let me look into the diagram


thx


Do you know what shape is the blue box ?


The blue shape is called Parallelogram


Formula to calculate the area of the parallelogram is base * height


yes


In the problem you have , can you guess what the base is ?


good job


what do you think the height is ?


so they give us 5 for height of triangle


not sure if you can see that


Yes, you are right


So, the height of the triangle is same as the height of the paralloegram


Ok


So, what do you think the area of the parallelogram in this case?


In your diagram, is 5 the height of the triangle ?


It is not clear and hence I am asking


So, I can explain accordingly


yeah


cool, thanks


ur we5lcom


The formula of the parallelogram is base * height


Here the base is 4 inches


Height is 5 inches


The formula to calculate the area of the parallelogram is base * height


what do you think the area is ?


20 cause no half


good job


wow fel dumb


You are doing great


ok can you make one quick for me


sure


like odd shape, to prctic cuase i want


paste the problem you would like to solve


can i come bck on weekend


have other hw


sure, no problem


have a great day!


Jordan


on wknd


uir company


whatcha hours>?


Tutor Provider platform is available 24*7 7 days a week


halulayah


So, it is available anytime


nice nme amd nic help might name


lizard ur name


bye, have a great day!


bye


hi


Hi Liam! How are you?


I'm good and you?


I'm good as well :) How can I help you today?


I need help with this problem


Okay! Do you have an idea where to start?


no


So the composition described is like applying g to f, so g(f(x))


Then, the inputs to g, the domain, should be the outputs of f(x)


Those for which g(x) is defined


Any questions so far?


Then what do you think the domain is for g(f(x))?


Actually, I'm sorry the domain of g(f(x)) should be values you can input to f(x) whose output from f(x) you can input to g


I need help I'm stuck


First we compute f(x). Then we send that output to g. So to find the domain of the composition first we need to find numbers in the domain of f whose outputs can be input to g.


Can you circle the domain of f?


yes


Great!


Can you circle the outputs of f?


Very good! Now we want to see which of the outputs of f we can input to g


Can you circle numbers in the domain of g that are also in the output (range) of f?


Nice work!


So these are the outputs of f that can be passed to g


ok


what inputs to the domain of f originally gave those three outputs?


These inputs will be the domain of g(f(x))


Nice! That should be our domain


To find the range, find the outputs of 0, 3, and 7 using g. Those are the outputs of f for which g is defined


Are 5 and 9 in the range as well?


Awesome!


I have another one


ok :)


So this composition is like f(g(x))


we want to find all inputs to g(x) whose output we can input to f


6 and 7 are in the domain. Let's double check 8. Using g, 8 outputs 1. Can 1 be input to f?


no


So then 8 can't be in the domain of f(g(x)) because we have to pass the output of g(8) to f and f(1)) is not defined


I would also double check whether 2 and 9 are in the domain!


2, 6, 7, 9 is the correct domain!


How about the range of f(g(x))?


Let's double check whether 4 is in the range. What inputs to f output 4?


That's the input to g that outputs 4. What about inputs to f that output 4?


What's f(3) as well?


4,5,6,7 is the range of f(g(x))?


What did you mean by 4,5,6,7?


those are the Domain of f


the domain of f that can be output by g


And what do we get by inputing 4, 5, 6, and 7 into f?


yes! So what's the range of f(g(x)) then? Does it include 4?


Very good!


I have another one


ok :)


Any ideas on what the domain of g(f(x)) is?


domain would be 3,8


3 and 8 are in the domain


Why do you say 5, 6, and 9 are not in the domain?


yes they are in the domain


Can you double check for me that all the outputs can be input into g?


Hint: one of the inputs to f has an output that can't be input to g


in other words, one number in the domain of f outputs a number that is not in the domain of g


So that number that does that can't be in the domain of g(f(x)). We only want inputs to f that have an output that can be passed into g next


oh ok


What would your answer be for the domain of g(f(x)) then?


Yes! very good :)


How about the range of g(f(x))?


To find the range of g(f(x)), you first find values in the domain of g that are output by f. Then, you see what values those values in the domain of g output


so ultimately, all values in the range of g(f(x)) should be in the range of g


But we only want to look at the output of inputs to g that could themselves be output by f


So first step: find values in the domain of g that are also in the range of f


1 and 8


That's not quite correct. First, which values in the domain of g are also in the range of f?


8 is! What about 1, 2, 3, and 4?


yes


Are you sure every value in the domain of g is in the range of f?


Yes very good!


What values do 1, 2, 4, and 8 output when passed to g?


That will be the range of g(f(x))


Which one of 1, 2, 4, and 8 outputs 8 when passed to g?


But 3 is not in the range of f. 3 isn't an output of f. Therefore, we don't include g(3) in the range of g(f(x))


We're only looking for the outputs of g when passed outputs of f


Since 3 is not an output of f, we don't include g(3) in the range of g(f(x))


ok


So what would you say the range of g(f(x)) is now?


That's not correct. We identified 1, 2, 4, and 8 as numbers in the domain of g that are also in the range of f. Now we want to look at what g outputs when passed those numbers. The outputs of g given 1, 2, 4, and 8 will be our range for g(f(x))


oh ok


What would your answer for the range of g(f(x)) be now? :)


2 and 8


That's not correct, but good try! We want to find the outputs of g when passed 1, 2, 4, and 8, which are the values in the domain of g that are also in the range of f.


So can you find g(1), g(2)), g(4)), and g(8)?


g(1)=3 g(2)=1 g(4)=1 g(8)= 3


Very good!


So the outputs are 3 and 1


So what is the range of g(f(x)) then?


Nice work!


Do you have any questions on this problem?


no


okay :)


Any more problems?


yes


what's the first step for finding the domain?


Domain would be 0,4


That's almost right! Why do you say 1, 3, and 9 are not in the domain of g(f(x))?


oh ok


I'd like to hear your reasoning :)


I thought it was just the ones I see in the g(x) domain those are the only two numbers that are same as the f(x)


I see! So we actually want to look for numbers in the range of f that are also in the domain of g first


Can you circle those numbers in the range of f in different color?


Those numbers in the range of f that are also in the domain of g


We're checking this first because we need the numbers output by f to be able to be input into g


Can you circle only the values in the range of f that are also in the domain of g?


Okay!


So to find the domain of g(f(x)), now we just see what values in the domain of f output those circled values


Again, the circled values being outputs of f that can be input to g


This is because the domain of g(f(x)) is values input to f that output values that can be passed again as inputs to g


So overall, to find the domain of g(f(x)), you can find which inputs in the domain of f output 2 or 4


4 inputs are 1,4  2 inputs are 0


very good!


So what's the domain of g(f(x))?


We only include input values from the domain. Not the red circled values


We want the numbers in the domain of f that output the red circled numbers when passed to f


Those numbers will be the domain of g(f(x))


1 and 0


You identified them here: 4 inputs are 1,4 2 inputs are 0


The domain is the input numbers to the circled numbers


You're very close! Can you try again to find the domain of g(f(x))?


The domain will be the values on the left of the highlighted yellow lines.


You can see that these values in the domain of f output values in the domain of g!


yes


yes!


Next let's find the range of g(f(x))


Now, can you choose a new color and circle the values in the domain of g that are also in the range of f?


Can you circle values in the domain of g, not the range?


Is five also in the range of f?


Can you circle 5 in the range of f?


If you can't circle 5 in the range of 5, that means 5 isn't in both the range of f and the domain of g


oh ok


The values you want to circle in pink in the domain of g are the values you circled in red in the range of f!


That's because those values were the numbers that were both in the range of f and the domain of g


Now we want to find and circle those same numbers, but this time, in the domain of g


Can you explain why you circled 5?


Liam, are you still there?


Can you explain why you circled 5 and not 4?


How are you feeling? We've been working for over 3 hours


ok


Okay! Are you still thinking about how to answer my question?


yes


okay :)


Liam, I think I'm going to end the session now because I think it would be good for you to take a break. Over three hours is a long time to be doing math


Do you have any final questions? :)


no


Okay! Have a nice day :)


Great work today!


thank you


Hi, what are we working on?


Hello, I'm using my voice type because I think it's so much easier and faster to communicate


Hello


Sorry.


Hello hello.


Um, so I'll upload what I'm taking a picture or what I'm doing.


Sure


So I kind of started on this problem.


but


sorry, it's loading


No worries. OK, let's see.


Let me know if you want me to zoom in


Nope, it's fine. I can zoom in on my end as well. Uh, so this is problem 8, right?


Yep


OK


Great


So distribution for the selling price is approximately normal.


and we have the mean and standard deviation. OK, so it looks like you started eliminating some of the options, right?


Yeah, I don't know if they're necessarily right, but


yeah, my work's down below. So I understand that um the 68th percentile is between


uh like the first two bars and then the


Mhm


Yeah


2, I don't really know how to say it, uh, the like, yeah, the bars or like the first bar I guess, and then the 3 balls is, yeah.


So


So 68% are within one standard deviation.


yeah


Uh


little different than percentile, so make sure you're being careful with that.


Um


Um, OK, so


what's the


difference


uh, yeah, so percentile is 68th percentile would mean 68% of the samples are


below that point, but um, like, here, let me draw. Oh God, sorry, this is a terrible bell curve. Um


but


uh, 68% are between this range.


which is, so if this is the me in here.


then this is 68% of the sam samples.


Yeah, OK, I get that.


Yeah, but 68th percentile would be somewhere like


year-ish maybe, uh.


and then extend all the way to the bottom.


Does that make sense


OK, so


you


It's not super important for this question, but I just want to be sure


uh, you know what the 68% refers to here.


hm


OK, could you explain that one more time? Sorry.


Yeah, so, OK, um, let's do it with the numbers. So we have the mean is 19,500,500, uh, so the mean minus 1 standard deviation is


uh hold up, let me get out a calculator.


Uh


2500 minus 2260.


is 17,240.


Um, so, how do you, OK.


so what I understood was that like.


OK, so between


Uh-huh.


Mhm


what you said, the 68%, um, so I do like 19 or 19,500 19,500 to get my, like, I don't know what that's called the upper back, like I don't


know.


Yeah, upper bound works, yup.


OK, upper bound, um, and then, uh, so to get your lower, you just subtract 2260


Yes, exactly


and then um for the 95%, so then you would just, um, so you've multiplied 2 times, 2260, and then subtract that from 19,500.


Yup, exactly


Oh, OK, OK. I just didn't know how to do that, but now I do.


OK, yeah, great, exactly like that.


OK, I'm gonna do that really quick for all of them.


OK, yeah


Oh, I'll take me a second


Yeah, no problem


Sorry, I'm someone who types really slow and like calculator.


No, it's OK. I am using my phone calculator, so it's kind of slow too.


OK, I have them.


So I have the upper and lower bound, so


um


when


Mhm


OK, I understand how to do that now, but now I'm kind of still confused like


so when it says approximately 68% of all used Toyota Camrys help selling prices between 149,802,400,020. um


well, that's not right, is it?


We have our upper and lower bound.


No, because, uh, so our lower ground was higher than that. Yeah.


Right. OK. And then the maximum selling price of a used Toyota Camry is 26,280. Um, is that, that's right because the 99.7% is to like that that's right, right?


But that's 99.7%.


So, but yeah, that's why I was like, uh, what is the maximum?


Yeah, so there's still some above that, basically.


Right, OK, OK


That's why I kind of left the mark because it's 99.7%%.


Yeah, if it's uh generally for normal distribution, you don't know what the maximum is.


OK, I'm gonna write a note


Um, and then see approximately 95% of all used Toyota Camrys have selling prices between 12,720 and 26,000,280


Um


that's not right either because the lower bound is 14,980.


Yup, that's what I got too.


And then approximately 16% of all used Toyota Camrys half selling purses less than 17,240. Uh, I don't really understand that, but if we're doing the same thing that we've been doing


um, that wouldn't make sense at all, right, because


Good.


wait, I don't know. Well, I feel like that wouldn't make sense because


um 68%, the lower bound is what it says in the um answer.


So how would it be 6% like.


OK, yeah, so this is a neat trick you can do with a normal distribution. OK, let me draw a fresh one because that first one is terrible.


So when you have the mean here.


Uh, do you know what percent is between the mean and like the lowest value.


um 50%?


Yep, exactly. So this side is going to be 50%.


Um, and then if you take within one standard deviation. So between here and here, we know from before that this is going to be 68%, right?


Yeah.


OK, so what part of that 68%


will be


on the left side.


OK, um, for that,


So, basically what percent is in this little area.


OK, well, I don't get is like


Uh-huh


so I get the 50%, um, so writing the two other bars on the other side, I, I don't get like why are we doing that?


Yeah


Yeah, so, um


Mhm, yeah


with a normal distribution, you know, like the 68 and the 95 and the 99.7, right? So anything else, any other percentages, you have to figure out using those. So, uh, it's kind of like a little, a mini algebra problem. So if you have uh this area is 68%, and you want to find what this little area here is, so if we call that X,


right.


OK


We just subtract it


then, uh, you basically have two acts equal to 68.


OK, I just don't


OK, I, I think I might understand that. I also just don't


um


OK, could we do like an example question that's just like exactly that it's a different percentages to make sure I like actually understand what you're saying right now.


Makes sense


Yeah, sure. So, um


if you have some type of a distribution, right? Maybe it's not exactly normal. And I tell you


that this part is like 50%.


which probably isn't for this one, but it doesn't really matter what the picture looks like.


And then I tell you that uh


this part around here, it is uh like


And then I want you to find the overlap basically.


Uh, so if you assume that these


that this is like the midpoint. So, uh


yeah.


OK


So if I want you to find it in this like shaded region here.


Mhm


That, that would be like 10% of like or I, I don't like, yeah, I really don't get that, um, cause 60, it doesn't like make sense in my brain how, OK, if it's 50% is over 50% over to the right. Um,


or so, yeah, to the right, um, and then you have 60%, but how is the 60% overlapping the 50%. That does not make sense.


Yeah, good question, right? So let's say you have some numbers in, in your normal distribution. So, uh, you know that the cars um


some of it


Yeah.


it's like 19,500, right? And let's say I want to find uh


if I ask you what percent of the cars are $19,500 or less. You would say 50%, right? Because that's the mean.


Um, but then if I ask you like, oh, what percent are between 1,950,017,240.


Right, like between the mean and one standard deviation.


instead of 2


Uh, does that make sense


Kind of


I think


maybe I should just


yeah, I don't really, yeah, I'm not really sure why not understanding that, but we can just move on to the next problem, I think, cause


I don't, yeah


I don't.


OK, are you sure


Yeah, well, could you go back to the uh two X equals 68. Could you solve that? And maybe I can just understand it.


Yeah, so basically if I'm saying, so I want to know what percent are between 17,240, so this is


And


mean, uh, you write it as I'm just going to do M. I don't know if you do mu or M, but we'll just say, um, so m minus standard deviation, uh


uh


will work. And then this is M, right?


So what percentage of the cars are between these two.


Um


which is the same as like finding X here.


OK. Um, so I would, so like,


it, it would be so like the difference between 60 and 50?


or


OK


OK.


Uh and not exactly, um, so see here where I have the equation is going to be 2 x is equal to 68, right?


So I'm dividing 68 by 2.


Yes. Does it make sense why, based on this picture, so 68 is just from this uh lower bound to this upper bound. So it's not like fully, uh, it goes further than the 50 does, because the 50 stops here and 68 is a different range.


Does that make sense


It makes sense why it goes straight, but I also just, yeah, I don't know why. I just can't like wrap my head around the fact that like the 68 like why is it going back?


and overlapping. Well, actually, I actually think I do get that. Um, OK, I do get that. It's just


the line


that the 6 starts at.


Mhm


I guess that kind of keeps.


Yeah, so that's gonna be the 17,240 that you calculated earlier, right? One standard deviation below.


And then, so that's where the 68% starts and it ends at the


I forgot the number, but 19,500 plus 2260.


right


So I want to know just what's between these two.


Like what that basically


Mm


OK.


The 50 doesn't really matter right now. It's going to come back in like a second. So I was kind of jumping ahead there, but you can, you don't have to worry about that for right now. Just, you know that you have 68% and it's like 2 X and you just want to find X


OK


Does that make sense


Yes, OK, I think I get that.


OK, so what's X gonna be?


Um, but that's just 68 divided by 2, right?


Yup.


So


Um, so then 34


yep, exactly. Um, so X is going to be 34. So now what I want you to find is how much is in this range. So below 17,240.


Um


and this is where the 50% comes in handy.


because, so like you just said, uh, X is 34, right?


So you know that uh uh A is 34 and over here you have 50. So if I just want to find the shaded region, what would it be?


Uh, just 50.


So.


No, uh, sorry, the, uh, 50 goes all the way up to the X.


OK. Oh


and I want to find the part without X.


um, OK, so if we know that X equals 34, then we would do 50 minus 34.


Yep, which is


16, so that would be so the D would be correct.


yes, does that make sense?


Yeah, it does


OK, great. Sorry, I probably jumped ahead with the 50. I hope that wasn't too confusing.


No, it's OK. Um.


for, OK, and then


I'm just gonna read, um, approximately 97.5% of all used Toyota Camrys have selling prices less than 20, OK, so


that's not right because my


wait, actually, I don't even know because we would have to do the same.


Yeah, you'd have to do the same thing except with the 95 instead of with 68.


OK.


um, which you're welcome to do it out if you'd like to make sure. Um, might be good practice, but if you want to go to the next problem, that's fine too.


OK, um


could, could you like kind of work it out with me so I could try and see if I can.


it.


Yeah, sure. So, uh, basically, we, you have the bounds for the 95% from before, right?


Uh yeah


Uh


from the 94 and 95.


uh, sorry, 95, yeah


Yeah


Uh, it was


yeah


OK


Uh, 14,980 for the lower bound, and then the upper bound was 24,020.


OK. Um, cool. So the way that we're going to do this now is we want to do 2 standard deviations instead of just one.


So, um,


you can also try to draw it if you want.


That might be helpful


Mm.


So it's


so I'd have to find


um


uh, I


drew


Yeah, could you go I explain a little bit.


Yeah, let me try to scroll


yeah, so we just start with the, you know, a normal distribution, bell curve.


and then I always just like to draw the midpoint, so I know where the meat is.


So then you have one standard deviation.


and then


2 standard deviations.


Right


So you


OK.


And then that would be the


well, that's the 90


5 %


yeah, so that's gonna be 95% are between there.


Mhm


Uh, so now like we did before, I want to like split it in half basically. So I just, so if we just want this part.


uh, how would we get get that


Um


um


so the whole thing is 95, but we just wanted that part, um.


just the half


What?


That's, yeah, that's below the mean.


I don't know. Would you do something with like the 50% again or no?


Uh, no, this is like what we did with the 68. So I drew like X and then X on the other side. So you can do the same thing here. If I say that this is X


uh


then what would this other part be?


yeah, I don't know


OK


OK, no worries. It's just, it's also gonna be X. It's because it's symmetric. So it's going to be the same on both sides.


Oh, OK


Does that make sense?


Yeah, I get that


OK, so then if we calculate x, uh


it's just gonna be, um, what would it be?


And you calculate


X on both sides


Um


Uh


it doesn't really matter which side because it's, it's gonna be the same, but


so


wait


I don't really know like what you're asking, like 90.


oh yeah, I just wanted to like, what is the value of X? Like, what is the number?


um


so does it


like for the first one, for 68 and 50, like why did we get two X? Like where was the 2 coming from, like 2 standard deviations away from them.


Yeah, so it's X + X is 2 X.


OK, but for the um


the 2 x equals 68, like wasn't it only one X, so wouldn't it just be like 68.


Oh, yeah, so I guess you can call this 2x if you want, but we don't need like all four parts. We only need this half.


OK


um,


yeah, I don't, I don't know. I think I'm just gonna ask my teacher about this cause like, I don't know why this is not registering in my brain right now.


You


OK, no worries. Um, let me just walk you through and then you can think about it later and see if it makes more sense. Um, so basically the side is going to be 7.5.


Uh


and same on the side.


you just divided it by 2.


Yup, just divided it by 2.


Um


OK.


and then if you want to go, whatever percentage is in


this range


It's going to be um


so you have the 50


from the side all the way to the end.


And then you have 47.5 from


uh


this region over here.


yeah.


is going to give us the 97.5 from the problem.


Does that make sense?


Oh, I think you just cut out.


Oh, sorry. Um, yeah, I was just saying, so if you take, you have 50% from half of the curve.


and then


we want uh just this part that we just calculated, which is going to be 47.5.


So if you add those, you get 97.5%, like it said in the problem.


Like, you add the 50% and the 47.5%.


Yup.


OK.


Um.


And then um


so this


what is like the 21,750 come into play.


yeah, so, um, so what was the upper bound for the two standard deviations?


I think it was, let's see.


uh


It


It was like 23,000 something, right?


um


sorry, I think it's glitching right now.


Uh, sorry, I don't know my.


Oh, I, I can hear you now. I can hear you.


Oh, OK, great. Um, so I was just gonna ask, what is the number that goes here, so 2 standard deviations above the mean.


Um


sorry, I don't know what's going on with my phone right now. It's like glitching.


Could you say something and see if it works.


Uh, yeah, yeah


Can you hear me


Yeah, that's weird. Uh, hold on.


OK, I think I can hear you now.


OK. Uh


Oh, sorry.


no worries


Uh, yeah, last thing I said, I was just asking what value goes here. So this is 2 standard deviations above the mean.


Oh, so then wouldn't it be the 24,000?


Yup, exactly, um, and that's what we got for the 97.5%, so you can see it's like not the same.


as the one in the question


OK, yeah, OK.


Does that make sense


Yeah.


Yeah, I would say like try drawing it out yourself. It might make more sense also if you draw it on a real standard curve because then the symmetric stuff is easier to see.


Um


Yeah


that was so difficult for me


yeah, sorry, I can't draw very well.


No, it's um, OK, I'm gonna upload this next question.


Sorry, it's taking a second


OK, can you see it


Yup.


OK, great


4s are normally distributed


Uh


oh, I think it


so it cut off with the meanness, but I can see the rest. So,


Uh, OK. The mean 150.


OK, cool. And the standard deviation is 10.


Yeah.


Elena scored 165 and her friend scored at the 75th percentile.


Um


OK. So, I, I'm gonna like try I like.


yep


I, I know how to do this score. So I'm just gonna do that for Elena. Um,


Mhm


OK, so Elena's


OK, so she scored 165


and then you subtract um


So


but her deviation.


Wait, sorry, it was the main


OK, cool


So then


under 65 minus 50 is 15, and then you just divide that by 10, so you get 1.5.


Yup, exactly


so that's Elena's um


Z score


Yup


I guess she's like 1.5 standard deviations above the mean is that.


OK, um


and then for um


uh Maria


Mhm


um, who scored in at the 75th percentile, I always forget, like, how to


do that


Mhm. OK


Um, I don't know how to do this percenta like I've probably asked this 3 times, and I just forget every time. Do


like, I don't know if it's like you have to like write out the bell curve or like you just see like 0.75 times something.


I don't know


You have to do out the bell curve.


You, you have to do the book curve.


Yeah, at some point, you'll kind of start having like the common values memorized, um, but for now, I would say do the bell curve. Uh, so we want 1.5 standard deviations is where Elena is, right?


So 68 percentile.


I don't know.


Uh, how did you get that? Or did you just get it?


OK


Yeah


I have no idea. I just don't know like anything about the bell curve, like, everything I've done is just like


on calculator. I have not done the book er basically at all.


Sure. So, OK, let's just start with uh


um


one standard deviation and do that, and then we'll use that to get 1.5, OK?


Um, so do you know what a percentile is.


Like, kind of like


this, I don't know, like I can find it. OK, so like when there's 10 numbers, right? I mean this is the simplest form of like 10 numbers and like the.


Hm


when it's like with the 70th percentile and then I just will pick.


Mm.


Mhm.


whatever the 7th numbers, like I get that and I also know that there's like a way to find this 75th percentile, but like, dividing something and then I don't know some, I don't know, like you like the vibe and then you like multiply a value or something and then you like add it to like whatever it is or something. I don't.


Yeah, so if you have to describe it in words. What does 75th percentile mean?


uh, 75.


like um


like people like uh you're like 70


like 75% of the people score like less than you or something. I don't know.


Exactly, exactly


Or it's like even like the same as or less than you.


Yeah, the same or lower, yeah.


Yeah.


Yeah


Um, so we know Maria scored at the 75th percentile. So, uh, there's two ways to do it. You can either find the Z score of Maria's percentile or find the percentile for Daisy's Z score. I personally find it easier to do the percentile from the Z score.


Um, so we're just going to start with that


OK. Does one involve like not doing the bell curve or do they both involve you both?


No, you, you need the bella for both.


I hate the book


Yeah, uh, for a normal distribution, you almost always need the bell curve.


OK


OK, uh, so let's try um


let's try shading this in like we did before. So I want to know what percentage is less than or equal to one standard deviation above the mean.


So this is just like we did on the previous problem, uh, because you know the 68 and the 95 and the 99.7.


Right.


Yeah, I don't, I don't like get out like how am I supposed to draw like


um


I just feel like there's like no


I need like a formation or like a


I don't really know how to say it, like a way to like, like always draw like so.


how like I don't know how many like lines I'm supposed to put for like where I'm like.


So actually you can do it without drawing. For most people it's easier with the drawing, but let's try it without and see if that makes more sense to you.


OK, it probably will.


OK, sure. So, um, let's say


uh, let's go within one standard deviation of the mean. So the mean 150, right? And the standard deviation is 10. So if I add ten. What percentage are between those.


Um, like


do you


like divide


like one


160 or do you try like the difference. I just don't know like what you're supposed to, like, what you're supposed to do.


OK, so this is the mean, uh, I guess I'm gonna do mute this time, minus


So


1 standard deviation.


yes


uh, and then this is the mean plus one standard deviation.


So for a normal distribution, what percent


will that take up


so me minus uh standard deviation plus what you said?


Uh, and then to the upper bound is mean plus the standard deviation.


OK, lower bound and then upper bound.


So, I just do um


so it's kind of like IQR yes, in a way.


Kind of, um, let's try it the reverse way. So if you want to know like 6 the 68% range.


How would you get it


Hm


Yeah, I, I have no idea. Like I didn't, I have no idea.


Yeah.


No, no, it's, it's just like the last one, right? When it said, oh, which of these statements is false. There's 68% between these ranges. You knew what to do there, right?


Yeah


So it's, it's just the same thing.


OK


So if I want to know the range, that will be 68% of the test scores.


How do I get it


So it, it'd be like 150.


Yes, exactly


Um, so now if I want the 95% range, how would I get it?


and the 95% range, um,


well


so we're find the 68% like


Yeah, you found the 68%. It's 150, this is


yeah, the mean is


like, but what was, what numbers were we using, so we were using 150 cause that's the mean minus 10 and then so do we have to


like find like the max like or like the, I don't know what you're supposed, I don't know.


Um


So if I want to find in the 95% range, uh, so if I did one standard deviation for 68%.


How would I do 95%?


Oh, you multiply the standard devi, so it'd be like 20.


Yup.


yep.


instead of 10. OK, I think I get that.


OK


So, so then you do


you still use the mean, but you do 150 minus 20


Yup


and then


the lower bound


and then for the upper bound, you just, it'd 150 plus 20.


yep, exactly


OK. So that's going to be the 95% range. OK.


So, now I want to ask, what percentage scored 170 or below.


What percentage scored 170 or below. Well, if we just found the range of 95%. Now you're asking for like


Mhm


exact, so would that be like exactly 995 or I don't know cause that's what I don't get like, how can 95% be like a range, but then at the same time, like you're asking for like


Mhm. Right, so 95% of people got between a 130 and a 170.


OK, so


OK.


Yeah.


So, and now I want to know what percentage 170 or below.


It'll be like 95%.


So, 170 and 170 and below.


wouldn't that


still be 95%? Like you you draw in


No, because some people got lower 170 and we're not counting that right now.


uh, would you do like


um


170 minus 130.


Uh


You get like the, I haven't, I don't know. Yeah, I don't know.


Yeah


yeah, this is where the picture tends to help people, um, so if I put those numbers on this graph, maybe that'll help. So we 150 here.


Uh, 1.


60 here.


Uh, and 140.


Let's just start with those, and I wanna know like what percentage of people


are in this range, basically. 170 all the way to the bottom.


Um


I like,


what it seems to me like is like, would you like keep


going down by 10, 130 31, like, but I don't know like when you're supposed to stop or like.


It, it technically doesn't stop since this is like a test, like we know it's not gonna be below zero, but technically


OK


it doesn't stop. So actually what we're going to do, OK, what percentage of people scored 150 or below.


um,


uh


68 I don't know.


I


Uh, that's between 140 160.


was 68%


But I wanted to


well, between 140 and 150, right?


150 is between 140 and 160, yeah.


So wouldn't it 68%%?


Uh, not exactly. So what if someone scored 120?


That's not in the 68%, right?


No, that would, yeah.


But it is below 150.


So that wouldn't even be on the bell curt I don't.


It would, it's like somewhere over here.


Oh, OK, so


yeah, I don't know


OK. So it's actually just going to be 50%.


It's always 50% below the mean.


Oh, what is the


Uh, like 50% of the scores will be less than or equal to the mean.


yeah


but


Uh, 150 is the mean.


So that basically is


00, OK, OK. Yeah, I did not. I guess I did on that first.


yeah, so that's another way to say that uh this is the 50th percentile.


Does that make sense


Mhm


150, so that's the main, and then 50% something lower. I don't know.


Yeah, cause remember what you said earlier, percentile is like,


that much percent scored at that score below.


Yeah, yeah, jazz are less than, yeah, OK.


below


it.


Yes, so, 50% scored 150 or below. That's the same thing as saying 50th percentile.


OK, OK


That makes sense


Yeah, that does


OK


great


Uh, so now we want to know uh


what percentile 165 will be, right? Because we want to know what percentile Elena is.


So like


we have the bars of like


Mhm


160 and 170. So then we have to do like in the middle.


of that


So like do you put like X or like is there just like an easier way to, well, I guess cause then wouldn't it be like


between 150 and 160, that'd be


another 10%, like, wouldn't that be like


Uh, that's not 10%. That's like 10 points, but between one like between 140 and 160, we have 68%, right? Not 20%.


Oh, OK, so then


it would lie, like I guess in the 95th percentile.


But


Uh


I


so it's between the 95th percentile and what percentile?


the


68%, so I don't know.


Yup, exactly. Um, so it's between the 68th percentile and the 95th percentile, so we know that


Elena scored in this range. Uh, the problem is 75 is also in that range, so we need to be a little bit more specific.


OK


Um, and so she scored exactly halfway between 160 and 170.


Right


170, yeah.


So what, how do you think we'll get that percentile?


Um


do you do like


yeah, I, I really, I couldn't tell you.


OK, 160 is at 68th percentile.


Yeah


right? Like you just said.


170 is at what percentile?


Right. And I want to know what


You do like 90


what?


Yeah, go ahead


this is definitely wrong. I just don't know. Do you do like 95, like minus 68 to find the 70. No, that's I


Uh


OK


OK.


close, so 95 minus 68 will tell you what percentage is in this range, but we want to know


uh, what, that'll tell you how much is between 160 and 170, but what you want to know 165 and below.


Does that make sense


OK, so, um


we want the point halfway between 160 and 170. So that's halfway between the 68th percentile and the 95th percentile.


Uh, OK


So like


you do you like find the difference and then divide it by 2.


Yeah, basically


Yeah


Um, so like, you do like 95 minus 68 and then divide it by 2. So it'd be 13.5.


yep, and then what do you do with that?


Um, well, that's where the 75th percentile lie, I mean, I don't really know.


Right, but the 75th percentile isn't it like a score of 13.5, right?


No, I don't know what 13.5 has anything.


to do with


OK, no worries. So 13.5 is the distance between like 68 and 95.


Well, it's half the distance.


have to, yeah


Uh, so if I want like what number is halfway between 68 and 95.


That's


13 or is that like the 75th like I don't.


So.


Uh, so that's just gonna be 68 plus 13.5.


yeah


It's gonna be


So what does that have to do with like,


the 5th


Yeah, so that will be the percentile of 165.


score


OK


um


is there like a way to do this on the calculator or like.


Hm


maybe


Is this like AP so


I don't know, I just, yeah, I just like don't, yeah, I don't know. I just like.


I feel like there's a no calculator section still, right?


um.


probably we haven't been on the no calculator section yet, but


Yeah, I, it's been a while for me, but I feel like I remember these being on the no calculator section.


oh OK


Uh, so I want to make sure you can do it without a calculator.


OK, yeah, I was just, yeah, I really


I don't know. I don't know. I don't understand that.


Uh, there might be a way to do it on the calculator, um, but I'm not entirely sure.


Yeah


Um


yeah, what I would suggest doing to get a little bit more familiar with this.


is like


um


to draw


uh with like one of these examples and to write what percentile, like different numbers are, like, like if I asked you what percentile


120 is


or something like that


Um, that would be good practice to see if you're more, more comfortable with like the drawings or just doing the math, um


OK


Does that make sense


Yeah, yeah, that does


Uh, do you know the answer to this question?


oh,


did we ever find like the


75th percentile, like what that was for like,


Uh, so actually we were looking for what percentile Elena is, um, and you just said it was going to be halfway between 68 and 95.


Oh, OK, so you just do like 3.


So we just did the 13.5 thing.


weight plus the 68.


Yup


Oops, I just typed that in now


OK, so


I guess Elena's Z score is.


higher than


um


yep.


Maria's.


Um


like, even though we don't know Maria's


score.


Uh, yeah, you can calculate it if you want.


I don't know how.


yeah


Is that like also bell curve thing?


it is, uh, I'm trying to double check if there's an easier way to do it. I don't think there is, um


Yeah, I was gonna just like ask my teacher tomorrow and he'll probably like explain it to me and I'll be like, oh well that was easy and I don't understand why I didn't understand. I just do that a lot, so.


yeah.


there might be a way for you to do it with a calculator. Um, that I have forgotten by now.


I mean, maybe like there's like uh maybe like like 2 bars, is that like ring ring a bell? like normal PDFs, normal CDF inverse norm. Does that like ring a bell, maybe?


Mm


Yeah, I.


it shouldn't be any of those. Well, I guess technically it is a normal


CDF


cause it is a cumulative distribution function.


Yeah, if you do normal CDF of uh


mm.


because we have mm


well, we do have the m


I don't know. We'd have to like find like the upper and lower bound of, I don't even know actually, but we have the mean, and we have this.


yeah, uh, for normal CDF it should only ask for


like you should just be able to put in a higher bound.


I


Um


It does give a lower one, but you can just like put like,


yeah, I guess you could just put like 0 or something.


Yeah


Um, so if you put in


a lower bound of zero and then the upper bound of 1.5


Oh, the upper bound would be 1.5, like that's like Elena's score.


Uh


oh wait, no, sorry. Um, you want to find Maria's Z score? Is that what we're doing?


Yeah.


sorry, I'm trying to


remember what normal CDF, how it works on a calculator.


normal CBF of


hm


Well, I feel like


like 0.6 I don't.


um


Yeah, I don't know. I do feel like there probably is a different way because


I also like wasn't here, I guess, for a couple days, but


I do.


Yeah, I think there is a way to do it on the calculator, but as far as I remember, this type of thing would be on the no calculator section, so it's good to know how to do it both ways.


Yeah, yeah


OK, um


so


Yeah


OK, I'm gonna upload this picture


These all are bell curve. I'm


not gonna understand them, but it's


OK, I think I'll have time to help with one more and then I have to.


OK. OK.


Oh, I just see that.


Uh, number 5.


Yeah.


OK. Uh


let's see


Um


oh, OK


So


how did you get the Z score on the last question? Do you remember?


Um, just like the formula.


Uh, yeah, you just did like


whatever the minus the mean divided by the standard deviation.


yep, exactly


Um, so


they converted


from minutes to hours by dividing by 60.


Um, and the score was X before they did that, right?


OK


So, um, when they did, basically they did like X


was the score for the participant, let's say.


because


Me is


does the um


the score ever like


I don't know, like


Mhm. Yeah.


does it change when you do anything, like when you divide or multiply or subtract or add, like, is there like a thing where it's like, oh cause I know there's rules to like the mean and median are like the center, so like they all change and then


like stuff like that. So does the Z score like ever change or does it not ever change?


Or does it


go about?


Uh


do you think it would change?


Like based on the formula, right?


Would it change


like I wanna say yeah because it says it's dividing by 60, but at the same time I feel like it's not, you're not too like.


I don't.


to


OK, um, you have the correct intuition, uh, like it shouldn't be changing.


but


Yeah, I don't think it


yeah, but just to go over


a little bit, um, so


they're multiplying, or sorry, they're going to divide X by 60.


What about the mean? If you divide like all of the individual values by 60. What happens to the mean?


uh well


I don't know. Doesn't the meat


uh, I don't know, it's like


0 division is 1. I, I don't know if it's like plays into anything.


Right now, I just


Yeah, so, um, if you have time, like you should draw this out with an example because um just to make sure you follow, but the mean will basically also get divided by 60.


OK


because the mean is just like a sum of a ton of numbers, right?


Yeah


divided by something. But if you divide all those numbers by 60, then the mean will also be divided by 60.


right?


Yeah, cause it always it always changes.


Yeah. So then how about the standard deviation? How do you get a standard deviation?


Oh


Um, actually he like never taught us like how you actually get us in deviation and just like


we just like have, yeah.


Yeah, OK, so basically it's going to be the sum for all of your values. You do like the value minus the mean.


uh, and then you square that.


um, and then you take the sum of that over, oops.


over all of the values.


um, and then you divide it by


uh one sec, uh


you divide it by N


where N is like the number of samples you have.


Is that


uh


Yeah


you don't have to worry too much about the formula. Um, I basically just wanted to show you that like


if you'll divide this X by 60, and then you'll divide the mean by 60.


So


if you divide everything by 60, then like it'll all cancel out.


is I guess what I'm trying to show you.


Uh, yeah, I get that.


OK.


Yeah, so I'm just trying to explain, like, you're right, the Z score doesn't change.


OK, yeah


I just like couldn't have


Yeah, I just wanted to explain it a little bit


to make sure, yeah


yeah, I think you remember, yeah, um.


OK, the disease changes no matter if it's like adding, multiplying, dividing, subtracting.


Uh, I think I can change, well, OK, it depends. If you're doing, if you're multiplying or dividing, for all of the numbers. Z score won't change.


But if you're


But if you're adding or subtracting, it will.


oh


yeah, I did


OK, so


that.


because um to get like a Z score, you're doing like multiplication and division, right?


So, uh, if you're adding some stuff, then it will change.


Mhm.


OK, um, OK, so then like, OK, I know the media, median and mean always change, um.


and then


IQR and standard deviation only change with multiplication and division.


Mm, I don't think the


oh yeah


Standard deviation. Yeah, if you shift all of the values by the same amount, then the standard deviation shouldn't change.


like you


Yeah


So like if you add one to everything, it shouldn't change, but if you


multiply or divide, then the standard deviation does change. Yeah.


OK, and then


yeah, and then like


it's like 0 and then see the deviation is always one.


right?


For, I don't know, some specific


question


like after I


Yeah, I guess it'll depend on the question. Um.


yeah, after converting like all


like something into these scores, it'll be like what will that be the new mean and standard dimension.


Mhm


Um


yeah, I think


that just be your own one. Yeah, OK.


Yeah.


OK. Cool. Um, yeah, hope that was helpful. Um, sorry, my drawings weren't the best, but I hope it makes more sense now at least.


No, it helps.


Yeah


Well, thank you.


Yeah, of course. Good luck. Bye.


how are you Jamie?


Good, how are you?


good


What can we discuss


I'm doing right triangles and hypotenuse


ok are we good with basics


yes, I just don't understand how to simplify the square roots that are not perfect


Ok should i share an example and you can share your Q


yeah, that's good


My legs are 8 and 9, it's asking me to get the hypotenuse in the simplest form


is the board eg. clear


yes


what is the hyp?


in sqrt


find its factors


ok


5 x 29


this cannot be simplified further as they are both prime


ohh


so the simplest form would be?


like square root version


ok! I have one more question about the example


how does the order you put 3 and √5 matter?


not really


its easier to read if sqrt is later


okay, thank you :) this helped


glad to help


ok, bye bye :D


Is this Tenth Grade math


yes


Oh OK c u next time. Good day


you too!


hi Alice! :)


hello i ahvea test oming up onthursday ut i only rlly have today to study and i sorta have a study guide but i just want to make sure ik how to solve all te problems on my own at the end


hello


how are you


im good, thank you for asking! how are you?


of course! what do you need help with?


im great thank you ,well yea i just need preparing for my test


ill write my question on the bored


okay :)


is that right


one sec!


okk


hi! so sorry for the wait, yes this is right :) good job!!!


thats okayy


okay ill m ove on to my next question lemme just get something real quick


sure!


sorry my computer is acting s slow


no worriesss


there's a text option if that makes it easier for you :)


yes but then my computer takes longer toload :(


aw okay no worries then!


yep!


nice work!


Ben


thx


you're welcome! is that all you need?


oh sorry i dint see this no


yes Alice! no problem


is this right


i believe so, yes


okayy


is that right


one secc


okk


what was the formula you used?


i just did 10/x=15/13


is that 8.6?:)


yea


yes that's right


either 8.6 or 8.67 rounded


okayyill do my next question


Alice!


yesss, you're a natural :)


lol thanks ,ok lemme erite down and then ill go next question


Alice


yupp


Ben


il writew next


okii


is hat right


are you supposed to find the parallel equation to that?


yes


yes that's right :)


oay ill write next question


is this rihg


yuppp, but don't forget it's +-


oh yea okk


I'll writr my next quesion


how many moree?


kinda lot ,how long can you stay


is that right


i can stay for about 10 more minutes :)


if that's alright with you


yes that totally fine


alrightt one sec


Ben


is that 8.5 or 8-5?


ahh, i don't think dats right unfortunately. how did you get that answer?:)


i put ti intop my calculator


and thats what i got


ohh rightt


are you just supposed to simplify this or?


yea


i think this is the answer


ohh okay ,ill write my next question


alrighttt


i'll have to go after this one </3


yess okayy


is that right


the denominators are right however, if im not mistaken, the numerators should be different


is that right now?


yes!! :)


okay great


wel thank you somuch for your help i greatly appreciate it


of course, you're welcome!!! goodluck on your exams, i'm sure you'll ace it :))


have a great rest of your day!


yes lets hope have a great day bye


hi


k


I need help studying for my quiz tmmr


its about parallel lines cut by a transversal. its about the postulates and theorems, and the different kinds of angles that are formed. Also, I have to write 2 collumn proof about my reasoning, and I may have to do a flow chart


good evening Alex


can you help me with my quiz prep


yes


do you have the review question or something similar?


umm lemme check, one sec


Its like a proof about 2 lines, cut by 2 transversals


yup


lemme try to draw


Do you want me to go over what you are confused or do you want me to go over everything (which takes long time)?


because it has multiple knowledge in it


I just need to memorize the different postulates and theorems, and learn how to apply it in proofs and stuff


suree


sorry about my drawing


can u somewhat see it?


yes I see it


beautiful


alr


so can you help me solve this problem, and some other similar problems


Yes I can


I'm writing every postulate and theorems on the board


it takes little time


oh ok


so what is the relationship between angle 2 and angle 11?


you can use the bridge property


what's the bridge property?


bridge property: if 2 things are both equal two another thing, they are equal to each other


for example if a = b and c = b, then a=c


is that the same thing as transitive property?


yeah, that is the other name of it


umm what do you mean by relationship between the two?


are they both congruent to any angle else?


umm tbh idek


alright, so we can start with angle 1


using those 5 postulate and theorems, what is angle 1 congruent to?


angle 1 is congruent to angle 6 and angle 3


is that right?


yes


what else?


um


angle 9 and angle 7?


correctttt


yay


now, we have angle 1 congruent (which means equal to) with 3, 6, 7, 9


we can do the same thing for angle  2 and eleven


we can say that 11 is congruent to 3?


may you please list out the angles that congruent to each of them?


wdym?


can you name the angles that are congruent to angle 2 and then name the angles that are congruent to angle 11


hi! how's your day going?


good how are you


i'm good! what do you need help with?


I have some questions


I'll post a photo


ok perfect!


this is a good question, do you know a method to turn the first equation into the second one?


not really


that's okay! when the x-3 has a 6 outside the parentheses, do you know what that means?


multiply?


yes exactly, it means the x-3 is being multiplied by 6


to get to the second equation, we need to get x-3 by itself on one side


do you know how we can get rid of the 6 so that x-3 is by itself?


sub tract


good guess! since the entire expression of x-3 is being multiplied by the 6, we can remove it on that side by dividing by 6


do you know what you would have to do to the 48 on the other side in that case?


devide by 6 aswell


exactly!


so after you divide the 6 from both sides, what is the equation left over?


yes, that is what the 48 would turn into after dividing by 6; what would the entire equation be including the other side?


close! if you divide by 6 on both sides, the 6 outside the parentheses of x-3 goes away, leaving you with x-3 on the left side, and the 48 turns into 8 after being divided by the 6


so with this information, what would the final equation be?


x-3 = 8


yes, x-3 = 8!


so we just found out that simplifying the first equation turns it into x-3 = 8, which is the second equation


now, since the problem is asking you why the solutions to these two equations are equal, can you explain why they are?


Wait, so it's asking how did we get the um answer.


it's asking why the solutions to the equations, or the x-value that makes the equation true, are equal, so we can say that the solutions are equal since simplifying the first equation showed us that it is the same as the second equation


in a more simple way, we could say that the solutions are equal because the equations are equal


ohh ok


sorry if my explanation was a little weird, do you still need clarification on any parts of the problem?


oh no


how long do you have


i can stay and keep helping! no worries


amazing


I'm posting it


ok perfect! which part of the question confused you?


um I have B


because I decided 72 by 8


that's the right answer! can you explain how you got it?


yes perfect! good job factoring out the 8


so I'm right


yes that is the correct answer


I have 1 more


I don't get it


ok no worries! do you need help with all parts of the question?


yes


ok let's start with part a; it's asking for a value when the distance is 20 kilometers


do you know where to look on the graph to find 20 kilometers?


yeah


ok great! so since you know to look where the x value is 20 (representing 20 kilometers), now all you have to do is look for how many miles it is equal to at x=20


can you mark the y-value where x=20?


the one you just marked is correct; there, the x-value, or kilometers is equal to 20


now, can you mark the point where the line hits at that x-value?


yes exactly! that's your answer


for part b, now it's asking you to find kilometers where the miles, or y-value is equal to 20


since you already marked where the miles equals 20 on the graph, all you have to do is mark the point where the line hits that y-value, which is similar to the problem we just did


exactly!


now for part c, do you know where we have to look on the graph to find the number of miles that is equal to 5 kilometers?


perfect! now, since that y-value isn't a whole number, the problem asks you to estimate


and the y-value looks like it is about halfway to 5, so what number can we estimate it is?


I meant 4.5.


that's a good guess! the y-value might be a little over halfway to 5 (which is 2.5), but it doesn't look too close to 5


somewhere between 2.5 and 4 might be a good estimate


ok


now part d gives you the equation needed to convert kilometers to miles, using m to represent miles and k to represent kilometers


if it's asking to convert 20 kilometers to miles, how do you think you will use this equation?


also this one might require a calculator to get the exact value


let me know what you get when you plug it in to the equation!


do you need any help to plug it into the equation?


umm so


I couldn't figure it out


no worries! do you know which variable we will plug 20 into?


close! we will substitute it in for k, since k represents kilometers


so the equation would become that


and to get an exact answer, you might want to type that in to a calculator


what decimal place does your teacher usually have you round to?


we haven't done that yet


oh ok! no worries, you can just round to the nearest whole number (no decimals)


let me know what you get for your answer!


Well, OK, so what


I


what's the newest phone number for 1.609.


oh wait sorry i said that in a confusing way! i didn't mean to round the numbers in the equation to the nearest whole number


you can just type the equation i wrote on the screen straight into the calculator


and then i can help round to the nearest whole number once you get your final answer


if it helps, this is exactly how i typed it into the calculator


um I got 12.4


yes perfect!


so now that we have the number, we can round it to the nearest whole number (number with no decimals) by looking at the first number after the decimal point


since 4 is the first number after the decimal point, do you think we will round up or down?


up


not quite, but it's okay! for figuring out whether to round a number up or down, you look at the first number after the decimal point (which is 4 in this case): if the number is less than 5, we round down, and if the number is 5 or greater, we round up


now that we've reviewed rounding rules, can you determine whether to round to 12 or 13?


yes perfect! so that would be your final answer


and make sure to include a label with your answer, which in this case is miles


ok


that's all


okay! i hope i at least helped you understand some of these concepts a little bit :)


bye


bye bye


Hi Ahmed. How's your week going?


Hello


yes


good


your head


Yes


I


Sorry I can't hear you for some reason


Hello, can you hear me now?


OK.


I can't hear you


I can't talk because there is noise & radio here


But I can hear you


OK


Do you have a problem to work or just trying out the system?


Um, I have a test that's coming up, so I wanna do um um little equations.


uh


I wanna do


Do you have some examples or want me to make some up?


I also wanna do algebraic expressions.


with


articles


Radicals?


Yes


you could just make them up


Are you doing one-step equations? Two? Linear?


I'll start with one


and then I'll do 2


and then we can move on


Do I solve it


Yes 😀


OK.


Careful


Oh, wait, wait, wait, wait, wait


Oh.


Great.


OK. Thank you


What did you say?


What


OK, work on this one


I can't see over there on the right. Did you say x = -4?


Yes


Good. that's right. A faster way:


OK


here


So X equals -4.


since 5(something) = 0 then something must be 0 😉


Hm.


Can I solve in my notebook and give you the answer, cause it's hard to draw with my mouse.


Sure.


Is it -15?


Let's see


So is it this that I draw?


1/2. Is it correct?


Oh, thank you


Correct! You're pretty good at this. I'm not sure you need a lot of practice.


OK, so I'm just gonna go do the science. Oh no, I'm gonna do a history.


What about radicals?


OK, let's practice radicals.


Can you give an example of what you mean


Can you make up one


I don't know what you're doing with them.


No, like radical equations, like radicals in equations.


solving radical equations.


Oh


Like that?


Hi! How can i help you?


Hi!


I need help with this


To solve this problem, you first work on each inequality separately. Starting with n-2>4, you add 2 to both sides and get n>6. For the second inequality, 3/5n≥6, you multiply both sides by 5/3, which gives n≥ 10. Since the word connecting them is “or,” the solution includes all values that satisfy either inequality. Because all numbers greater than 6 already include all numbers greater than or equal to 10, the overall solution is simply n>6. In interval notation, this is written as (6,∞). On the number line, you show this by drawing an open circle at 6 and shading everything to the right. The graph in the screenshot is incorrect because it starts at 10, but the correct graph begins just after 6.


can you show it visually


The black line shows the the number line you shared.


Do you have any questions?


nope next one


To solve this problem, we start by working with each inequality separately. From the first inequality, n minus 2 is greater than 4, we add 2 to both sides and get n greater than 6. From the second inequality, three fifths of n is greater than or equal to 6, we multiply both sides by 5 over 3 and get n greater than or equal to 10. Since the two inequalities are joined with the word "and," the solution must satisfy both conditions at the same time. A number greater than 6 and at the same time greater than or equal to 10 must be at least 10. Therefore, the solution set is all numbers starting from 10 and going to infinity.


This next


To solve this compound inequality, we begin with negative five less than negative three x plus four less than or equal to one. First subtract four from every part of the inequality, which gives negative nine less than negative three x less than or equal to negative three. Next divide each part by negative three. Since we are dividing by a negative number, the direction of the inequality signs must be reversed. This gives three greater than x greater than or equal to one. Rewriting in order, the solution is x greater than or equal to one and less than three. In interval notation, the solution set is written as bracket one comma three parenthesis.


now divide all by 4?


If you were to divide everything by 4 instead, it would not isolate x correctly, since the term with x is multiplied by negative three, not by four.

So the subtraction of 4 was the right move, and the next step is to divide by negative three, not by four.


oh i meant 3


[1, 3)


3/-3 is -1


We had this step after subtracting 4:
-9 < -3x ≤ -3

Now divide every part by -3. Since -3 is negative, we flip both inequality signs:

-9 ÷ -3 > x ≥ -3 ÷ -3

That gives:
3 > x ≥ 1

Rewriting in order:
1 ≤ x < 3

So the endpoints are 1 and 3, not 3 and -1.


ohh i see


it was a neg 3 sorry im tired lol


and this is wrong


oh nvm its bc i put it at -1


it should be this?


or would the line go through it?


like this


The correct graph should start at 1 with a closed dot or bracket, end at 3 with an open dot or parenthesis, and the segment in between shaded.


yep i did that, its correct


here's the enxt one


We are solving:
2 ≤ (2x + 1)/3 < 4

Step 1: Eliminate the fraction
Multiply everything by 3:
2 × 3 ≤ 2x + 1 < 4 × 3

6 ≤ 2x + 1 < 12

Step 2: Subtract 1 from all parts
6 − 1 ≤ 2x + 1 − 1 < 12 − 1

5 ≤ 2x < 11

Step 3: Divide everything by 2
5 ÷ 2 ≤ x < 11 ÷ 2

2.5 ≤ x < 5.5

Step 4: Interval notation
[5/2, 11/2)


Hi Emily, how can I help


Wsg i need help with rounding


ok


i have an assignment


alright lets work this together


There


ok do you know the rules when it comes to rounding?


I think so its like 5 and up you round up 4 and down you keep the same


is that right idk


yes thats right


alr


when the digit is 5 or higher, round up, when its 4 or lower round down


Ohh okayy


so now for whole numbers, you look to the tenths digit to determine


im going to underline the digit


that is the only one that matters when you do nearest whole number


alright so do you have an answer for this question


Not rlly


ok thats totally fine


so as i said before, when rounding to the nearest whole number


look to the tenths digit


for this case it is three


because three is not 5 or greater


we round down


it would 3.0 because you are showing that you rounded down


its kind of like showing work for rounding


Oh i got that and it was correct


oh ok


so i guess it does not really matter


srry


your good


both works


do you have anymore questions?


Yes do you mind


no I dont mind, lets do more


ok


ok this is the same deal as the last one


Yes it is


ok do you have an answer or do you want some guidance


Hmm lemme try rq


I figured it out


yes thats correct


alr


good job!


Tysmm!


Ooo this is different noww


bro you still there


yes im still here


David


oh


i didnt see the question


mb


Wsp all good


ok so first we need to locate where the hundredthousandth digit is


Yup


do you know where it is?


i could show you if you need


Sure


Sry bout that


youre good


WOW how do u right like that


yes its kinda weird


NO its gooddd


oh really ty!


ofc! anywaysss


i always count like this when tyring to find it


now the question says nearest hundred thousandth, meaning we need to look at the digit after it


Ohhhhhhh


mb


its like how when we did nearest whole number


we had to look at the tenths place


to determine


samething for this its always the digit after


however this one is a little tricky


do you kinda know where to go with this or do you want some help?


The 5 rounds up than everything after it means nothing right?


i tthink soo


yea so 93 does not matter


but when you round up with the 5


Yup


the digits before it change as well


So what do i do to change them


ok do it like this way


so the 5


becomes a zero


and the 9 becomes a digit higher so 10


but we can fit a two digit number in a one digit slot


so you have to use the number before it


Okayy


This is all a lil confusing like all the writing


ok my bad, lets just erase the things before


Sorryyyyyyyyy


youre gooood


ok back to what i was saying


now when this 9 becomes a 10


we have to carry it over


Ookayy


and you do it again


so the final answer is


I ToTaLlY understood that


ok im sorry, could you tell me which part you need more explanation with?


This


ok


hmm


let me do a simpler way


im going to show you something that may be easier or more confusing


oki


ok so the 5 needs to round up right


so lets add a 0.00001 to increase it by .00001


now we just add


its the same thing with rounding up


we want to increase it by just the next highest digit


now do the addition


There


yes now this addition is the same exact thing as rounding and its easier to visualize


the 9 digits are going up by one due to the rounding so it has to carry it over


Wait that was rounding


so 46.265 is right


yess


this is essentially how rounding up works


its just add numbers so that the following digit goes up by 1


David i just did thatt


yessss


That right there was WAYY easier btww


ok thats good to hear


i felt like the other was complicated as well


David its just to much for some odd reason


ok Emily, im sorry to say but i have leave now


Its okk


thank you for your work today! have a great christmas, if you celebrate!!


Thank youu David christmas


hi


HelloHello


srry my computer is very laggy


oh it's fine


what would you like to work on


Ah, so here we are looking at a system of equation problem, basically we need to find two equations, one that counts number of pizzas and the other is price


So out first step should be labeling our variables, try this part on your own :)


If you have any questions lmk


helo?


u there?


hi sorry


I was fixing my internet


it's good


try naming the two variables prsent in this problems


problem*


alr, which part r u confused on cuz u basically got it


I'm stuck here


I don't know what to do now


ah ok, now from this we have to evaluate


do you understand how i got this


yes


alr, try simplifying his equation


by subtracting 14.95 from 10.95


Not quite, you have the subrtact -14.95 from 10.95, you did it the other way around.


if u r confused lmk


I am confused


Do you understand how i got that


if not js tell me


let me  check if I get the same thing


okay!


hey how can i help you today?


Hello


Um, I just had a question on how do you like when you like you, when you rationalize and simplify, how do you like check your answer, like using a calculator.


like, you know


wait can you say that again


but just never mind.


are you sure?


We actually, can you check my work?


I don't even know what the tutor was saying at this point. He was saying it. I, he wasn't even telling me how, so that's why I was asking you.


like, you know, I don't know


what he was talking about, never minds.


yea sure just show me the problem and i will


Which one that just do right here. Oh yeah, this one, can you check?


And it's simplified to the core, right? Like I don't have to simplify more.


the picture didnt upload


oh wait it did


And then like, I'm just asking like, how do you, can you check your work if it's right using a calculator?


you know, Is there even a way to do that at this point?


yea do you have a graphing calculator or a scientific calculator


also that question is right


My answers is right


yes


And like, I'm have a final on this, and it's like one of the things in my final, like what other notes should I take?


on this or like should I just write down that problem cause I like did a few of them on my own and I got them right. So, like, should I write extra notes on them or do I just put those types, you know.


do you know how to simplify square roots that arent perfect squares


like do you know how to do the square root of 40


we have to simplify like 32.


It is a rationalized and simplified. Why are they asking us to also simplify the


i mean if that is on your final?


uh, the 30 and stuff.


Wait, how do we send


I don't know, it doesn't say anything specifically. It just says rationalized and simplify. Oh no.


Now how do we simplify this 50, I mean 30.


you know


yea i know what u mean


if thats on you r final tho?


Girl, I just say I don't know, I just say it's rationalized and simplified. I don't know.


I don't know what we're doing.


yea okay i gotchu do you know how to find the square root of liek 40 tho


i can give you a quick rundown if you want


Uh, it's, it's dirty for me.


like, do like times about something.


yea 30 cant be simplified down in this case


but lets say you do square root of 40, that can be simplified down


and neither can


so thats why im asking do you know how to do that


um, I did one earlier and 10 couldn't be simplified either 30 couldn't either.


54 can be simplified


Show me how


okay i will ill use 40 as an example


im sorry for not being able to use my mic right now normally i can its just bugging right now


basically when taking the square root of 40 we want to think about the factors of 40


so lemme write on the board


after listing the factors


we want to see if any of the factors are perfect squares


in this case 4 is a perfect square so lets work with the factors 4 and 10


since 4 is a perfect square, the square root of 4 is equal to 2 so it can be simplified down to 2


on the other hand, 10 has no factors that are a perfect square so 10 cannot be simplified which is what you told me earlier


after simplifying the most we can, we multiply what we have left so we get  that


the square root of 40 is equal to 2 times the square root of 10


if you have any questions let me know


Can you give me a minute real


yes take as much time as you need


I’m over here please don’t disconnect. I’m here. I promise. I just have to do some other problems real quick for you to check them real quick you know


how long would it take though


Couple of minutes


okay thats fine let me know when ur back


How


Hello, can you hear me


Hello


yes im here


OK, so I had asked, I'm sorry about that. Can you turn on your mic and just like explain to me I how do we simpl 54,050, what went on 54.


okay give me one sec real quick


Mm OK


Silita


ba ba ba.


OK, can you hear me?


you.


hello. Can you hear me?


Yeah


Yeah, I can hear you


OK


Um, to get the square root of 40, basically from the beginning, we wanna list like the factors of 40, and so, um, I listed all the factors of 40 and we got 1 times 40 gives you 40, 2 times 20 gives you 40, 4 times 10, 5 times 8, and that's all the factors of 40. Um, and then basically after that, um, you wanna see if any of the factors are a perfect square. So in this case,


we saw that um 4 was a, a perfect square, and 4 goes along with 10, since 4 times 10 gives you 40. And so we're gonna work with the factors 4 and 10. So that's why I split the square root of 40 into the square root of 4 and 10. And then from there we're gonna, um, we're gonna take the perfect square that we saw and the perfect, um, the square root of 4 would be 2. So I simplified that down to a 2, and as you said


earlier, um, the square root of 10 can't be simplified, and that's because um the factors of 10 are 1, 10 and then 2 times 5, and none of them are perfect squares, so it can't be simplified. So the thing that we have left is 2, as a whole number and then the square root of 10, and then basically in order to put it all together, we get that the square root of 40 is equal to 2 times the square root of 10. Does that make sense?


I do.


What


So the factors for uh


54 would be like 3 or something.


Um


well, I, yeah, 3 does work, but in this case, um, as I said, after listing out like the factors of it. So after listing out the factors of 54, um, you would see that there's a factor of 9 times 6 and 9 is a perfect square, so we would work with 9 and 6.


So I said I put a picture of it, so I would just do uh


that


I.


like that.


Um.


um


So right here, I would, I would just put like


Oh.


yeah, so you're like almost there. Um, the square root of 54, so


Yeah


God.


OK. Um, let's do it here.


The square root of 54.


What factors would you use in order to simplify it?


Yeah, and then, um, based on the one that was your perfect score. Um, OK, when you do, like, put it underneath like the lines, make sure you include like the square root on top of them, because then it allows you to like keeping track of like which one you have simplified and which one you're still working to simplify, because like right now when you didn't include the perfect square symbol, it like, basically says that it be like factored down to the


pot like whole numbers of 6 and 9, and that's it.


But we're still like square rooting them, if that makes sense.


Oh, after all that, for that step, actually the answer I didn't get 54/30 I got uh 6 square root to 6 cause uh


oh ****, OK


Do you get enough


Yeah, I'm gonna upload another picture and we're basically just doing that.


right? to some flowers and food.


I pulled the picture, can you see, like, we're basically just doing that, right?


Yeah, and then that should be what you end up with.


But your way is like shorter. Like we don't have to show all that, do we?


Hm


No. Well, like on your final, it would really help you to like um really see what's happening and it's like a more shorter, like easier way. So yeah.


Then like obviously our answer would be 6, but why not 9?


What do you think it would be 9


I just wanted the factors.


Yeah, it is, but um, basically when you do factor down 54, you get 6 and 9, right? But 9 is a square root, I mean, a perfect square. So, um, remember when we factored it down and then I told you to like remember to put the square root sign on top of each of them. Basically, when you're going from there, taking like the square root of 9, you would get just the number 3 by itself. So there would be no uh square root on, like on top of it because that's what it simplifies down to


But then you still have the square root of 6. So then you would get 3 times the square root of 6 on top as their numerator, and then 3 on the numerator and 3 on the denominator cancel each other out, so then you're just left with the square root of 6.


Is there anything else you need help with


I'm just writing this down.


We almost final like we can use a paper. So should I write like on a like


factors.


of the numbers, 40, you know.


if you want, you dont have to but it would help you


Well, I don't know what numbers are gonna be on there cause I, I don't wanna waste like the sheet because around that I use like one sheet.


yea its fine you dont really have to


I am uploading a problem is it write


yea ill check send it


Is this simplified enough


where is it


oh wait i see it


yes the square root of ten cannot be simplified anymore so it is simplified down to the most


Okay


Ima do another one tell me if sorry


Write


yea of course


course


hey are you still there?


Hello?


hello!


hi could yu turn on your home office


i dont have one sadly


i dont have my mic on m


ok so i will take phots of my prolems and share them


okay i got it


okay


so is it the bottom one?


yes problem 7


so


we know that if i line is horizontal


it has to add 180 degrees


so what we would first do i set up the equation


3x+2x+x = 180


understanding so far?


nice try but not exactly


do you remember combingin like terms?


have you learned that yet?


yes but i dont quite know


by the way you can upload your photo here if you dont wanna be share screening the whole time


but


let me make an example


of adding like terms


so we have that right


do you know what we have to do next?


we just add the x's and y's


we would get that


that is just a simple example of adding like terms if you remember


so are you understanding so far?


yes


okay now let me stop backtraking


i will get to your problem now


so we know all of the angles MUST add 180 degrees


so do you know what our equation would be?


Great!!


now just add the other x


to get 6


so now what are we left with?


6x/6 to get x alone


not quite


we would get


6x = 180


oh wait


actually


you might be right


i think im wrong


so yeah you would devide both sides by 6


MY BAD


your good


so yeah after we get that we would devide both sides by 2


by 6 i mean


and boom


we get our answer


yea


should i try making another example?


so we can practice it one more time


or are you good?


i have about 3 more assignments i need help with


okay


just upload the picture here and i can help!


question 89


i see


so


basically


so we would have


4x = 62


because


they are opposites


they both must equal the same thing


so our equation here


would be


could you solve that for me?


firstly do you understand why the equation is like that


cause its a supplementasy angle


not quite


supplomentary is when angles add 180 degrees


so like that example you showed last time


that was a supplementary


because it was a stright line


but this one


is a little diffrent


complementary


also no


but nice guess!


they are vertical angles


they are two angles


make from crossing lines


but the rule for these angles are that


they must ALWAYS equal the same  thing


because the are opposites


understanding so far?


YES


k nice!


so we do this equation because since we know one side is 62


the other must also equal too ...


that is why the equation is formed like that


so would we divide both sides by 54


by 4 yes


could you do that for me?


use like a calculator or something


YESSSS


niceeee


there you go


you got your answer


simple as that


is there any more problems you would like me to go over?


we did the wrong problem


there was one at the very top you misseed


ohhh


its okay


the more practice the better!


trust me


these things take alot of practice


took me awhile to learn


ok


ill enlarge


could you write the question in chat


it might make it easier


angle p and q are supplementary detrmine the measur of angle p if angle q is 95.7


okay this one is super easy once you understand


do you know what supplementary angles must add up too?


Yeah


so we already have the first value


so just subtract 95.7


i mean


subtract 180 by 95.7


and you get your answer


yeah


see


easy


very simple question once you undestand it


ok uploading the the next problem


okay ima do one more problem because i have to go soon


okay i wrote it down now


you dont have to share screen


so basically


remember what we did with the question where it added 180 degrees


its litrally the EXACT same thing!


sooo do you know what the equation would be?


Yes exactly


since this is a complementary angle


because


its a 90 degree angle


instand of the flat line we had before


so actually it would be 2x + 26 = 90


you were really close tho!


just a small math error


so we divide 2 on both sides then add our awnser to 1 80


so first actually


we need to move the 26 away


because we need to isolate the x


basically a fancy way of saying


put it alone


but isnt the 2x the one that needs to be isolated


yeah


but first


we need to take away the 26 from the side where the x is on


you have the right idea


so we subtract 36 to cancel out


so yeah we just move the 26 to the other side of the equal sign


so basically


we get this


so now the x is finally alone


you keep saying 26 but the problem is with 36


oh really


my bad


it dosent change much


there you go


so are you understanding so far what is happening?


yes


it would be 2x = 54


do you know the final step?


divide 2 on both sidesd


yeahh!


yeahh


nice!


Thank you for the help Mr. Green


np man


you have a great rest of your day!


you too


Hello!


How can I help?


I need help with this study guide


Sure!


I got 6 more questions left to do


Ok


skip 5 I got that done


Sounds good, so you want to start on 6?


yup


Sure, it's sort of a weird one since it doesn't tell you how much it is rotated by, we just need to check the possible answers


Let's start by using what we know and draw out CD


so c at origin and d and 3 4?


yes!


then what


lets mark each of the possible points for


D


Do you see all of those marks?


yes


Great, now think about how a rotation affects CD, do any of these points look ood?


can you like explain that again


sure


Do you know what happens to a point if its rotated around the origin?


its opposite?


not quite, thats a reflection


A rotation around the origin means the point will circle around the origin


See the green marks?


thats showing the rotation of point D


yeah


so if we know D' is the result of a rotation, which D' option must be wrong?


b


Great job!


thats because b results in a shortened CD, and a rotation will not effect the size of the line


well done!


its very important to understand what an operation


(like rotation or reflection)


means and how it effects the coordinates


Are you ready for 7?


Great, let's start again with what we know


I'll highlight the important stuff


Do you know what rigid means in this question?


no


Sure, in this case it means that the shape will stay the same exact size


so each line must have the same distance through the transformation


It's very important to remember that


Now that we know that, let's draw the original shape. Can you mark D,E and F on the board?


Awesome!


Ok, now mark D' and E'


Nicely done, I'm just gonna change the color so we don't get confused


Ok now remember what the question asked, we need to find the possible last coordinates for F'


What we know is that it must make this second triangle the same size as the original one, so go ahead and draw extra points to complete the triangle!


It might help to check the answers they give!


d?


Good! I like that answer too


Are you ready for 8?


yup


For a problem like this, you can either picture the transformations in your head or just check the answer choices and see what fits


can we walkthrough actually


Sure!


The first thing i look for is that points that change the most, see how far apart P is from P'?


yeah


What transformations look like they would cause a change that we see in this shape?


rotation


Thats an option! But let's see what happens if we do the rotation in d


-x -y


Go ahead and draw it out!


just for Q!


Remember all the points need to be in the right place so you can just check one change


oh q is translating up


Yes it gets too high after the rotation


I'll show you how I do this!


I'll make a color for each answer


which color is correct?


blue?


Yes good job! The key here is to compare the answers while just check one point


Im going to undo all my changes real quick


how did you get blue


Follow the transformations and see what happens!


Look at A and do what it says for point Q


wait is it A or B


The answer was B but I want you to find it for yourself now


Can you try the changes in A for point Q?


i see how


ok good


next questions


for these types of questions, since there are many possibilities its good to check the changes yourself


Sure!


go ahead and upload them


I got three more


alright do you know how a translation works?


yeah but this kinda confusing me


Sure, lets make it easier by looking at one point and then doing it in steps


Lets look at A, what do we have to add to X to make it in line with A'?


(even if it means adding a negative, weird way to think of it but that's how this one is)


Good!


5 or -5?


perfect


now how do we change y to make it the same as A'?


up


not quite, lets draw our steps to make it easier


my fault I was looking at B


haha don't worry


well done!


I'm ready for the next one if you are


yeah


good go ahead and upload it


wait thats it


all i see is 10


do you have more?


I mean the answer


yes!


a translation is just moving a coordinate by x and y, the rule is just saying by how much <-5, 3>


Leo


Okay


Let's work one point at a time starting with A


If it rotates around point A, what will happen to A during that step?


circles A or origin?


A


so whatdo I do


We follow the steps one at a time like I said


So if A rotates around A, will it change at all?


no


Good!


Now it translates <-4, -6>


Draw that for A


On the right side


explain questions likethat first


Sure


So in this question we have two steps


First we rotate 90 degrees clockwise around A


then we translate 4 to the left and down 6


no just the rotating


So we just do these steps for each point


ah


so for any rotation, if it rotates around itself it must not change


its like spinning a circle, the middle will never move


like a wheel!


what are the exceptions


thats why its so nice


so if any point rotates around itself it will never change


but what would it say if it had to move


well if it rotated around the origin it would move


but since it rotates around itself it doesnt move


igh


would it be easier if we start with another point?


nah I get it lets move on


Ok


So the rotation is the first step, now lets do the second translation step for A


And then you can draw that in the right side since thats the final step


-2 -2


Good!


put that on the graph in the right side


then dothe same for other points


yes!


rotate then translate


Whats the rule


90 cw


Since its around A you have to treat A as the origin


yeah it will stay 00 but what bout the others


whats the rule for 90 cw


The rule is a little different since its not around the origin


so how do I find B and C


Let me find an easy way to explain it real quick


Ok so around the origin the rule is (X, y) becomes (y, -x)


However to make this accurate for our problem, we need to translate A to the origin so we can find it for B and C


What if I show you how I do it for B and then you do it for C


yes


Ok so A to the origin is <-2, -4>


Therefore we do the same to B


(5, -1) translated with <-2, -4> becomes (3, -5)


We can then rotate it around the origin (A) with the rule (y, -x) which makes b become (-5, -3)


ok


thats it for B?


And then we have to translate B back to its correct place by reversing the translation of <-2, -4> so we do <2, 4> which makes B' (-3, 1)


can you undo the lines your drew for A?


ok i redrew A


Ok now that we have B as (-3, 1) we have one last step


because thats after the rotation, now we justt do the translation the question asks


so B (-3, 1) after <-4, -6> becomes (-7, -5)


Now I know that math is complicated, do you think you can do the same for C?


its like so many steps


lets see


Yes i understand


you translated first?


yes to make A become the origin


and whatever that translation is you do the same for C


i got -5 -7


close


remember its <-2, -4>


to set A to 0,0


so do that to C


when did we -2,-4


When we set A to 0,0


A is 2, 4 so we need to set it to 0,0 so we can make rotating C easier and use the origin rule


well done!


now we use the 90 cw rule which is (y, -x)


so what does -3,-5 become


Perfect! now we undo the translation we did to put it back in the correct place


so with -5, 3 do <2, 4>


you did it backwards just double check


(-5, 3) after <2, 4>


where do I plot -5,3


i wouldn't plot it, its just one of our steps


we're still just doing math


is -5 on x


ah yes


the rule does not flip x and y literally, its just how to do the math


so x, y = -5, 3


and then you do the <2,4> translation to -5, 3


perfect! thats the rotation all done! i know its difficult


now we just do the translation the problem tells us to do


<-4, -6> to (-3, 7)


not quite


remember this means (-3 -4, 7-6)


so what do we get for our answer here?


Perfect! and thats our answer


go ahead and plot that


and then on your homework sheet you can fill in the coordinates like it tells you to


So as a recap A' is (-2, -2)


B' is (-7, -5)


and C' is (-7, 1)


Great job working through that one it was a tough one


last one


yes!


So first I'll plot  the original shape


Ok and to flip over a line, make sure to draw the line!


Let's do the flip first, we can do this without math, just use the line to reflect!


the pink dots are the new points after the reflection, does that make sense?


hold on


sure


a is on the line


does it stay the same


yes! good catch


remember a reflection is like a mirror


so it changes sides but stays the same distance away


so if its on the line, there will be no change


270 ccw is same as 90 cw so y -x


yes! well done


and you can then draw the shape on the right side with the points


A -2 3 B -4 -2 C -1 -5


Perfect!


Great job with all of these problems


Are you all set?


Thank you for your help


have good night


Of course, happy to help, you as well


Hi


Hello


What would you like help in?


I just need to deepen my understanding on quadratic formula


alright, would you like me to walk you through the formula and then we can do some practice problems?


Yes please


just a second


Okay


would you like me to derive the formula?


or should we go on to the practice problems?


practice problems


ok


I'll write down a few questions, solve them please and then we'll check the answers


1. x^2 - 5x - 14 = 0
2. x^2 = 11x - 28
3. 6x^2 - x = 5
4. x^2 + 5x + 6 = 0
5. x^2 + 2x = -1


By the way, do you know factorization?


yeah


i was never that good at it though


i would suggest trying that too then, on these questions


do the formula first


then check it with factorization


depending on how much time you have currently


alright


are those the right numbers?


for number 1


just a second


checking


Okay


yeah so you've made a slight mistake


b = -5


not 5


your roots would be 7,-2


ive highlighted it in the first step


since b = -5


-b = 5


not -5


so the negatives basically cancel themselves out to make it a positive?


yeah


ohhh


the quadratic formula is -b right


so the negatives cancel


but im on the right track right?


like im not entirely wrong?


no no


just that one sign change


the rest was perfect


basically you'll get -2,7


the negative will be on the other root


alr i get it now


alright continue


one second


you've made a mistake in the process


the sign wasnt it


whenever we apply the formula


we can only apply it when all the terms are on one side


so you need a form ax^2 + bx + c = 0


so you need to rearrange the terms onto one side otherwise, yes, you do end up with sign problems


this is getting just a tad bit confusing now


alr, ill slow down a bit


so basically the variables a,b,c in the quadratic formula are the coefficients of the terms when they are all on one side


in the form of ax^2 + bx + c = 0


in our case, the terms are not all on one side


do you get it?


kinda


basically you need to see a 0 on one side of the equation to be able to use the formula


OH


so you just make it equal to zero?


yes


so shift the terms around so that it's equal to 0


now you can apply the formula


did i get it right?


yes that's correct


okay


did you apply the formula again


Yes


ok great, move on


and if you have a question in that part then feel free to ask


I have to go actually


oh alright, have a nice day


You too


your a pretty good tutor


your a pretty good student too!


Thanks


hii!


what do we need help with  today


i have been STRUGGLING so i am retaking a test tmro, so i just wanted to review the one page that i ate poopy doopy on :)


and other pages too :)


hahah okay!!


so lets take a look at the first problem


so i got the part of no correct but my op teacher did not like my reasoning


ohh so do u want to skip that one or try working on reasoning


well i think i didn't know what was going on


so keep going plz i just wanted to mention


ok!


so in congreunt triangle they are the EXACT same . BUT in similar triangles only the angles are same


k


so since they didnt give the measurements for the sides we cant assume that the traingles are congreunt


ohhhhh


if they gave the side lengths we could


but they didnt


do u kinda get it?


so my reasoning is not becasue we don't have enough information, on the lengths to prove they are congruent


yes!!


yay!


yayy


ok now let see


so same thing


since they didn't give us the side lengths we cant assume they are equal


ok


so B and C for problem4


so yes u just have to make sure just since they look the same u cant assume


and then lets see 5 a


now look at the diagram I drew and look at problem 5 a


k!


is ab perpendicular to cd?


so it would be false


ohhhhhhh


yaaa


should we move on?


how would i reaon it?


or still stuck?


u could draw a diagram and show


ohhhhhhhh


i see


okay Alright get the next page


okyyy


also dont mind how terrible i did


it was 7 am


on a monday


no no trust me iv done worse


kk hold up


ok! lemme know once ur ready


k


this was mad confusing


the purple pen is correct


the pencil is not :(


aww ok!


ok so look at the end of the a)


it says not warm


so the NOT makes it a contrapositive


but was about inverse it is the same?


or would i know by the statement


no for the inverse it is if not warm then frozen so basically just switches the order


oh


HI there!


Hi!


How can I help you?


I was wondering if you could help me with my Geometry homework


Ofc!


Is it okay if I can send you the files? Its on paper


And can you also check my answers for them?


I can't check your answers due to policies but if there are questions you aren't sure about I'd be happy to take a look!


Oh


I just wanted to know if I had them right though


Yea unfortunately I can't. However, I


I'd be happy to walk you through them


Okay!


Great!


Alright so as of right now, what question are you most concerned on?


Can you help me with the one thats says Given the midpoint M(0,3/2), Ex:4 and the DO later?


And the Your Turn


Oh okay let's start there.


So first of all for Ex.4


Do you see the ones I circled?


yea


Alright so for Ex.4


there is a pattern shown


going from point R to point M


in the x value and the y value


we just need to apply that pattern to m to find s


What do you mean?


can you see my pointer>


Yes


Do we add?


okay so basically


what is the x value of point R


Yeah. Now, what the x value of point m


Yup!


Now


What is the different of 5 and 1


Yes!


So do we put 4 for the x value of RS?


So basically, we subtracted 4 from 5 to get 1. Now we need to subtract 4 from 1 to get the x value of S.


So 1-4 would be -3.


so now we have the x value of s


Wait I thought it was 4 though


Okay, what was your process to get 4 as the S value?


yea but that's just the pattern


we need to subtract 4 from 1 to get the S value


because we subtracted 4 from the the x value of R


Oh


Yup! Does it make a bit more sense now>


Wait I think I have to go now


Im so sorry


All good!


Thank you so much for helping me though!


Bye bye!


Anytime!


Bye!


Hello, how can I help you?


hello i would like you to solve the questions on the white board


Ok.


i would like to turn this in


today


thank u


So since the roots are -2, -1, 3, and 4


You can can get equation (x-2)(x-1)(x+3)(x+4)


This is derived by creating a factor (x - r) for each root 'r' and then expanding the product, maintaining the leading coefficient of 1.


ok


However this is more of a pre-calculus topic rather than algebra 2 for further reference


For each root 'r', the corresponding factor is (x - r).


For root -2, the factor is (x - (-2)) = (x + 2).
For root -1, the factor is (x - (-1)) = (x + 1).
For root 3, the factor is (x - 3).
For root 4, the factor is (x - 4).


Multiply these factors together to form the polynomial.
f(x) = (x + 2)(x + 1)(x - 3)(x - 4).


Now we can do(x + 2)(x + 1) = x² + 3x + 2
(x - 3)(x - 4) = x² - 7x + 12
(x² + 3x + 2)(x² - 7x + 12) = x⁴ - 7x³ + 12x² + 3x³ - 21x² + 36x + 2x² - 14x + 24
f(x) = x⁴ - 4x³ - 7x² + 22x + 24


However this step is optional and not  necessary


The final polynomial equation, in factored form, is f(x) = (x + 2)(x + 1)(x - 3)(x - 4).


so is that the answer for number 12


Yes


next question ?


Ok.


f(x) = -x³ - x² + 14x - 24
The signs of the coefficients are: -, -, +, -.
There are two sign changes: from -x² to +14x, and from +14x to -24.
This means there are either 2 or 0 positive real zeros.


Did you understand that?


kinda


ok.


f(-x) (for negative real zeros):
f(-x) = -(-x)³ - (-x)² + 14(-x) - 24
f(-x) = x³ - x² - 14x - 24
The signs of the coefficients are: +, -, -, -.
There is one sign change: from x³ to -x².
This means there is 1 negative real zero.


ok


Imaginary zeros:
The degree of the polynomial is 3, so there must be a total of 3 zeros (counting real and imaginary).
Since we know there is 1 negative real zero, the remaining zeros (3 - 1 = 2) must be either positive real zeros or imaginary zeros.
If there are 2 positive real zeros: 2 positive real + 1 negative real = 3 real zeros. Therefore, there are 0 imaginary zeros.
If there are 0 positive real zeros: 0 positive real + 1 negative real = 1 real zero. Therefore, there must be 2 imaginary zeros to make up the total of 3.
So, there are either 0 or 2 imaginary zeros.


So there are 2 or 0 positive real zeros, 1 negative real zero, and 2 or 0 imaginary solutions.


is that the answer for number 13


Also I have to leave now, I hope this helped, bye!


hello'


Please help me understand this


How would you move from point G to get to point G'?


I do not know


I cant see it very well, but it looks like you would move 7 to the right and 8 up


Ok so now that I see that what is the awnser


actually maybe 9 up,


So it would be x+7 and then y+9


Yes, I think so


Ok


Ok I got it I am trying to get this assignment Algebra 201 so I have a few more if you are not busy


How many?


You should really try these yourself first


I have been but it is too difficult to understand and I usually have 1 on 1 support at school but today they were busy


OK.  I have time for a few, depending on how long they take


I cannot see that image well enough


give this a try.


I got it good bye


Hello! How may I help you?


Hi


What do you need help with?


Alright, I see it on the board.


What are you stuck with?


I'm using a metapen


Okay, what do you need help with?


I circled it


I see, is there a particular thing you need help with on these


Six


Seven


Is there a particular thing you need help with?


no


Then why did you ask for help?


This


Ohhhhh


I see


Let's start with the first question.


No answer


Good?


Hello?


Hi Sarah


hello


How can I help


i need help with math


Ok


Like on what


What part


box of whisker plot


So that's stats


I have the expertise