ch. 4.7 - Solve the system by graphing: {x+y2y 2 3x1 .Ch. 4.7 - Solve the system by graphing: {3x2y6y 1 4x+5 .Ch. 4.7 - Solve the system by graphing: {y3x2y1 .Ch. 4.7 - Solve the system by graphing: {x4x2y4 .Ch. 4.7 - Solve the system by graphing: {3x2y12y 3 2x+1 .Ch. 4.7 - Solve the system by graphing: {x+3y8y 1 3x2 .Ch. 4.7 - Solve the system by graphing: {y3x+13x+y4 .Ch. 4.7 - Solve the system by graphing: {y 1 4x+2x+4y4 .Ch. 4.7 - A trailer can carry a maximum weight of 160 pounds...Ch. 4.7 - Mary needs to purchase supplies of answer sheets...Ch. 4.7 - Tension needs to eat at least an extra 1,000...Ch. 4.7 - Philip’s doctor tells him he should add at least...Ch. 4.7 - In the following exercises, determine whether each...Ch. 4.7 - In the following exercises, determine whether each...Ch. 4.7 - In the following exercises, determine whether each...Ch. 4.7 - In the following exercises, determine whether each...Ch. 4.7 - In the following exercises, determine whether each...Ch. 4.7 - In the following exercises, determine whether each...Ch. 4.7 - In the following exercises, solve each system by...Ch. 4.7 - In the following exercises, solve each system by...Ch. 4.7 - In the following exercises, solve each system by...Ch. 4.7 - In the following exercises, solve each system by...Ch. 4.7 - In the following exercises, solve each system by...Ch. 4.7 - 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