BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

1st Edition

ISBN: 9781608408382

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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Question

Chapter 3.4, Problem 28E

To determine

To find: and interpret the intercepts.

Expert Solution

Answer to Problem 28E

x -intercept = (27,0)

y -intercept = (0,18)

Explanation of Solution

Given:

The total point scored by the team is modeled by the equation 2x+3y=54 where x is the number of 2-point baskets made and y is the number of 3-point baskets made.

To find the x -intercept substitute y=0 in the equation 2x+3y=54 ,

2x+3(0)=542x+0=542x=54x=27

Thus, the x -intercept is (27,0) .

Here, the x -intercept 27 means that 27 two-point baskets were made whereas none three-point baskets was made.

To find the y -intercept substitute x=0 in the equation 2x+3y=54 ,

2(0)+3y=540+3y=543y=54y=18

Thus, the y -intercept is (0,18) .

Here, the y -intercept 18 means that 18 three-point baskets were made whereas none two-point baskets was made.

To determine

if the number of 3-point basket can be odd.

Expert Solution

Answer to Problem 28E

Explanation of Solution

Given:

The total point scored by the team is modeled by the equation 2x+3y=54 where x is the number of 2-point baskets made and y is the number of 3-point baskets made.

The total point scored by the team is modeled by the equation

2x+3y=54

Here, the right hand side is 54 which is an even number.

Now, it is known that the sum of two number is even only if either both the numbers are even or both the numbers are odd.

In the left hand side of equation, the number 2x is always even as any number multiplied by 2 is even.

So, it implies that 3y also must be an even number. But it is possible only if y is an even number as product of two odd numbers can’t be an even number.

But y is the number of 3-point baskets made.

Hence, number of 3-point basket can’t be odd.

To determine

To graph: the equation and find two more possible solutions.

Expert Solution

Answer to Problem 28E

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 3.4, Problem 28E , additional homework tip 1

Two more solutions of the equation are (6,14) and (15,8) .

Explanation of Solution

Given:

The total point scored by the team is modeled by the equation 2x+3y=54 where x is the number of 2-point baskets made and y is the number of 3-point baskets made.

From part (a), x -intercept = (27,0) y -intercept = (0,18)

Plot these points and draw a line joining them.

That line gives the graph of the equation 2x+3y=54 as shown below:

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 3.4, Problem 28E , additional homework tip 2

Any point which lies on this line is the solution of the given equation.

So, two more solutions of the equation are (6,14) and (15,8) .

Chapter 3.4, Problem 27E

Chapter 3.4, Problem 29E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

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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