The coordinate plane below represents a city. Points A through F are schools in the city.graph of coordinate plane. Point A is at 2, negative 3. Point B is at negative 3, negative 4. Point C is at negative 4, 2. Point D is at 2, 4. Point E is at 3, 1. Point F is at negative 2, 3.
Part A: Using the graph above, create a system of inequalities that only contains points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: William can only attend a school in his designated zone. William's zone is defined by y < −x − 1. Explain how you can identify the schools that William is allowed to attend. (2 points)
Answers
First, we choose the lines...
y = -x + 2 has C and F above it and all other noted points below it. y = -x + 9 has all the points below it on the graph.
So if we include all points above the first line and all points below the second line, we obtain our intersected shaded area. To do this changes our linear equations to linear inequalities.
All points above y = -x + 2 would then be y > -x + 2
All points below y = -x + 9 would then be y < -x +9
Part B: Verify that these points satisfy the system of inequalities by substituting (x, y) for both points into both inequalities. [Pick any random point outside this shaded area to prove that it coordinates do not satisfy the system.]
Graph the line y = -2x + 2. That will be a line that has a y-intercept of 2 and a slope of -2. Then shade *below* that line (we shade below because it is y < ...). The schools that will be in the shaded region are B, A, and D.
Hope this helps-Maranda
Related Questions
Find the coordinates of the vertices of the figure after the given transformation, translation: (x, y)→(x - 4, y + 4)A) J'(1, 0), N'(5, 0), M'(5, 3), P'(2, 5) B) J'(-2, 5), N'(2, 5), M'(2, 2), P'(-1, 0) C) J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1) D) J'(-1, 0), N'(-5, 0), M'(-5, -3), P'(-2, -5)
2 4/7 times 1/4 plz help i need help but m extremely stupid plz help
Please help me its due tomorrow
1 over 3 = and 2 over 5 =
Answers
To go about solving this, do this:
2/5 and 1/8
2*8/5*8 and 1*5/8*5
16/40 and 5/40
Hope this helps!! :)
You need to multiply 2 by 8, and 5 by 8 to get 16/40.
Then you need to multiply 1 by 5, and 8 by 5 to get 5/40.
The final answers are 2/5 = 16/40 and 1/8 = 5/40.
Answers
Decimal: .3
Answers
Answer:
w = 7 7/8
Step-by-step explanation:
w + 1/8 = 8
First, subtract 1/8 from both sides of the equation
w + 1/8 = 8
- 1/8 - 1/8
w = 7 7/8
Answer:
alternativeforms:
step-by-stepexplanation:
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.
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.
4.Graph the algebraic model in the first quadrant only. Let the x-axis be the number of hours spent dog walking and the y-axis be the number of hours spent washing cars. Click here for a sheet of graph paper to print..
5.Use the graph and algebraic model to answer the following:
a.Why does the graph exist only in the first quadrant?
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?
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?
d.If you work for 10 hours walking dogs and 10 hours washing cars, will you have earned enough money for the holiday gifts? 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? Click here for a sheet of graph paper to print..
6.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? What type of line represents "more than"? Graph your new algebraic model .
7.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?
8.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?
Answers
#2. Let y be the number of hours spent washing cars, then the amount of money earned washing cars is 18y.
#3.
Answer:
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.
Answers
Answer:
Step-by-step explanation:
Ron and Pam each have 20 pennies.
Ron will put his pennies into 4 groups.
In each group of Ron the number of pennies =
= 5 pennies
Pam will put her pennies into 5 groups.
In each group of Pam the number of pennies =
= 4 pennies
Ron will have 5 pennies in each group and Pam will have 4 pennies in each group, because Ron will make less groups of pennies than Pam.
Hence Ron will have more pennies in each group than Pam.