explain what the second inequality was in the system tells us about the situation

1.

x= number of dog walking hours; x≈300

2.

y= number of car washing hours; y≈300

3.

Ax+By≥600

4.

The download

5.

a- The graph can only exist in the first quadrant because you cannot work a negative amount of hours and/or get a negative amount of money.

b- You are able to earn a exact $600 if you work 23 hours of dog walking and 18 hours of car washing.

23x12=276     18x18=324     276+324=600

c- It is possible to earn greter than $600.

30x12=360     22x18=396     360+396>600

all combinations that occur on the graph are in quadrant one

d- If you work for 10 hours walking dogs and 10 hours washing cars, you will not have enough money.

10x12=120     10x18=180     120+180=300     300<600

(10,10) is not on the line therefore it is not a possible solution for the equation

6.

The model would be changed from Ax+By≥600 to Ax+By>600 becuase you need to earn MORE than 600 so there should not be a line under the symbol. The graph of the model would not be changed because you still are earning $12 and/or $18 an hour. A dotted line and the shaded area under the line represents more than.

7.

The difference between a dotted line and a solid line is that a dotted line is either more than or less than, while a solid line is more than or equal to and less than or equal to. When graphing, you would use a dotted line for equations that are not equal to or more or less.

8.

You determine whether or not that a shaded area is either he solution to a problem or not the solution.

Part 1) see the explanation

Part 2) see the explanation

Part 3) see the explanation

Part 4) The graph in the attached figure

Part 5) see the explanation

Step-by-step explanation:

Part 1) Assign a variable to represent the number of hours that you will spend dog walking in November. Write an expression to represent the amount of money you need to earn while dog walking

Let

x ----> the number of hours spent dog walking in November

so

solve for x

Part 2) Assign a variable to represent the number of hours that you will spend washing cars in November. Write an expression to represent the amount of money you need to earn while washing cars.

Let

y ----> the number of hours spent washing cars in November

so

solve for y

Part 3) Write an algebraic model using inequalities that represents the total amount of money earned by dog walking and washing cars during the month of November.

Let

x ----> the number of hours spent dog walking in November

y ----> the number of hours spent washing cars in November

we know that

You need to earn at least $600 during the month of November

The word "at least" means " greater than or equal to"

so

Part 4) Graph the algebraic model in the first quadrant only.

we have

using a graphing tool

The solution is the shaded area

see the attached figure N 1

Part 5) Use the graph and algebraic model to answer the following:

a) Why does the graph exist only in the first quadrant?

Because the number of hours cannot be a negative number

b) Are you able to earn exactly $600? Use the solutions of the system to find possible combinations of outcomes that equal exactly $600. Where do all of the combinations occur in the graph?

Yes its possible to earn exactly $600. All the combinations of outcomes that equal exactly $600 occur in the solid line 12x+18y=600

c) Is it possible to earn more than $600? Use the solutions of the system to find possible combinations of outcomes that are greater than $600. Where do all of the combinations occur in the graph?

Yes its possible to earn more than $600. All the combinations of outcomes that are greater than $600 occur above the solid line 12x+18y=600

d) If you work for 10 hours walking dogs and 10 hours washing cars, will you have earned enough money for the holiday gifts?

we have the ordered pair (10,10)

substitute in the inequality

----> is not true

therefore

You must not have earned enough money for holiday gifts.

e) Where does 10 hours walking dogs and 10 hours washing cars fall on the graph? Is this location representative of the solution to the algebraic model?

The ordered pair (10,10) fall below the solid line 12x+18y=600

This location is not representative of the solution to the algebraic model, because the solution of the model is above the solid line

f) How would the algebraic model be different if you needed to earn more than $600? Adjust your algebraic model to show that you must earn more than $600. Would the graph of the model be different from the original? Would you include the line in the solution?

we know that

----> represent a linear equation that show the possible combinations of outcomes that equal exactly $600.

The solution is the set of ordered pairs belong to the solid line

----> represent a inequality that show the possible combinations of outcomes that are greater than or equal to $600. The solid line is included in this solution

The solution is the shaded area above the solid line (The solid line is included in the shaded area)

g) In complete sentences, explain the difference between a solid line and a dashed line when graphing an inequality. When graphing the two algebraic models, how did you determine which type of line to use?

we know that

When the inequality is of the form ≥ or ≤ we have a solid line

When the inequality is of the form > or <  we have a dashed line

The difference is that in the solid line the line is included in the solution and in the dashed line the line is not include in the solution

h) How did you determine which part of the graph of the inequality to shade? What does the shaded area tell you? What does the area that is not shaded tell you?

we know that

when you have an inequality of the form

y> ax+b or y≥ax+b

The shaded area is above the line

when you have an inequality of the form

y< ax+b or y≤ax+b

The shaded area is below the line

The shaded area is the solution set of the inequality (ordered pairs that satisfy the inequality)

The area that is not shaded are the ordered pairs that are not solutions of the inequality (ordered pairs that satisfy the inequality)

1.

x= number of dog walking hours; x≈300

2.

y= number of car washing hours; y≈300

3.

Ax+By≥600

4.

The download

5.

a- The graph can only exist in the first quadrant because you cannot work a negative amount of hours and/or get a negative amount of money.

b- You are able to earn a exact $600 if you work 23 hours of dog walking and 18 hours of car washing.

23x12=276     18x18=324     276+324=600

c- It is possible to earn greter than $600.

30x12=360     22x18=396     360+396>600

all combinations that occur on the graph are in quadrant one

d- If you work for 10 hours walking dogs and 10 hours washing cars, you will not have enough money.

10x12=120     10x18=180     120+180=300     300<600

(10,10) is not on the line therefore it is not a possible solution for the equation

6.

The model would be changed from Ax+By≥600 to Ax+By>600 becuase you need to earn MORE than 600 so there should not be a line under the symbol. The graph of the model would not be changed because you still are earning $12 and/or $18 an hour. A dotted line and the shaded area under the line represents more than.

7.

The difference between a dotted line and a solid line is that a dotted line is either more than or less than, while a solid line is more than or equal to and less than or equal to. When graphing, you would use a dotted line for equations that are not equal to or more or less.

8.

You determine whether or not that a shaded area is either he solution to a problem or not the solution.

The ordered pair (-3,50) is not a possible solution, because the number of hours cannot be a negative number

The solution in the attached figure

Step-by-step explanation:

Let

x-----> the number of hours worked to dog walking job

y ----> the number of hours worked to Computers & More, Inc job

we know that

-----> inequality A

----> inequality B

using a graphing tool

The solution is the triangular shaded area

see the attached figure

The ordered pair (-3,50) is not a possible solution, because the number of hours cannot be a negative number

Is not a possible solution

Because the number of hours can not be negative

Step-by-step explanation:

Let

x------> the number of hours in the dog walking job

y----->  the number of hours in the sales job

we know that

-----> inequality A

------> inequality B

Remember that

If a ordered pair is a solution of the system of inequalities

then

the ordered pair must satisfy both inequalities

we have

------> Is not a possible solution

Because the number of hours can not be negative

No, this is not a possible solution because it does not satisfy all inequalities of the system.

Step-by-step explanation:

Let x represents the number of hours spent on dog walking and y represents the number of hours spent on sales job at Computers & More Inc.,

Given,

Total hours can not be no more than 60 hours,

⇒ x + y ≤ 60

Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour.

Thus, the total earning = 7x + 12y

According to the question,

Total earning ≥ $ 450

⇒ 7x + 12y ≥ 450

Also, hours can not be negative,

⇒ x ≥ 0; y ≥ 0

Hence, the system of inequalities that shows the given situation is,

7x + 12y ≥ 450;  

x + y ≤ 60;

x ≥ 0; y ≥ 0

Since, -3 ≥ 0 ( False ),

Thus, the point is not satisfying all inequalities of the system,

Hence, it can not be the solution.

The ordered pair (-3,50) is not a possible solution, because the number of hours cannot be a negative number

The solution in the attached figure

Step-by-step explanation:

Let

x-----> the number of hours worked to dog walking job

y ----> the number of hours worked to Computers & More, Inc job

we know that

-----> inequality A

----> inequality B

using a graphing tool

The solution is the triangular shaded area

see the attached figure

The ordered pair (-3,50) is not a possible solution, because the number of hours cannot be a negative number

(8,10) is not a solution

Step-by-step explanation:

Cuz it’s not on both inequality shaded part but just one of them and also when we substitute one is true and the other one is false

2x + y _< 8

2(8) + 10 _< 8

18 + 10 _< 8

28 _< 8 false

X + y _> 4

8 + 10 -> 4

18 _> 4 true