MeowLover17
  • MeowLover17
Part A: Using the graph above, create a system of inequalities that only contain 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)
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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MeowLover17
  • MeowLover17
MeowLover17
  • MeowLover17
@Loser66
MeowLover17
  • MeowLover17
@Hero

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MeowLover17
  • MeowLover17
@Z4K4R1Y4
MeowLover17
  • MeowLover17
Hey Z4 Got any input??
MeowLover17
  • MeowLover17
@jim_thompson5910
MeowLover17
  • MeowLover17
Hmm
Z4K4R1Y4
  • Z4K4R1Y4
|dw:1433034312051:dw|
MeowLover17
  • MeowLover17
So what do i answer for part A?
MeowLover17
  • MeowLover17
Like where is the system of inequalities or how do i make it???
MeowLover17
  • MeowLover17
Jim please help
jim_thompson5910
  • jim_thompson5910
you can make up anything you want BUT it has to be where the solution for both has to have A and E in it (and only those two points)
jim_thompson5910
  • jim_thompson5910
|dw:1433034502120:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433034513862:dw|
jim_thompson5910
  • jim_thompson5910
here is one possibility |dw:1433034550716:dw|
jim_thompson5910
  • jim_thompson5910
notice how it's the combination of two inequalities
MeowLover17
  • MeowLover17
So how would i write that as a system of inequalities??
MeowLover17
  • MeowLover17
I dont understand how to answer it :/
jim_thompson5910
  • jim_thompson5910
what two points lie above point E? ignore the other points A through F
MeowLover17
  • MeowLover17
(3,2) (3,3)
jim_thompson5910
  • jim_thompson5910
ok I'm going to toss out (3,3) and replace it with (4,3) that way we can draw a line through those two points. This line will be completely above point E
jim_thompson5910
  • jim_thompson5910
what is the equation of this line?
MeowLover17
  • MeowLover17
Okay.
MeowLover17
  • MeowLover17
y=x
jim_thompson5910
  • jim_thompson5910
nope
MeowLover17
  • MeowLover17
I know the slope goes up by 1, but im not sure of the y-intercept.
MeowLover17
  • MeowLover17
y=x-2
MeowLover17
  • MeowLover17
Is that the equation of the line?
jim_thompson5910
  • jim_thompson5910
1 Attachment
jim_thompson5910
  • jim_thompson5910
what is the equation of that green line?
MeowLover17
  • MeowLover17
y=x-1
MeowLover17
  • MeowLover17
am i wrong o-o
jim_thompson5910
  • jim_thompson5910
yep y = x-1
jim_thompson5910
  • jim_thompson5910
we want to shade below this line, so we could have y < x-1
MeowLover17
  • MeowLover17
Okay
MeowLover17
  • MeowLover17
So now i'm guessing we have to make another line with 2 points under A then shade where they overlap receiving the system of inequalities??
jim_thompson5910
  • jim_thompson5910
that is correct
jim_thompson5910
  • jim_thompson5910
something like this
1 Attachment
MeowLover17
  • MeowLover17
Indeed.
MeowLover17
  • MeowLover17
So could help me create the answer to part?
jim_thompson5910
  • jim_thompson5910
I'll brb, but I can do so when I get back
MeowLover17
  • MeowLover17
ok i'll be waiting here
MeowLover17
  • MeowLover17
Part A: So to graph the two lines first i must chose two points above points E, in this case i chose points (3,2) and (4,3), now i must draw the line going through these points and i should hit the y-axis at -1. Next i must choose two points under point A, so i choose (2,-4) and (3,-5) one i've drawn the line through these points i should hit the y-axis at -2. Now i must shade where both A, and E are within these instersecting lines. Which would be on the right side of this graph. Equations= y=x-1 & y=-x-2
jim_thompson5910
  • jim_thompson5910
ok back yes the two equations are y = x-1 and y = -x-2 the inequalities are y < x-1 and y > -x-2
MeowLover17
  • MeowLover17
Is that proper?
jim_thompson5910
  • jim_thompson5910
graphing both inequalities at the same time gives you the shaded region |dw:1433036051038:dw|
jim_thompson5910
  • jim_thompson5910
proper? what do you mean?
MeowLover17
  • MeowLover17
@jim_thompson5910 Sorry i lost connection
jim_thompson5910
  • jim_thompson5910
thats ok
jim_thompson5910
  • jim_thompson5910
hopefully you see how I'm getting what I wrote above
MeowLover17
  • MeowLover17
Okay so i meant is my answer for Part A, okay?
MeowLover17
  • MeowLover17
Yea i understand.
jim_thompson5910
  • jim_thompson5910
they want inequalities, not equations
jim_thompson5910
  • jim_thompson5910
but the equations are useful in forming the boundaries
MeowLover17
  • MeowLover17
oh ok
MeowLover17
  • MeowLover17
So was my answer for part A feasible?
jim_thompson5910
  • jim_thompson5910
it's close to being complete
MeowLover17
  • MeowLover17
I put the inequalities under the equations part on my worksheet.
MeowLover17
  • MeowLover17
What else shall i add?
jim_thompson5910
  • jim_thompson5910
add in info about the inequalities and their shaded regions
MeowLover17
  • MeowLover17
Yea i did, but I'm not sure how to explain the "shaded" regions.
jim_thompson5910
  • jim_thompson5910
equation |dw:1433036725634:dw|
jim_thompson5910
  • jim_thompson5910
inequality |dw:1433036745339:dw|
jim_thompson5910
  • jim_thompson5910
the inequality includes the shaded region which extends forever downward and to the right (below the line y = x-1)
MeowLover17
  • MeowLover17
Okay i see the difference between an inequality and equation, for an inequality you must shade or make dashed depending on if its equal to or not but for an equation you just draw the line.
jim_thompson5910
  • jim_thompson5910
correct, I forgot about that part
jim_thompson5910
  • jim_thompson5910
since y < x-1 has no line under the < sign, we need a dashed boundary line
MeowLover17
  • MeowLover17
Yes
jim_thompson5910
  • jim_thompson5910
but you can easily make it \[\Large y \le x-1\]
MeowLover17
  • MeowLover17
Okay so let me show you my answer for part A: Its the same as i showed above just with the inequalities underneath it because i don't know what more to explain.
MeowLover17
  • MeowLover17
This is for an online course so i can't draw graphs or anything i just type explanations :/
jim_thompson5910
  • jim_thompson5910
then do your best to describe the equations/graphs. So mention the points involved and the direction of the shading, and the boundary line type
jim_thompson5910
  • jim_thompson5910
|dw:1433036996621:dw| this boundary line goes through (3,2) and (4,3) it is a dashed boundary line (assuming you go with y < x-1) the shading is below the boundary line
MeowLover17
  • MeowLover17
Okay let me explain it here then ill transcribe it. Part A: Continuation - After graphing y-x-2, i shaded above it because when i test points below it does not work, now i can shade infinitley if i wanted too, but i am only shading where both shades meet from y>-x-2 and y
MeowLover17
  • MeowLover17
If i add that on to my first answer does it make it complete?
jim_thompson5910
  • jim_thompson5910
yes that wraps up part A
MeowLover17
  • MeowLover17
Okay now could you help me answer parts B and C???
jim_thompson5910
  • jim_thompson5910
Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.
jim_thompson5910
  • jim_thompson5910
I'll show you how to verify point A and I'll let you verify point E
MeowLover17
  • MeowLover17
K
jim_thompson5910
  • jim_thompson5910
verifying point A point A is (x,y) = (2,-3) y < x-1 -3 < 2-1 ... plug in (x,y) = (2,-3) -3 < 1 ... this is true ------------ y > -x - 2 -3 > -2 - 2 ... plug in (x,y) = (2,-3) -3 > -4 ... this is true ------------- since y < x-1 AND y > -x - 2 are true at the same time for the ordered pair (2,-3), this confirms that point A is indeed in the solution set of this system of inequalities
MeowLover17
  • MeowLover17
Oh i see so you just tested point A for both inequalities and it proved true.
MeowLover17
  • MeowLover17
Now i would have to do the same for E
MeowLover17
  • MeowLover17
right?
jim_thompson5910
  • jim_thompson5910
correct
MeowLover17
  • MeowLover17
Okay do i have to show this work or can i just explain it for part B?
jim_thompson5910
  • jim_thompson5910
showing work is always a good idea, but I guess you could explain it if you want. It will depend on how the teacher wants it
MeowLover17
  • MeowLover17
Okay ill just show your work for A then explain for E.
MeowLover17
  • MeowLover17
Okay now on to the final part C
jim_thompson5910
  • jim_thompson5910
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.
jim_thompson5910
  • jim_thompson5910
so the goal here is to figure out which points (A through F) satisfy y < -x-1
MeowLover17
  • MeowLover17
oKAY
jim_thompson5910
  • jim_thompson5910
and you can use steps similar to what I had done in part B
MeowLover17
  • MeowLover17
Btw pOINTS a THROUGH f ARE SCHOOLS in a city
MeowLover17
  • MeowLover17
So do i just test all points in y>1-x to solve for c??
jim_thompson5910
  • jim_thompson5910
you mean y < -x-1, right?
MeowLover17
  • MeowLover17
Oh okay so my Answer for Part C would look like Part C: William can only attend schools that satisfy his zone which is y<-x-1, to figure out which schools would satisfy this i must plug in points A through F into this inequality and see which are true, those that are true are schools that William can attend those that are false or don't make sense are those that he can not attend.
MeowLover17
  • MeowLover17
Is this correct???
jim_thompson5910
  • jim_thompson5910
so which points make y < -x-1 true?
jim_thompson5910
  • jim_thompson5910
you provided the explanation as to how to find the points, but I think they also want the points listed
MeowLover17
  • MeowLover17
It doesn't say that.
MeowLover17
  • MeowLover17
It says "Explain how you can Identify the schools that william is allowed to attend" Not list the schools
MeowLover17
  • MeowLover17
So does that mean my answer is correct???
jim_thompson5910
  • jim_thompson5910
yeah if they don't want the list, then you have it completed
MeowLover17
  • MeowLover17
Okay i have one more question could you help me on it??
jim_thompson5910
  • jim_thompson5910
ok
jim_thompson5910
  • jim_thompson5910
what's the question?
MeowLover17
  • MeowLover17
Oh, its like a whole other problem with parts a,b,c
MeowLover17
  • MeowLover17
Could you give me about 10 minutes or so, i just wanna transcribe the work on here to my worksheet.
jim_thompson5910
  • jim_thompson5910
alright
MeowLover17
  • MeowLover17
Thanks

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