Please help me 1,2,3 or 4
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Hey there! :)
Answer:
The bag is cheaper because one litre is roughly $1.00, compared to the carton which is $1.99 for one litre.
Step-by-step explanation:
Given:
Bag of 4 litre milk = $3.99
Carton of 1 litre milk = $1.99
Find the price per litre for a bag of milk:
Cross multiply:
3.99 = 4x
Divide both sides by 4:
3.99/4 = x.
x = 0.9975 ≈ $1.00
Bag of 1 litre milk ≈ $1.00
Carton of 1 litre milk = $1.99
$1.00 < $1.99
Therefore, the bag is cheaper.
We have the following equations:
So we are asked to write a system of equations or inequalities for each region and each point.
Part a)
Region Example A
Region B.
Let's take a point that is in this region, that is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region C.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region D.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Point P:
This point is the intersection of the two lines. So let's solve the system of equations:
Accordingly, the point is:
Point q:
This point is the
of the line:
So let:
Then
Therefore, the point is:
Part b)
The coordinate of a point within a region must satisfy the corresponding system of inequalities. For each region we have taken a point to build up our inequalities. Now we will take other points and prove that these are the correct regions.
Region Example A
The origin is part of this region, therefore let's take the point:
Substituting in the inequalities:
It is true.
Region B.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region C.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region D.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
So we are asked to write a system of equations or inequalities for each region and each point.
Part a)
Region Example A
Region B.
Let's take a point that is in this region, that is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region C.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region D.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Point P:
This point is the intersection of the two lines. So let's solve the system of equations:
Accordingly, the point is:
Point q:
This point is the
So let:
Then
Therefore, the point is:
Part b)
The coordinate of a point within a region must satisfy the corresponding system of inequalities. For each region we have taken a point to build up our inequalities. Now we will take other points and prove that these are the correct regions.
Region Example A
The origin is part of this region, therefore let's take the point:
Substituting in the inequalities:
It is true.
Region B.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region C.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region D.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true