BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 3.2, Problem 44E

(a)

To determine

To calculate: To find if the table represents a linear or non-linear function

(a)

Expert Solution

Answer to Problem 44E

Thetable represents a non-linear function

Explanation of Solution

Given: Table showing the distance car B is from rental store

Time (hours),t	Distance (miles), d
1	60
2	180
3	310

Formula Used:

Linear functions are polynomials with degree of 1 and have constant slopes. Graph of linear function is a straight line

Non-linear functions are polynomials with degree of more than 1 and have a slope that varies between points. Graph of non-linear function is a curved line

Calculation:

Given table showing the distance car B is from rental store

Time (hours), t	Distance (miles), d
1	60
2	180
3	310

Slope of function is calculated as

m1=180−602−1=1201=120

m2=310−180302=1301=130

Since slopes are different, thus table represents a non-linear function

Conclusion:

Hence, table represents a non-linear function

(a)

To determine

To calculate: To find if given claim is true

(a)

Expert Solution

Answer to Problem 44E

Theclaim is correct

Explanation of Solution

Given: Given the linear function d=50t represents the distance d (in miles) Car A is from a car rental store after t hour

Formula Used:

Linear functions are polynomials with degree of 1 and have constant slopes. Graph of linear function is a straight line

Non-linear functions are polynomials with degree of more than 1 and have a slope that varies between points. Graph of non-linear function is a curved line

Calculation:

Given the linear function d=50t represents the distance d (in miles) Car A is from a car rental store after t hours

Time (hours), t	Distance (miles), d
1	60
2	180
3	310

Claim is “Car B is moving at a faster rate”

Rate of car A is calculated from equation d=50t

Rate=50

Rate of car B is more than rate of car A

Conclusion:

Hence, yes, claim is correct

Chapter 3.2, Problem 43E

Chapter 3.2, Problem 45E

Chapter 3 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - 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