um, from the two shapes, what is X the same as on ABCD.


Yes


From this one to this one or just this one?


Yeah, from that one to that because now we know that AD equals 14 and FG is X


GHJF


Um, not quite. You know how on the tree problem we figured out that 3 is similar to 24.


O F G H E.


Uh, for this one, it we're only focusing on X and 14. So those two would be similar, because if you rotate it, it would be on the same angle.


Yeah.


Yeah. Oh, OK.


OK, so those two are similar, right? So, knowing that,


this, for this one, I think we have to find a letter.


Are these all the equations on the table, or is there more?


The, oh, there's familiar.


This


Well, let me try to find it away


Hm


Oh


OK, so which one, which sizes did we say were equal X.


14 X


Wait, what did you say again? What's the question?


Oh yeah, which sizes did we say were similar, like the, the letters to 14 and X


Um, A, B, and.


HG.


Yeah, exactly. So we have to find something that's, um, saying that AD is equal to fg.


this one


Mhm. And you should check your work to make sure the top sides are also the same.


Oh, OK


Oh, it was right. It's just that like when you put it in, there might be multiple, so you have to make sure.


Oh OK


it's the same


because if you look, it means that 12 and 18 are similar, and that is CD and FJ.


OK


which is the same as the top one.


um


Yeah, so we got, you got that one right.


OK.


All right, which one do you want to do next?


Um


we can do


OK. So what was the 1st, 1st step that I told you to do?


to find the primary


Mhm. That, that works. So which bottom one does that correspond with?


X


Perfect. And then, so what, what should that look like on the


ratio thing.


The ratio um.


The fraction fraction


12 over X.


Mm, close, cause, because the two shapes are different. We can't put 12 over x, otherwise the ratio wouldn't work.


Oh, so we have to put a letter.


Oh no, we're not due for this. So for this one, we have to say that because we're similar, 12 would equal X because they're similar, but they're not exactly the same, so they should have the same ratio but not the same.


they shouldn't be similar. I mean, they should be similar, sorry. So, if we look at that and then we have to find


you know how like the tree one we did 3 equals 24.


Mm


Yes


So I have to do the same thing for the triangle one too.


So like


um, you have to have the same shapes, the same shapes be equal to each other. So you would use 8.


or 8, 72 and 18.


No, 72 and 12 because they have to be on the same shape if you're going to go over.


Oh, we why?


Uh, OK, here, wait, can you go to the drawing board? I'll show you real quick.


OK


OK.


So this is our first one and this is our 2nd 1, right?


Yeah


This one is


72 and the other one is 12, I think, yeah.


12 and this one's 18


OK, so if we rotated this one.


it would look the same as the one right here.


So it would look like


oh shoot, uh, that one's not bad.


Mm


It would look like this, correct


Yes


STC, yeah, cause when you rotate it. So this one over here


would be the similar to this one and this one would be similar to this one. So in that way, you would have to do a ratio.


ratio equals this ratio.


So


which two sides are the same, similar?


Um 72 and 18.


OK, perfect. So we put 72 right here.


and we'll make 18 here.


And what about the other sides


12, and X


Mhm. OK, now let me explain how this, why this works, OK?


OK.


So if you divided this, it should be the same as 18 and X So that way it's saying that this ratio should be exact same as this one, even though they're not the same exact length, the ratio is similar, and that's why it's a similar triangle.


OK


So if you did that, the ratio would be 6, this one over here, it would be 6, right? This would equal to 6.


So that means when you've solved this one, when you solve for X, this should equal 6.2. That's how you know they are similar triangles.


Mhm. So on your equation board, which one is there anything that looks like that?


Mm yes


Yeah, exactly, it's that one.


Mhm.


Uh, OK, we'll just


Yeah, this one


this was


Yeah, yeah, good job. So which one should we do next?


Um


this one


Mhm


OK, so does this one need to rotate the shape or no?


Yes


If you rotate it, which ones would be similar?


Um, XN 8 ft and


24 and


Yeah, perfect. So do you find any numbers on the board that look like that?


No


OK, so that means we have to use the letters this time.


This is


So


um


OK, so looking at the letters, if you do it the same as the one I just told you, which one would correspond, which letter to which letter?


CND and


BNC


Like over or equal to?


Oh


over to


Yeah, yeah, good, good. And then what about the other one?


the other one, KNL and


and


KNL and BNC.


Mhm. Yeah. So can you find anything that looks like that?


00, there it is.


Yeah, you're getting it. You're getting it, that's good. OK.


You know why it's not the one that you almost clicked, right?


Yeah, cause BNC and


DNC, they're the same thing, like they're not


Yeah I don't see it. Yeah, yeah, yeah, OK, you're getting as good, good. OK.


Um


I think that one's the last one on the bottom, right?


Yeah


OK.


Mhm


this one


Mhm.


It


um


I think it's this one


Yeah.


Yeah, good job. All corrects.


OK


Thank you.


Yeah, is that it


Um, I had another one.


Yeah, that's fine


I watched the video.


Wait.


Oh


like this one is um it's just like to find this


just like.


Mhm


Do you understand how to use the butterfly thing to solve it?


yeah


the um cross multiplication.


Yes, yes


Wait, 6.


Um, that's close. You have to cross multiply the since you cross multiplying the 3 in the X, yeah, perfect, yeah, mhm.


And then you have to simplify the


the X


Yeah, divide each.


Yeah.


24 divided by


Yeah, it's good


And you just do the same thing for this one.


OK


It was it


15 times 12, right


Um, 15, yup, uh-huh.


OK, OK


What we


oh


I'm Y


Uh yes


Um, do I say 3HH3?


Yes, you say 3HH3. It doesn't really matter what the


Oh, you say 3HH3, same thing. Doesn't really matter what the variable is as long as they're only one variable, it's possible to solve, OK.


In variables can be like any type of


letter. It doesn't have to just be X


Mhm.


For this one, I got 10.93,500.


Should I write all of that down, which is like simplify it.


I got that too, so, um, decimals, they like make a lot of long numbers at the end, so it's likely right.


All right


You just gotta be confident in your multiplication.


If I write the whole thing


Mhm. Yeah, you can do that


cause in the answer key there're, they're just finding the, they're just trying to find X, I mean D, so


you can write whatever you want until you get the answer.


Mhm


OK. Thank you


OK, is that it or is there anything else you need help with?


OK, thank you


Yeah, no problem


Hello! Thank you for choosing MathMinds! What can I help you with today?


To calculate the slope of a line we can use rise over run


Yes


its the other way


slope of dotted line


is -1/2


and line of reflections is 2


Thanks


of course


Equation of line of reflection


Hi! How are you?


Good


How are you


I'm pretty good, thanks for asking.


This is the one I'm doing.


Have you learned how, um, what cross multiplication is?


Do you know how to do that


yes.


That's the basic way you solve this. Yeah, just like that.


So


if you do


-2 x 33


What do you get


Yeah, and the 66 would be equal to x x 3.


Not quite


negative, negative


Not quite. So


from, so you would get um um 66 is equal to


3 x


and then to solve for X, you would divide by 3 on both sides of the equation, so you get X is equal to -66 divided by 3.


OK


No


Close


66 divided by 3.


is


66 divided by 3 is -22.


Yes


So X is -22.


well.


you


Yeah, that's right


That's right


would be -21?


Yeah.


Thank you


I have one more


Wait, isn't this how you do it?


Not quite. You just solve it the same way that you do for the other equation that we just saw.


OK


OK, I already finished it


Wait, can I simplify?


What answer did you get?


I got 98


You can simplify I think


how did you get to 98


2 X equals 98, and then, oh, I forgot to divide. Oh.


we never mind


OK, 98 divided by 2.


So it would be 49


Yeah, that's right


Uh


um, my computer said it's wrong.


That should


Eta


be


that, that should be right


Oh


it's wrong


Oh, I think it would be -49.


Oh, OK


cause it's


00, there is a negative.


No, no, no, I said, I've put 94 instead. Oh my God.


OK, thank you for helping.


Do you need any other help?


Yeah


So, you solved this the same way as all of the other problems.


I don't, don't I have to isolate eggs.


So first you cross multiply, like before, right?


Yes


And you would, you would get


10 times X is equal to -3 times 20.


So that's basically and then you just sell for X.


That's and then you just isolate X


OK


Wait, can I just isolate X first or you can't?


Well, in actually in this case you can, you can isolate X.


I


It doesn't on the right side, the 20 and denominator cancels out the 20 denominator, leaving X


yeah, it's just, yeah, that's right.


Wait, how do I do like to rea like this one.


What, what do you mean


I just like cancel that one out.


Yeah


but not on that side


Oh, the other side.


I divide 20 and 10.


Yes


X equals -6.


Yup


This one was a little easier.


Because it looks great.


Yeah, it's right


OK, thank you


Of course


Hello!


hi


What would you like to work on today?


i need help with a question


sure!


could i post it on the whiteboard


alright :D


Let me know once you have.


it took a minute my computer was being weird


Marcus


So when they say find the value of f(7) are they looking for 7 on the x axis or y axis?


x i think


Great!


Now pinpoint the Y value where the line crosses 7 on the X axis.


Awsome! You got it!


so thats just the answer? y=f(-3)


close. it's f(7)=-3. This is because the f(x) value is already given and all we are doing is finding the y.


ok


Marcus. Do you have any other problems you would like to work on?


could you help me with a few more questions? im reviweing for a unit test tomorrow and im not super confident


Ofcourse!


ok i will post the next one


Great! What do you think they are looking for in this problem?


uh


the values when it crosses zero


What values, X or Y


y


Not quite, we are given the y values, zero, but we are looking for the X values when y=0.


oh ok


What values of x do you see that cross y=0?


Hmm, not quite. Let me circle which points i'm refering to.


oh oops


perfect! those are your answers


if you are asked to write them you would write it as f(-7)=0 and the rest of them


ok


on my computer it just had me put in the values into different boxes that had x=


In that case you can just write the values u gave me


rip I have a bio test im cramming for :sob:


lol i hate bio


i just took my unit 3 test and i got an 87


rippp


Do you have any other problems to work on?


i have one more i think


Okay!


First off, do you know what the x intercept is in this problem. hint, it is the value of x when y is 0


great! what about the graph?


can you explain what you mean


We have two different functions, the plane(the one you just did) and the graph with the x and g(x)/y values. Right now we are trying to figure out the x intercept of the graph.


wait so how do you get that\


sorry im lost


no it's fine lol


which part are you confused on?


i get the x intercept but i dont get how to get it for the table


oh ok. As I mentioned, the x intercept is when the y values are 0


so in this case


the y values are g(x)


so when g(x) what is the x value corresponding to it?


i think i get it


oki


and for the last part what are the dropdown options?


you can either pick greater or smaller


So which one would you think it is?


F(x)=-2 and G(x)=-3


so my answer is -2,-3, greater


for the boxes


yeah!


ok thank you


Ofc!


thats eveything i had questions on


I had a great time working with you today. Hope you do awsome on your test tomorrow. :D


GL


Hello


David


Can you turn your mic on?


Yeah, sure. Uh, can you hear me?


Yes, I'm hearing. Yes, I can hear you.


Yup. So, what can I help you with today?


Homework assignment, I'll upload it.


Um


wait, what's it, what's it about? Like, what topics is it about?


Yeah


and that's


multiplying decimals


multi.


s


Oh, mostly that's what. OK, so, uh, can you give me an example of what's on your sheet, uh homework sheet.


Yeah, uh, I can see the thing, I can see the thing.


So, um


uh


so you want help with that problem, specific problem?


Can you just check this for me?


Oh, sure, I mean,


um


very good


Um, 6.


wait.


Uh, it, yeah, it's overlapping.


Um


Yeah, it's still kind of a bit weird.


OK, so, uh, how do I, I'm sorry.


Yeah.


Um, let me try using this. Yeah, yeah, OK. Let me grab this one and bring it right here. OK, so let's


OK, so


OK, so let me look at the um the one at the bottom.


pack of ribbons


So, uh, can you look a number of pro problem too.


uh, on this bottom one, like this one.


Let me, let me highlight it


Oh, let me just look real quick.


OK


I'm sorry


Mm


Yeah


yeah, this one, do you see the one I'm, uh, sorry, do you see this one? I'm holding this one. So, you might want to, yeah, you want, you might wanna check this first, sorry, let me make it. You might want to check this one out.


Yeah, um


yeah, the decimal portion, good job. Uh, but you might wanna look at the integer portion of this one. The


the number 2


So what's subtracting


Uh, uses


yeah, so, uh, we start with um a length of a pack of ribon is 97 inches. That's the total, right? So, if you use something, you


if you use something, you.


Uh, so if you use something, are you, what are you doing to the original amount?


Hello


Yes


Yeah, if you're using something, what are you doing to the original amount?


Are we adding it


Uh, let me give you an example. So if I have a one-feet rope of twizzlers, right? And I rem uh and I use AKAE um, half of it


um, do I have less in the end, or more in the end?


less


Yeah, so let's look at problem two. if you start with, if you have a total of 97.


and Maria uses set up some amount, uh, how how much remates?


What would, what, what would that be, addition or subtraction?


uh will be um


uh subtracting.


Yeah, good job.


So, uh, oh, OK, it's gonna be a bit harder to, hard to write on here.


Oh sorry


OK.


Yeah, so, can you write, let me write the numbers uh down here. Let me write the numbers.


OK


Uh, give me a second and uh wait, 73


OK. So


uh, now let's try to do this one.


uh, give, yeah, are you, yeah, kind of, yeah.


Mm.


OK, so


Mhm


Mhm.


so, um, so yeah, uh, let, let's do the subtraction problem.


OK, uh, do you see this? um,


Yes, I see it


Yeah, OK, yeah.


OK, you try it, you try it, and then I'll, I'll help you uh on the way. Like I'll help you as well.


I'll tell you if you do it


That's it.


All right


Wait, you know what, uh, let me do an easier example. We do an easier example.


cause, uh, then you can just do this like


um it'll be much easier to get this one.


So let me do, wait, here like right next to it?


Yeah


OK. So I'm gonna write, uh, I'm gonna do an easier one cause you're, you're gonna have to like do some mental math and yeah, like.


it's gonna take a little bit, so I'll give you an easier one. So like 8.12.


minus, sorry, uh, uh, 6.2, uh, I'm sorry, 8.2 minus 6.2.


So, see this one? Do this one real quick.


Yeah.


OK


Let me have the 0, let me add the 0 at the end to make it clear.


I was supposed


Mm


You said, um, you said do this, which one?


Uh, the one next to the other one, so the one next to this.


Oh, I see it


yeah.


Oh, are you doing it on paper


OK, I'm doing it right now


I went to go get the paper.


Yeah


Yeah, do it on paper because it's a lot easier on paper.


The answer


Yep, you got the answer?


is, is 1 in 92.


Yeah.


It's 1.92.


Yeah, OK


right.


So, OK, yep, good job. OK. So now let's do that on the big problem, sorry, the big problem. I mean, you know, you get it right. So let's do that on that big problem.


OK


Uh yeah


Are we going to do a cook


like


uh the teacher even.


the big one.


people.


and.


Mm.


do


to


Hm


Uh, are, are


the


uh yeah


is the answer 23.85.


Uh, sorry, what? 823. 0 sorry, chocolate.


points


Let's see


Uh


Yup. Oh, what did you say? What did you say? 23.85.


Yeah


Are we sure about are are you sure about the decimal place?


Well, let me see something real quick


Yeah. Are you, are you sure about that? Yeah, are you sure about the best?


we do.


is the, is the answer 23.15.


Yeah, good job. Yup. Good job. Wow, nice.


Yeah, some these word problems uh try to trick you, so.


yeah


The best thing to do with work problems is to like imagine the stuff.


like, you know


OK, let me


do


I'm back


the job. Yeah, you can update that on your paper. Um, I just


yep, now you can update that on your um that uh papers, yeah.


OK


12, 34.


Chloe


You


easy


OK, then


Yup. OK. Now, let's move on to number 3. let me, let me check number 3. Let me show you. Um, you might, OK, oh, sorry, let me.


Yeah, I can see it


uh, you see number 3. I'm just gonna highlight this. I'm not gonna highlight stuff. Yep. So, OK


Leo likes to take walks. He walked 3.5 miles on Monday. 7 miles on Wednesday, and 6.2 miles on Friday. How many miles did he walk in 3 days? What do you, do you, what do you think that is? What do you think? Do you think it's an addition, subtraction problem? What do you think it is?


Uh


it's wait, is it probably is it adding?


Yeah, I mean, well, do you, OK, if I walked, if I ate, so if I wanted to track


how how far I'm sorry, how many Twizzlers I've eaten, and I ate one twizzler in the morning.


12 twizzlers in the evening, and 3 Twizzlers at night.


Was that an adding problem


And I, and I want to know the total of how many Twizzlers I ate.


Is that an adding problem or is it tracking problem?


it's subtracting.


but I added, added, added.


Uh, are you sure? Are you sure? Um, cause I'm, I'm sure, yeah, good job. So think of that. Think of that, like with this question, like, if I walked 3 days, uh, if I walked some amount and then walked another amount, and then walked another amount. How much did I walk in those three time periods? Is that an addition problem or a subtraction?


What do you


addition


Yeah, good job. OK, um, now,


uh, do you wanna do it in like chunks? You wanna add what it.


Sorry, excuse me, um, uh, so yeah, now you can just uh do that. You can try, uh.


write, write the three numbers and then like, you know, do the thing.


and the big


Well


OK.


I think it's broken


What the heck


Oh


Oh no, wait, uh, let me get that.


Oh, actually, you got it?


What


OK, there it is. It's nice and deep.


Why, why must be blue.


What do you


Oh yeah


yeah


You know to see.


Yup, yeah


Oh, let me remove this stuff.


Let me remove the previous stuff


OK


My bad


Oh wait, did you, did I get the lead in? Yeah, it's fine. Um, you, you, you have the questions on paper, right?


Yeah


Yeah, it's fine. Uh, just type it into chat, just like type in.


like the gist of it.


Oh my gosh


No


What am I doing


Mm


mm.


Oh yes.


So I'm gonna put up and cha again


Huh


What do you want me to type in chat?


OK, so, uh, no, no, no, it's fine. You, you put the picture up, up, up front, so it's fine.


Um, I just wanted you to do that problem, like.


yeah.


Hi


Yeah, I need to see like the problem and then you can, you can just use the paper.


cause it's kind of hard to see on the screen.


so sleepy.


Did the answer 10.7?


Um,


uh, are you sure about that?


Wait, OK


Uh


OK


Uh, are you sure? You want you wanna review that again. So if we, so he walked 4.5 miles and then 7 miles and then 6.2 miles.


Yep, tell me when you're uh done with the thing.


Do I include the 7


Uh, which one? The 7 miles. I mean, uh, at the end of the question, it says, uh, how many miles did Noah and walk in 3 days in all 3 days, in 3 days.


So, does that answer your question?


Kinda


So, I mean


if you, so if I ate Twizzlers 3 times a day, and I ate 3 in the morning, 4 in the afternoon, and 5 in at night. Well, how many values do I have?


Like, how many numbers do I have in that thing, like, you know?


Uh, are you sure about pork? So I ate um ****, oh sorry, what, uh, I, uh, it's, I'm pretty sure, yeah, it's 3 numbers because uh I ate 3 in the morning


4 in the evening.


uh, I ate 30 in the morning, I, sorry, I ate 3 in the morning, 4 in the evening and uh 5 at night.


So that means it would uh it would add up, it would be 3 numbers.


blue


Hello


Yes


yeah


So, can you hear me?


Yeah, OK. So, uh, since there were 3 values, so, uh, like since, uh, the final part of the question says, how many miles did Noah and walk in 3 days. So how many, uh, do you think 7 is included?


Oh


Yeah, my thing is not working. My microphone is not working.


It's like saying great stuff


But what? Why is this? It's saying weird stuff.


but it doesn't


not


Hm


uh,


Are you here


are you here


Hey


Im going to end the session but you start a new one when your ready


hell Maria


bello*


hello*


hi


We can solve this problem via factoring


I need to use long division to solve it


Okay, we can do that too!


So that is our final answer


We take the constant multiplying the variable, and take the negative of it in order to cancel out the terms. We repeat until we get something we cannot divide, and then put it as the remainder, or put it over the divisor.


Anything else I can help you with?


I have another problem, that I have to use long division with


Okay, we can do that


Sorry can you put it back up?


so this is the same concept, but larger


Try dividing the first term


Just like I did in the last problem


I don't really understand how to, could you explain?


Yes of course


So take the first term


which here is -2n^3


since we are dividing by n, we have to reduce the exponent by 1 in order to multiply by n (multiplication is the opposite of division)


so -2n^3/n is -2n^2


now we multiply by the divisor, which is n-7


now we subtract


now we repeat


-4n^2/n is -4n


-4n(n-7) is -4n^2+28n


we just repeat until we arrive at a constant


So -2n^2-4n-2-(2/(n-7)) is our final answer


Is that clearer?


yes, thank you


No problem


Anything else you want me to go over?


no thanks, I'm good now I think


Okay


Have a good day!


Hey, I'm Ben, how are you?


Good how about you?


I'm good, what can I help you with today?


Feel free to just put it up or type a problem into chat when you want


Im trying to find the vertex of x^2 +6x+5


Okay, how do you think we should do this?

Also, if you ever don't know or want clarification on anything, just let me know


What should we start with?


the 5?


moving it over


Hmm, not exactly, but what did you have in mind afterwards?


taking half the 6 which would be 3 then squaring it to make it 9


so x^2+6x+9=-5?


I see, so you wanted to "complete the square" for this equation. However, completing the square helps us solve for the roots/zeroes.


Since it's asking us to find the vertex, we can actually just apply the vertex formula to figure out our x-value for our vertex.


what would be the formula?


-b/2a is our vertex formula. But remember, it only tells you the x-coordinate of your vertex


So, here what is our a and b value?


1 and 6?


Great, so if we plug these into the vertex formula, what do we get for our x-value?


But that is only our x-value right?


How can we figure out the y-value at x=3?


x = -3*


i dont know?


Always remember, whenever I have a function like
y = 2x for example, any value x I plug in, will return me a corresponding y-value.


So, if I had y = 2x, and I wanted to figure out what y-value corresponds to x = 1, I could just plug in 1 for x right?


right


So I could do the same here, and plug in -3 for x to figure out my y-value right?


do we plug it in into the original equation then?


Yes! Because that is the equation that gives us our y-value based on the x we plug in


-4 yes?


Great, so what is the coordinate of our vertex?


Perfect! Do you have another question you want to try?


wait so what would have been the difference with completing the square?


Completing the square helps us figure out the zeroes of the function, which is where it crosses the x-axis


This function is going to be a parabola shape right?


It's going to look something like that right?


indeed


Completing the square will help us solve for those points


can you do that?


The vertex however, is the lowest point on the graph


Yes, of course! You want to try completing the square to find them?


please and thank you


Okay, so what do you want to do first?


move the 5


then take half of 6 which is 3 then squaring it to make it 9


so x^2+6x+9=-5


Great! But notice, you added that 9 onto the left side right? Doesn't that mean you must also add it to right side to maintain equality?


ouuu right


So we will have a +9 here too right?


Now what can we do?


like terms


so 4


Now what?


this is where i kind of get lost


Okay, that's fine, this is probably a pretty common point for that honestly.


Could you tell me what
(x + 1) (x + 1) is?


OHHHHH


Great! Did you do that by memory perchance or you solved it out?


EXACTLY!


LOL


Factoring


so like uh


Great!


hooray


wait


arent you able to combine them


And this is a perfect square number too, since we are multiplying two of the same thing together right?


Yes we can, how so?


so (x+3)^2?


Now, we have "completed the square."


What next?


move the 4 over..?


Not exactly, if I tell you
x^2 = 9, how do you solve for x?


square root


so 3


Great, so I have a perfect square on the left, so I can take a square of the left to remove the ^2 right?


right


would it leave you with a + and -?


Also, always remember, when you take the square root of a number, it is both the positive AND negative version of that number


Yes, exactly I was literally just typing that out lol


lol


But, going back to our other question, how can we solve for x now in

(x+3)^2 = 4


square root both sides


+ and - 2


then subtract 3


so


-5 and -1


So those are the x-values of our zeroes for this function.


question


Yes?


so for the original equation


if you factor that out it gives you (x+1)(x+5), is that considered like a short cut?


Not necessarily a shortcut, some equations you can just factor them out.


oo


Because what if the equation was
x^2 + 6x + 11
you can't factor it out now can you?


So you would have to solve for it manually.


But for this equation, completing the square is definitely extra steps


good to know


another question


disregarding this problem


okay how do you work your way backwards from i answers


like


Imaginary answers?


THAT


You want to figure out the original equation from the roots to an equation when tehy are imaginary?


yes


Let's think , if I have x = 3, 5 what is my original equation?


(x-3)(x-5) so x^2-8x+15


So, we just move the roots directly into factors right?


But, I'm assuming you mean you want to convert it back to a normal number without i


So, what is i equal to?


oh no


all ik is that i^2 is -1


That's fine, that's a great area to start too


Okay, so, how do you solve
x^2 = 9


square root


so it equals i?


ooo


interesting


Notice now too, why is radical -1 an imaginary number?


What happens when you square a negative number?


What about a positive number?


the i comes out if its negative


I mean, when I have a negative number like -4 for example right?


right


If I square -4
I get 16 right?

If I square 5
I get 25 right?


So, no matter what, if I square a number, the result if ALWAYS positive


Now, think about what taking a square root means.

If I take the square root of 9
It tells me -3 and 3 squared equal to 9 right?


So the square root tells me, what number can I square to get the number inside this square root symbol right?


yes


But if squaring a negative OR positive ALWAYS gives a POSITIVE number.


Then how could the number inside my square root be negative?


It would be like an imaginary number now wouldn't it?


Because there is no existing number that can be squared to make a negative


Anyways, I have gone quite off topic from what you asked


lol


But i is equal to radical -1


So, looking back at our old equation


I can rewrite it as


right?


But I can also rewrite 3 as radical 9
and 5 as radical 25 right?


right


So that is our original equation from hte imaginary roots


This isn't something you will get asked to do though


Actually, I can multiply this out too now


Nevermind, it does nothing for us here


Is there any other question you'd like to try though?


yes actually, finding domain V.A H.A S.A Holes


we have x^3+4x^2-5x / x^2+3x-4


I am going to clear that out is that fine? Or do you want me to leave that up and clear out the first question we did


you can clear it out


Okay, what do you want to find here? Domain, discontinuities, or all of the above


all of the above lol


okay so we get to it being factored right


Great, I was just about to say that, how can we factor them


(x-1)(x+5) / (x-1)(x+4)


X


FIRST FACTOR


lol


Great! Nice catch lol


Okay, now we have factors on the top and the bottom, is there anything we can eliminate?


so thats a hole..?


What does that tell us?


Great, it's a hole because we crossed it out


but


when you write it out


is it not equal to?


Well, I can plug in every other value except this one right?


right


So I just want to exclude this one value


What can we do next?


for domain its all real numbers?


cause it would go left and right


forever


Not exactly, what numbers can we not plug in for x?


What else?


Great, because if we plug those in, the bottom side of our fraction becomes a 0 altogether right?


And you cannot divide by 0, so there will be a discontinuity there


So, we write our domain as
x is not equal to 1 or -4


we need to write the fancy R (all right numbers) as the domain then now whatever the bottom 2 numbers are


would it be right to say that?


Probably, I'm gonna be honest, I don't know of this fancy R, but I do know, if I were asked this question, I would just write the domain as
x is not equal to -4 or 1


So, I'm assuming you don't need the fancy R


Ah, I just searched it up


You can't write this R


lol love handy dandy google


The R specifies all real numbers


right


But 1, and -4 are real numbers right?


And you can't plug those in, so our domain is just
x is not equal to -4 or 1


he says it as all real numbers EXCEPT for the numbers so here it'd be 1 and -4


I just learned from ChatGPT there is a notation for it to include excluded numbers


So, you definitely can do it that way


So, that would also be your domain


lol i feel like he excludes like the brackets and the slash


all he does is add the R in front


but thats probably the proper way


Do you mean your teacher does it that way?


yeah


I'm not sure, I never used this symbol, but you can also just write "all real numbers" as your domain if you want


When it is all real numbers, here you could just do
x is not equal to -4 or 1 though


Alright, what other discontinuities do we have in this equation?


vertical ascentote


which would be -4 since the hole is 1 yes?


Yes, you can't cross out this (x+4) so it would be an asymptote instead


And that is all for this function right?


now we have a SA since its top heavy


looking at the original equation


So, how can you figure out where that is?


orignal equation looking at the first terms on the top and bottom


exponents


Wait


wrong question


i reread the question i actually dont know how to find it besides plugging it into the calculator, but we can't use it for this


That's fine, for slant asymptotes we can figure out where they are by doing long division for our equation.


Or synthetic division if you'd like


taking the simplified equation?


Well, all I did was cross out (x-1) right?


right


So these equations are the exact same thing, except in one of them you can tell that x can't be equal to 1 while in the other you can


Let's use synthetic division to divide this out just to save some time


kk


Is everything alright with what I just did?


yeah im following


Now, what is our slant asymptote?


Great! So we just disregard the remainder from our division, and everything else is our slant asymptote equation


i actually didn't know how to write the remainder so thats something new lol


Oh lol


You just leave the remainder undivided though.


We couldn't divide -4 by x+4, so we just left it as
-4 / (x+4)


Now, that is all for our equation right?


yes


Great!


Unfortunately, I do have to go now, but, to summarize

To find the vertex, use your vertex formula to find your x-value, then plug that back in to get your y-value

Completing the square helps you find the roots/zeroes of your function

Crossing out a factor in your numerator and denominator gives you a hole in your function

Your vertical asymptote is where your denominator is equal to zero

Your slant asymptote is everything but the remainder from when you divide an equation.

And i is equal to radical -1


Is there any questions on anything you may want me to clarify that we didn't go through today?


I think I should be good


Perfect! Alright, whenever you are ready, you can just leave the session.


Have a good day!


Alright, thank you for your help!


Of course, anytime!


hi Jamie


hello


can i get help on a few problems today


it's hard to see the screensharing image and use chat


uploaded images are easier to manipulate


so do you want me to use the chat


let me know what is best


what's best is to upload an image instead of screen sharing


can you do that?


ok


is that good?


much better


yes


it has a graph to the left if you need something to reflect on


is that a pun?


pun?


"something to reflect on"


that means to think about


and the problem is about reflection


pun, get it?


oh yeah hahaha


your answer was reflected across y=-x


why do you think that?


i guess because the line of reflection is y=x but its negative


so i guess i thought the line of reflection was a negative line it would be y=-x


you think the shape is reflected across the green line I just drew?


no i guess it only y=x


that would be the purple line I just drew


wait no it reflecting over the x-axis


right, x-axis


what is the equation for x-axis?


im not sure what it is


do they want equation, like you filled in, or just words?


i guess equation


under the drawing it says Words, then it says Function


then words


i apologize


(and if equation, the x-axis is y=0)


ok that worked for solving  the blank next to "R" R(y=0)


ohhhhhhh


I was trying to figure out what they wanted there


so i guess the part that says wants words


never saw that "R notation) before


first answer should be x-axis


me neither this is the first time ive seen this


it said it didnt work


do you have an example of what they are looking for?


I dont think so


can you upload an image of exactly what you answered?


i just added it


I don't see it. Just the original upload.


oh, there it is


why a vertical line for the first answer?


oh thats just the type bar


dont mind that


I don't see the words x-axis


well i tried it and put exactly x-axis


why don't I see that?


because it deleted it


I don't know what else you can put


the x-axis


thats it


it wanted me to put "the" in front of the x-axis


x-axis is wrong, but the x-axis is right?


is this math or grammar?


yes


i know right


I'm afraid of #14, now


its alright i already solved it


y=x worked for the words part?


funny words, funny grammar


i know math should be strictly math


where to next?


i think thats all i needed help with


you don't need more grammar help?


I think i'll be fine


we could parse some sentences


just need to remeber to capitalize my


"I"s


Thank you again for helping me hope you have a good rest of your day


Hey!!! I need help on economics!


economics


Hi


hey!


how may I help


i need help on economics


yikes I only know math


would that help?


NOOO


yes


can you upload the question


economics is very simple math


it’s a couple questions i need help i got them wrong on my assignment


okay


it’s taking a while


it’s not uploading the question so i’m gonna type it


Mia  and Noah both specialize in the good in which they have a comparative advantage, total production in T-shirts will be _____ and the total production of Ice Cream will be _____.


Draw the PPF for both Mia and Noah with ice cream on the x axis.


is that the whole question?


there are no numbers?


Hi Marcus how can i help you?


hi! I need help solving these two I want to know if i'm solving the first one correctly tho


ill write out my work


Sure go ahead


is this right so far


yes you're going good


ok


and now i need to get the same denom again?


or combine like terms?


no you can just cancel out the x from 8x and 2x like this


and then 8/2 becomes 4


wait


this is confusinggg


so divide 8 and 2


bc they both have x?


see this might not have been taught to you but lemme tell you this and it will help you out a lot in algebra


and then distribute the 4?


basically if you have x in the numerator and denominator in form of multiplication(NOT ADDITION OR SUBTRACTION) then they basically just cancel out


look at the whiteboard I'll show you


and then it becomes 82


am i right?


absolutely


ok I am giving you another ques try it


k


try simplifying it on the board itself


hmm this is trickyyy


that?


nope that's not it you're going wrong


oh


Hello


My Tutor Provider wasn't working at first


finding period and asymptotes in sine and co tangent functions


Hey


hi!


What do you need help with today


I need help finding the period and asymptotes for sine and co tan functions


I am not great at that, but I can try


Okay! Thanks I will type an equation in


ok


can you just draw it


there that is one of the equations


that right


theres an x inside the () next to pie as well


oh I dont know how to find the asymtope for this sorry


You should ask someone else


okay, thank you for trying!


your welcome


also can you give me a 4 star atleast for the outro thing


Not really sure how this works tbh, my first time on here


oh k


nvm


bye then


see you later


adios!


Hi Alex, how can I help you?


hi


i want to figure out how to answer this


OK, from the graph or algebraically?


from the graph


What do you think about #1?


Does the graph cross the X-axis?


no?


That's correct, it doesn't!!!


What does that mean about real solutions?


i have no idea 😓


Real solutions exist if the graph crosses the x-axis.


When a graph crosses the x-axis, what is the Y value?


Yes!!   When Y=0, that is a solution.


ok! so for number 2 is the solutions infinite?


or like


idk


How about #1 first, real or imaginary?


imaginary


Yes!!!


The equation is quadratic, Alex.  How many possible solutions?


im not sure


The number of possible solutions = the degree of the function.  In this case, 2.


ok, i see


Alex


You're welcome!!


Do you want to solve it?


sure


Can you solve it using algebra?


Final step...


i know im supposted to do something else


but i forgot


One last step.  When you take the square root, how many solutions?


yes!


ohh


ok yea i keep forgetting that part


Don't forget that part...


Try #3


ok


Excellent!!  Can you simplify that?


i dont really know how to simplify sqr


Does 8 have a factor that is a perfect square?


idk 😓


Careful, the sqrt of 16 is what?


oh


How about #4?


Great, except what is 15/5?


oops


There you go!  Good work!!


yay


Do you often make that kind of oops?


Alex yea its not good for me 😭


How can you minimize that?


double checking


Yes!!  Plus maybe saying what your are doing in words to yourself.


okok


Just trying to help...


Anything else?


ya ill try to solve on my own tho if i mess up lmk 😓


OK, #9


Excellent!!


What happens when you take the sqrt of a negative number?


im not sure


What is the sqrt of -1?


It's the special number i


ohh


Have you learned that?


yeah but i forgot


Lots to remember.  lol


unrelated but its not looking good for precalc 😭😭


Why not?


apparently Northwood is way easier and im alr struggling with this


Is it -81 or +81?


oh


There ya go!!


I think you understand the concepts, but struggle with "careless" mistakes.


yea 😓


That's easier to correct than not getting the concepts.


What grade are you in?


11th grade


OK, good progress through the math curriculum.


thank you


You did Calculus 201% on your own!!


yippie


You even corrected a couple of oops along the way.


So close.


i is already a sqrt, don't take the sqrt again.  :)


Math takes practice to master a concept.


it is x = +- 6i?


Yes!!


ok!


OOPS, Alex i


alr


ok thats all


thank you for the help


Good job!


Keep up your mental checks and pre-calc won't be bad.


i hope so, goodbye


Alex


Hello! I have a basic understanding of how to solve these problems, but I often get stuck or confused. I've been using Method 1 to approach them. Could you please provide a few practice problems from pages 4–6 of the PDF, using different numbers but following the same concepts? I'd really appreciate it. Here's the link to the PDF: https://example.com/math-resources.pdf


Hello! ^^^


Hi! I'm looking


kk


I want problems like 18-21


ok


i just pasted one in there


so would it be x+1/y^2


and y+1(x^2)/x^2


tell me how you got each of those


answer is x^2/y^2


yes


next


that's right


yepp next problem


do you work with negative exponents yet?


there you go


would x^-1 be 1/x?


uh yeah this is tricky


where are you stuck?


the 2xy^-1


so if you see x by itself, it's really x^1, right?


but no one ever writes that


right


so your x is in the right spot. your y however has a negative exponent


so what should we do with that y


it goes on bottom frac


yeah!


is it this? i'm confused when its ^-2


you treat ^-2 the same way you treat ^-1, by putting it on the bottom it becomes positive


it becomes ^2


ok


ok what aboutt he other


see what i wrote up there


oh


and what about the other one


the one i put an arrow at needs to be fixed


ohhh


what about the numerator


correct!


so lets fix that


so it becomes


for the top?


yes that's correct


kk


and then bottom one is


x^2 times y


and 1 times y


yeah


let me write it out


right?


yeah!


ok


would i combine like terms for the numerator?


i would probably cross cancel where possible


with those two


im confused


so those two fractions are being multiplied, right?


are there any common factors that can be cancelled out?


that's x^2


ohh nvm i get it


so its just x


where


i rewrote it


yeah! 1y- what on the bottom?


yep


where u get the -1


make sure you extend your fraction line over the whole thing


so since you cross cancelled some of these variables, you are left with what isn't crossed out


i'm confused


the -1 just gets carried over from the original problem


oh


see how i wrote it down below


ok i see


so distribute?


you've got these concepts down!


you can, or you can just leave as is


it depends on what your teacher considers simplified


oh ok


so thats the answer


so no distribute


correct


ok next problem


would 5 be 10?


what do you mean


bc we do


4 times 2 x+5 times 2


can you show me on the white boar?


white board *


sure


is this right?


there is a lower common denominator than 8


i did 4 times 2


2 times 4


but cant 4 just be the common denominator ?


oh wait u find the common denom omg


so its 2-x+5 / 4?


yeah


it's actually 2-(x+5)


ugh this is so confusing its like i'm learning something new with each problem


so its -2x+10/4


Hello How are you?


I'm fine and you?


I am fine tnx How can I help?


Should I see something?


so I have a series of questions, and problems. But let's go one by one, so we are working with maximums and minimums


OK


i'll put smth on the board, one min


so there is this, and I made a sign chart for it, and we are asking if there is a local min and how many there are, I found 1, but apparently I'm wrong


OK Pls wait I will read it


ok


OK Wuld u like to show me what u did?


I must get my other eyeglasses


Can u write on bd while I get them?


yes


I am back


pls wait while I put on my glasses


there is what I did and based on my chart there is only one min


where I circled


OK and u say that is at x = -2?


now if you had to give theat min a vlaue what would it be?


that*


wym?


I mean if there is a minimum wouldn;t it have a vlaue? I mean a number?


yeah that's the -2


well I think that is the x vlaue


but what is the y value there?


i don't know


well I *think* it is -inf


and I think that might not counbt as a min


how do you know it's -inf, how did you get that?


I will circle in "pink" I hope


ok


I underlined instead


do u see it in the the ques itself?


does that help?


and not the other two limits after the underlining


note*


why note the other ones? does that say anything about the min?


becuase your grpah does not seem to show them


Also what does your grpah show bewteen x = 2 and x = 8 ?


Also does your  graph show f(2)  and f(8)?


no, it doesn't have to js bc I wasn't asked to, but yeah let's move on to the next question


OK


for this one we are asked if we have a local maximum


OK Ii will expand it and copy pls wait


OK what function does this new grpah show?


f'(x)


yes the *derivative* of f


Now what does the ques ask for?


the local maximum


OK let me think


If you have a local max *and* the func is continusous, whagt is the value of f' to th eleft of the max?


wym?


Let me rephrasae


what is the *sign* of f' to the left of a max?


positive?


Yes good


and to the right?


negative


ok


and *at* the max?


a number?


Yes


zero?


yes


so what point on this graph of f' meets all those requirements?


Yes x = 0 !!!


so basically for the f', wherever f switches from pos to neg, it's a max. But from neg to pos, it's a min?


Yes *except* I think we *might* need to be sure the func is continuous


But htis one is


so a local max and min can only be found at a continuous point?


no


I am not sure about that


BUT I mean the rule about left and right might apply only for continuous


You see I do physics and msot all funcs are contiuosu for us


but the mahgt folks have thigns that aren't


so you need to read your book or chk the Web about that'


See what I mean?


math*


I can look in a book here


pls wait


ok


Most of what I find applies to continuous functions


for now< I would not worry about the ones that ar enot


okay next question,


could you erase the board?


btw do u have an answer key?


no but it tells me if I'm right or wrong, and I have unlimited tries to get it right


OK


OK I see the function


Wha are we to do?


OK I will watch


yes now we are asked in the intervals is it increasing or decreasing or not defined


those


Now I suggest we start with (-3,3)


Dop you have an idea about that one?


wait, so to find it we have to plug those numbers to the function above right?


sort of


but I suggest you think about the sq root when x is between -3 and 3


I'm kind of confused on this one, can you go through it, I'll do the next one


OK well I will do my best


Let us start with (-3,3) OK?


ok


try x = -2


what do we get for the sq root?


root of -5


yrs good


and can we take the sq root of a neg number?


nope


no not using real numbers I agree


how about when x = 2 ?


that's still neg root


yes


which meand DNE


and for *any* x between -3 and 3 we have neg root


so what can u say about the interval (-3,3)?


it's not defined


I agree


confetti for that !!


thxx


so for the next one


OK Now for the first oen there might be a clever way tyo do it


BUT the obviosu way is to take the derivative


Do u know how to take the derivatve of this function?


BTW I grpaahed the function on my nice new claculaotgr


yes, but why can't we just plug a specific value


that will give us jsut one vlaue


what does the question ask?


infinity but like as long as we get the value of at least one number, it should work for the rest right?


Wait


we are asked for intervals where the func increases and decreases. Am I correct?


yes


That is euqiv (for a contin func) to asking for intervals wehre the deriv is +  and where the seriv is minus


see what I mean?


BTW there was an easier way to do the middle one


that interval is not even in the domain!


so we could have said DNE bsed on that


But for the other two, I think the most strightforward thing to do is take the derivative IF you knowp hw


Have you learned the quotient rule and/or the product rule?


i already found the derivative of it


OK


what is the sing of the direvitave on the intercal (inf, -3)?


sign*


interval*


oops


i'll just write the f' on the board


there


OK pls wait while I chk


I agree


now\


the numeraotr is always neg do you agree?


hint numeraotr is -9


yes


I mean the numerator of f'


and what about the denominator when -inf x < - 3 ?


hint is x^2 > 9?


Are u thinking?


wait sorry i was doing smth


OK


what's the question?


I have ten more minutes


I will repeat


the numerator of f' is -9


which is always neg OK/


yed


yes*


hint think about x^2


so what do you want me to tell you, the sign of the denom?


Yes when -inf < x <  -3


i think the bottom will be positive


Yes it will


so what is the sing of f' when -inf < x < -3?


sign*


negative


yes


so that menas the func is decreasing for -inf < x < -3


now how about 3 < x < inf ?


would it still be decreasing?


Yes


f' is neg for that interval too


Here is a link to a function grpah: (do not click on it) I will wxplain


do not click on it here in the chat


that might end the session


ok


U can if poosible copy it to your browswer


now I have a question though, so to find out if f was increasing, we have to find the f', then plug in the numbers and see if it comes out positive then f is increasing, if the answer comes out negative, then it is decreasing?


Yes for a continuosu function


this one happens to be decreasing everywhere in its dmain


soemtimes the sign of the deriv will change


so watch for that


does it mean to find the concanvity of that, we have to find the second derivative then plug in numbers?


let me think


I think for concavity the sing of f'' changes


sign*


that wasn't my question...


ok sorry


what aws the ques


my question was to find out the concavity in each interval, do we have to find out the second derivative of f, then plug in the numbers and the sign that comes out determines if it's conc up or down?


Yes BUT


soemtimes you can easily see the sign


Would you liek an example?


yes


Y = x^3 - x


what is shte second deriv?


Good


Now for what x is 6x > 0 ?


for numbers more than 0


yes good


and when is it neg?


when is what neg?


y''


for what x vlaues?


when x is neg


so I htink that means concave up for x > 0 and concave down fore x < 0


but I migth have that reversed


I am coreect


I grpap[hed


it


I have 3 minutes


okay now it's asking for the inverse of


how do we do that?


OK


of this function?


and it's also asking for the doman of the inverse of f


the one we were using?


yes this function


OK I will give you a three minute expantion


we write it as y = x/sqrt(x^2 -9)


OK to start?


then we repalce y with x and x with y


could you write it on the board, I'm more of a visual person


Well I do not have my stylus


I will try


The red is the origianl do ua gree?


yes


Now I swapped x and Y do u see that? In blue


Then I think we msut solve for y


Can you do that?


no, please just do it since you have to go soon also


well


I am not sure I cna it quickly


I will sq both sides


so we want y on  one side?


I think so


I have not doen this in a while Amazing what coaches forget over the summer LOL


lol


let me think


I am thinking


I wil  write


Does that make snes so far?


sense*


no cause what did you do with the other y^2?


see the pink arrow


the are two y^2


Yes


but I used distributive law


but doesn't become y^4?


no I subtracte -x^2Y62 from each side


oh you didn't show it that's why


I mean added -x^2y^2 to eaxh side


yes sorry in a hurry


Now u can take sq root of each side


I msut go now


okay bye


BYE BYE


thanks


You are welcome


hello


hi


i wanted help on my hw


ok


is it hard to read


kinda


i can read the question tho


okk perfect


wait


i said photographer


is this math or


yes geometry


ah


what grade are you in


no i mean


what kind of similarity are we talking rn


is there any previous questions?


yes


yeah can i have a preview?


does it make more sense


trying


oh


i get it


are you a teacher


are u studying similar triangle or something like that


no


im a college student


did you learn this before


you mean similar triangle or shape?


yes and dialation


ok


should i say When designing buildings architects have to create a scaled model or a blueprint. These smaller representations are similar figures to the final structure. This helps them make sure that the sizing of details like windows and doors are in scale to the rest of the house.


yeah that could be one


this hw might be a intro to similar triangle


this question is opening, so ur chill


no?


yesss


but the homework is similarity


what did the teacher talk about during class


still similarity?


scale factor


Sarah


you know what that means right?


yes😭😭


ohhh


i saw the similarity postulates


and that is about  the similar triangle


what grade did you get in geometry


pretty early


huh


high school? or even before


wait how


I'm Korean btw


so what did you do freshmen yea


i wish i was smart like you


ah, it's kind of weird, I was transferred


no


you better not


lol


i mean it's really stressful in Beijing


don't be one of those kids


whyy


you native?


idk


huge populations, need a competitive education system


ohh


college is really competitive


I think that's the essential reason


yea


UCLA do you want to go to


California


or


mit if I am lucky


you got this!!


thank you!


so what should i add for my number 2


oh


yes


is this"should i say When designing buildings architects have to create a scaled model or a blueprint. These smaller representations are similar figures to the final structure. This helps them make sure that the sizing of details like windows and doors are in scale to the rest of the house." your number 2


i would but my teacher would think i used ai


when i didnt


while the prompt said you can google


i googled the professions and it popped up


what would ur teacher think you would use ai


qwq


lol bc i used words i mostly never use


you junior? btw


then i think you're good


okk


Florida


now you need a third profession


yes but im not sure


emm


oh i have a good one


data scientist


or data analysts


they use small size of data to represent the macro society


what class do you take


like when counting the degree of liking for something, they can't count everyone's, so they just pick random guy to do the survey


AP calc bc


and AP stats


i have the next semester


isn't that kind of similarity?


but its not ap


i mean my explaination


oh ok, nice


it's really fun


what is


calc


how


my friends said its hard


i can only say it depends


hard but interesting, these aren't contradict


lol


geometry is boring


lowkey yea


ty for answering my question


np


have a good rest of you day


have a great day


you too


Seattle


bye


David


Hi Sarah, thanks for using TutorAI. What would you like to work on today?


how do i simplify a radical??


Do you know how to remove radical from denominator of a fraction?


not really my teacher hasnt got to that yet


OK, how about this one...


yes its like that


Let's identify some of the perfect squares we know about...what is 2^2?


ummm i dont know that one...


Maybe you don't recognize the ^ symbol, I'll write on whiteboard...


ohh 4


OK great. Let's write down a few more. What is 3^2


and 5^2 = ?


Great. Now look at the radical we're trying to simplify, and see if the number is evenly divisible by any of these perfect squares in order.


So is 18 evenly divisible by 4?


no its not


Is it evenly divisible by 9?


no


Hmm, please try https://www.math.com/simplifymplify 18/9


ohhhh sorry it is..


its 2


Great. So we rewrite 18 as 9*2. I'll put that on the whiteboard.


okay


Now the interesting part is that when you have the square root of a product of two numbers, you can rewrite it as the product of the square roots of those number. That's a lot of numbers, so I just put that on the whiteboard.


Does that make sens?


yes it does


Can you take the next step in simplifying?


I'll try to help. Earlier we made a table of perfect squares. I'm going to rewrite that as table of square roots...


Oops I'm having trouble with the whiteboard


Do you see how that second table of sqrt is related to the first table of ^2?


yes i do


Good. So what can you use to simplify the problem we're working on over on the left?


you want me to show you my problem on my homework?


Let's wrap this problem up, we're almost there...


ohh okay


We can replace sqrt(9) with ... ?


Yes. So let me put that into the problem...


So that's as far as we can go with my problem. We simplified the radical sqrt(18) to 3*sqrt(2). I'll rewrite that with square root symbols just to make it more clear for you.


If that makes sense let's go to your problem


okay


sorry its messy


No problem. Let's start asking the same questions. Is your number divisible by the perfect squares in that first table.


i dont think so


I circled the important numbers. You need to go through them one by one and see if your number under the radical is divisible by these numbers.


So we start with: 125 divisible by 4?


no its not


What's the next thing to check?


125 divisible by 9?


no


Next...


its not


divisible?


please keep going


is divided by 5


Yay! So rewrite  125 as 25*5 in your problem on the whiteboard.


Close, but the 25 still needs to be under the radical.


ohhh


like that


Not quite, let me help...


okay


So the 25 and 5 are still both under the radical.


ohh


Now you split it so they are each under their own radical.


Excellent. Now one last step, we know that 25 is special because that was in our table. So we can simplify sqrt(25)


it would be 5


OK. Please put that on the whiteboard to finish the problem.


so how would i write that


I helped you out because whiteboard is tricky


Does that all make sense?


yes it does


Do you want to work on any other problems?


yes


please


Go ahead


i have no clue on how to do that


No problem. Just focus on the part under the radical first. Remember we check if it can be divided by any perfect squares. So what is the first thing to check (hint, I circled the numbers earlier)


none of them can go into 27


Are you sure? What numbers are you checking into 27?


So rewrite 27 as ___ * ___


like that


27=9*3, so you still need the 3


ohh


Let me draw for a sec...


okay


Do you see that all I did was replace 27  with 9*3 ?


OK, now you can turn that single radical into two radicals


And what goes inside?


umm


What goes inside each of those radicals?


9 and 27???


Close, but you just take what was inside the previous and copy it...


so 9 and 3?


Yes!


ohhh


So this problem is almost done, but do either of those radicals simplify further?


Can you write it please?


like that


Close. But what I was looking for was to use the equation for sqrt(9) from earlier. I'll circle it above


oh


Does that make sense?


yes


And now simplify 2*3


ok


I must go but I think you're starting to get the idea.


okay thanks


To summarize, look at the number under the radical, and see if you can divide it by a perfect square (4 or 9 or 16 or 25)


Then rewrite as product and break it into two radicals, then simplify


okayy


I must go but please open another session if you need more help.


okay i will


Hey, how are you?


how may I help you?


ggood


and you


need help on my homework


I am doing great myself


I understand


alright


Do you have any specific questions within these problems?


yea


sure, ask away!!


that's the specific question I got to answer


I think the question got cut off a bit


you might have to reupload it


but let us solve question number 3 and 4 first


sounds good?


This series of problems will build your fluency with finding a pattern of change and using that information to classify the function. For each question below, find the pattern of change, classify the function as linear, exponential, or quadratic. For linear functions, name the slope. For exponential functions, name the growth/decay factor.


but this problem is asking for us to solve the question given below


if you could share the questions given below this, it would be great!'


yea but also to find if its linear,exponential, or quadratic


yes, but it is asking us to find those for the questions given below


ok


let find it then


if you could upload a picture of those questions, that would be great!


Hey I am sorry, but this is the same image you uploaded earlier


yea and the one I'm moving is the actually question


oh I figured


sorry for the trouble


but ok, let us solve it


so do you know how to approach the first problem?


no


maybe by using Ax+bx+c equatio


that is fine, but think about what the question is asking for


what does it want you to find?


the maxum area


Maximum area


yes, correct!


and do you know how to find the area in general?


Area= base times height


totally right


now, what is given in the question?


as a rule of thumb, it is best practice to write down whatever is given


that way, you wouldn't be confused about the question as much


80 feet


where to enclose a rectangular space


you got it!


so, you have officially completed almost half of the problem


the other half is just figuring the equation and solving


since the length and width are not given, we must assume two different variables for it


ok


but how do find the equation and solve it


that is a great question


to find that out, you must read the question very carefully


in that how many sides does farmer Sarah intend to enclose?


one side


yes, one side is already closed


because she is joining it with her backyard fence


how many sides are remaining?


three sides


great job!


and in those three sides how many of those are the "length" and how many of those are the "width"?


2 width 1 length


great!!


I am going to be writing this on the whiteboard, so it is easier for you to follow along


so using the given information, how can you write an equation?


equation for the length of the fence**


or in other words the perimeter of the three sides


A= 2b times L


A = 2w + l; Amazing work!!


actually it is the perimeter, so P = 2w+l


ok


so, what do you set the equation equal to?


I dont know


ok that is totally fine!


how long are the length of the three sides, in other words: what is the length of the fencing she bought to enclose the three sides?


80 feet


good job!!!


so now we know the perimeter, and we have the sides


could you find the area?


wait but how I'm confuses


it is totally fine


so, in the beginning you told me the generic formula for area


how do you find the area?


length X width right?


yea


so, what is the length X width for this question?


hmmm, try again


80 feet is the length of the fencing, not the area


80 x w = A


hmmm


not really, try again, you got this!


ok, so what are the sides for length and width


to enclose the regular space


yes


what two sides did we decide on?


the width


yes, and?


and length


correct


now what do you do with those sides to find the area?


multiple to find the area


but we have two variables


do you know how to proceed from there?


ok, walk me through the next step


so basically 80 feet is the minimum and close one side so to close all sides, this is not a square is a rectangle so 80 on both sides


wait NVM got confused


see, 80 is the length of fence that she used to enclose three sides of the full fence


one side is already closed


and we want to find the area


so do you mean 80 times 80


no, not really... but I see where you're getting at


80 has nothing to do with the area


it is just the perimeter


80= 2L+2w


that is the perimeter formula, you are right


so basically


20 times 20


mhm, where the 20?


because 2(20) = 40 so 40+40=80


you are very close


so in that case what is the area?


ok, you are a tad bit off, but that is okay!


now let us solve the rest of the question properly


you see what I did there?


ok


I solved for w in terms of l and plugged it into the equation


hold on give me a second


aight


hey, I am so sorry, but with the interest of time, I might have to end this session


sorry for not being able to answer your question


you could schedule another session, another volunteer could answer your question!!


sorry, and have a good one!!


Hi!


hello!


What do you need help with?


can you help me solve a question about volume?


Sure!


okk let me just upload the pics


can you see them?


Yes!


perfect!


Ok do you want to start by calculating the area of the top of object?


im pretty sure the 8 is supposed to be a 9


Yep!


So, I have broken the top into 2 parts. Can you tell me the areas of the two parts?


i 8!


oh ok


63 and 6


wait no


Correct! so when those are added together, we get 69. So now, if we multiple 69 by a height of two, what are do you get?


wait i though i did it wrong..


cuz i multiplied 9×7, but I didn’t see the two


138 is correct but I don't see it as a choice so I think the blooket is wrong


Yeah, I think you’re right. I’m just gonna choose an answer and then we’ll see which ones actually, right


it said 135 was the right answer


Well, I think it is wrong but I suggest that you also check with your teacher :)


Is there anything else you need help with?


I would do so, thank you so much for being patient and helping me. Have a great rest of your night!


nope!


You too!


Hi! I would like help on this assignment please.


Sure


Thank you


so its D?


Ok so since shape is symmetrical at the y-axis, it means that there is the same amount of units left and right. So yeah its D


:D good job


thank you!


Do you need help with any other problems?


yeah this one, please


Ok so to find the answer, you can look at how the coordinates changed. Let look at J and E


What answer choices can create the change in J and E


wait so its B?or D


because y is the same but x is the opposite


When you reflect across the x-axis, y-value becomes the opposite, and when you reflect across the y-axis, the x-value becomes the opposite.


okay so its D?


Not quite. relfecting acorss the y-axis flips the x values


Evelyn Ohhhh its B..?


Yes!


Thank youuuu!


No problem!


Do you have any other problems?


yes, so sorry


That's fine


okay on this one I have to Reflect the polygon on the graph below over the y -axis.


soo I'm guessing only on the x I flip it ? so if its -9 it'll be 9?


yes


okay so I change every single x-axis? but the y remains the same?


Yes, all x's beome their oppsite and the y-value stays the same!


okayyy thank you so much for your help today I really appreciate it!!


It's no problem!


oh that was pretty fast


Hello, what do you need help with today?


I would like to review a couple questions


Sure what are the problems


a mixture of algebra geometry stastics/Probabilty and arithmetic


Okay


is it alright if I screenshare it much easier for me


Yes


this the first one


Okay let me take a look


k


Okay how did you start off this problem


can I do it on the board


that the first step I took


Okay and that is for JM then


yes


Ok and based on the ratio 2:1:3 they give us we can say that JK = 2x, KL = 1x, and LM: 3x


yeah


Okay then by adding up all the ratios, you would get 6x and you can use this with the 24 to find x


alrighty


is the way I took good?


Yes i think so


ok les go to next problem


Okay


Ok dis another one


Ok let me see


Ok this one i think you can just solve for q in each equation to see if it will be positive


Is that how you tried it?


no I just guessed this one


Okay so for equation A you can solve for q and it would be 1= 1/r^2 right


yea


and by looking if r is squared it will never be negative and 1/+ is positive, so then q must be positive


did that make sense


OHHH just give the letter the value of 1?


and trial and error?


Basically


OHHH


Ok yeah that makes my life way much easier XD


the second one you dont really need to solve because you can just look at it


Okay thats good


wait but how abt the 3rd


cuz isn't that true?


Not really because if you solve for q it would be 1/r


R isnt squared and doesnt have any other property so we dont know if its going to be positive or negative


Maybe plugging in 1 and -1 would work better to confirm


ok


yeah it seems pretty easy now


Okay good


ok dis another one too


Alright


Okay so first I would find how many ties are either purple or striped


Okay and since they said out of the 8 purple ties 5 are striped we are kind of double counting 5 striped ties


if that makes sense


wait why


Because it first said there are 8 purple ties and 32 striped ones


and of the 8, 5 are striped


So im thinking its saying that 5 are both purple and striped


wait so wouldn't mean that 5 are included in those 8 tho


So you can either take (8-5) + 32 or 8+32 -5


Yes but the way we set it up as 8+32 i think we are double counting the 5 ties


Maybe check the explanation to make sure


wait lemme try to comprehend dis


Okay


Oh so the 5 purple stripes are seperate


Kind of


ok that makes more sense


I thought of another way to do it that might be easier


By keeping the 40 total that we have


of striped and purple ties


You can then take the total ties (60) - total purple/striped ties (40) = 20, then just add the 5 ties that are both


then you can find the probability or how many are not purple and dont have stripes


I dont know if that made it any easier


it did


thx


Okay great


srry Mark my battery 5% igtg


sorry


Okay, have a good day


you too


thank u so much


No problem


Maria


how can i help?


HI i just want to go over a question, i am going to put it on the whiteboard


okay


i know how to find the derivative but i am confused on how to solve this question type


so it really consists of two parts


let x = the walking distance for when youre getting into the water


well


x is horizontal position on how far you are from point P


and 60-x is how far you get there


and 60 is how far, perpendicularly, the point is from the shore


so its a right triangle


so youre trying to solve for time give distance


makes sense, how would that be formatted into a function? is there a specific formula to plug into?


we can use the pythagorean theorem


and the rates of walking and swimming


so let me show it like this


also, in this, we can make distance = x


does that make sense?


yes that makes sense, so how would that be formatted? because i am confused on how the speed and distance translate into the final function of T


great question


remember that rate deals with m/s so thats were time comes in


and x is distance (m) so it cancels out, basically


makes sense, so in that sense thats how the function output is time right


yes, exactly


so for example if i got this question on an assigment or quiz, how would i go about deriving the equation for part A


what would be the first steps and how would i go from there to the final function


okay


so i didnt explain all the steps thoroughly


but firstly


1. identify the right triangle


we have the triangle which helps us understand that we are dealing with the pythagorean theorem


2. identify a, b, and c


is there a specific reason as to what we put as A, B and C? or is it general


yes, there are specifics


in the picture, the running is one side of the triangle and the other side is the swimming


this question is asking what is the optimal path for the least time which is represented by the dotted "swim" path


and 60-x is the optimal run time


so what do you think x is in this problem?


the amount of meters from Q that the person starts swimming?


QP represents the horizontal distance to get the the stranded swimmer (i think previously i mistook point P as the stranded swimmer, sorry)


but what does x represent?


isnt QP the distance from the lifeguard. to the other side of the coast?


so would X not represent the amount of meters away from point q where you start swimming>


that is correct


okay


now lets actually find a, b, and c


so realistically, we are only using the pythagorean theorem to solve for the optimal swimming distance


but how do we find the function T in part a?


we add swimming + running


because we first have to run then swim to get to the stranded swimmer


ok


im going to solve for c


wait no


try to solve for a first


I do have to go now but thank you for the help. Daniel helped me clarify some of the stuff


okay great!!


Hi


How are you doing today and what do you need help with ?


im doing good


i need help with some PSAT practice questions


there I think 9 of them  need help with


Ok


I am also taking it this year so


Are you taking the 8/9 or the 10


Please let me know what questions you need help with


9th grade


let me paste the questions


ok


Do you know how to use desmos


yeah


the graphing one or the scientific one


grpahiung


graphing


yeah I know how to use it


Ok this problem is extremlyu easy


plug in both equations into desmoos


and the point they intersect


is the x and y values


can u see my screen


yes


im going to plug them in any questions please let me know


X value would be 18


you can see


was that helpful


yes it was


did u know how to do that ebfore


no


ok


whenver given a system


just plug it in


okay and then see where they intersect


One second ill be back in2 Minutes


okay


Exactly


will we be able to use desmos on the psat


have you taken a practice ytest yet


do you mind showing me again


yeah


like how to solve it


because I'm getting something different


for what


the question we just did


do we plug in exactly x+3y=29 and 3y=11


never solve these types as they take tto much time


yes


yeah I did that


but I don't get what u got


give one sec


if we were tos ovel by hand


The method i used is elemination


but is way faster and mroe efficent to plug into demos


is thre any other question you need help with


No I think I'm good


But thank you for the help


No problem


always try to use desmos


Okay


Try searching on yotube how to use desmos


there are lot of videos


that have lots of info and are very helpful


How can I help you


OK, um, I need help with like relationships with angles.


OK, um, do you have any particular


postulates or theorems in mind?


I do, let me just share it with you.


OK


I have a question. How do I share because I can't see the button for it.


Oh, is it online


like is it a shared screen that you're trying to do?


Yeah


OK, uh, I think the type of like session that you chose does not enable that. What I would do at this point is take a screenshot of the problem, save it, and then upload it through the 4th button from the left. Sorry, I'm in a public area.


Oh, it's fine.


Are you taking the screenshot


I'm just wondering, sorry.


I'm sitting there right now.


Sorry, have you uploaded it yet, cause nothing has appeared on the screen for me. I just need to know if it's a tech issue or not.


Is there any other way to upload it?


Uh no


Um, can you describe the problem to me?


Hello


Are you there


Um, could we like, is this


could I end this session real quick so I can take a picture of it.


Yeah, sure


OK


I'll just wait for you to log back on.


hi


How can I assist today


this


I see it, reviewing


ok


what answers are hovoem


given


idk


i cant read it


okay see board


no


Distance between Lincoln, Lancaster County and Denver, CO = 500 miles


Distance between Colorado Springs, CO and third city = 200 miles


We need to find the possible range of distances d (in miles) between Lincoln, Lancaster County and the third city, assuming the three cities form a triangle.


Apply the Triangle Inequality Theorem


For any triangle with sides 𝑎,𝑏, and
𝑐


∣a−b∣<c<a+b


Step 2: Substitute known values
Let:
a=500 miles
b=200 miles
c=d, the distance we’re finding.


hi


heyyy


how can i help


I need help with reviewing for a test


sure, do you have exampl eproblems?


yes


ok, post or upload a pic of them


can I draw out a question?


sure


there


any idea where to start?


plug in?


i see 2 approaches


you can take the derivative or graph/analyze the equation


the equation 2x-3 is linear.  so it has the same slope everywhere


given x=1 means nothing because of this


which method do you prefer?


graph or derivative?


derivative


whats the derivative of 2x?


not quite


use the exponent rule


(x^n)' = n*x^(n-1)


are you there


Hello


Can you hear me at all


And


Oh, OK


All right


Yeah, I don't know what's


uh.


Hi, yes, hi, how are you? My son needs help


I got you


So I come over here, please. Just he's just really shy


Oh.


Come on


Oh, that's fine


I would just text


Thank you. I mean, let's turn up the volume.


It's like


broken, I guess. It's not letting me cancel the shot.


Yeah, no problem. We can, we can, we can do this. Liam come buddy.


OK


Yeah, of course


All right, thank you. Let's go have. Thank you for your patience. Appreciate your patience. Come on.


Yeah, no problem


OK.


I don't know what's happening. It's like, OK, I keep on glitching.


but um


all right, so you wanna do this problem.


and it's telling us we want to isolate


H.


AKA sulfur H. So we want to have H alone


on one side of the


equation, right


Now let me ask first, can you hear me?


You can just like


draw a little something on the board if you.


Hi Mia, sorry, uh, we were just, can you start again, please, my bad.


Oh yeah, of course, of course


OK. Can you hear me?


Yes, thank you very much


OK, so for this problem right here, it's telling us to solve for H.


which basically means that we want to have H on one side of the equation, like you wrote here, just like by itself.


So, let's um, I guess just to like visualize it easier, looks like break apart the region.


OK, it keeps on like


refreshing my


Yeah, I, it's going on and off.


OK, that's weird. I, I don't know.


but


let's just break it apart


OK.


So you know how we have one half times age times.


Yes.


here. Let's just break it apart with um using like multiplication signs.


The entire equation is just this.


And then all this equals um A.


So if we want to isolate H


we're gonna have to take this, um,


this one half and somehow put it on the other side.


but also take this parentheses B + C and put that on the other side.


while just keeping H by itself.


OK


All right, so do you know the inverse of multiplication?


Say it to me


I


Huh?


Mhm.


Uh it's division, right?


Yep


OK.


OK, right, thank you some glitching again. Yep, so just the vision.


Um.


so if we have H being multiplied, so two of these things.


and we wanna like cancel out the multiplication.


Let's say for example we have


2 times


yeah, 2 times 3 equals, I don't know.


We want to cancel out this x 3 to 2.


instead of um we would just divide both sides by 3, right?


Yeah


You divide both sides by 3, we get


well, that isn't a good example, but


we, we'll just have two alone. I should use the variable for that. But um


we have H being multiplied by one half. We'll just go step by step, step. If we want to cancel out the uh H times 1/2? What would we divide it by then?


Uh


chill? Is it chill


Oh jeez, OK.


Wait, OK, honestly, let me just use a better uh example. So we have X


times


3 equals


And we want to isolate 3


We should divide both sides by 3, right? Because if we divide sides by 3.


then basically this entire fraction 3/3 is just gonna equal 1.


OK


But we're dealing with a fraction, so I guess


OK, it might sound a little weird, but um


really, if we just wanna cancel out the uh medication to one half.


We're just gonna divide it by 1/2 as well.


Because one half


divided by 1/2


if we use to have roll like keep change flip.


It'll just be like 1/2 times 2/1.


1, right


Yes.


OK, so we'll do that


We're gonna divide both sides by one half, right?


So


it's


divide both sides by one half. O and


Mhm


what's gone for me. What happened?


Uh, I can't see anything on the board. Road's glitching.


I know it, it, it, it's glitching really bad.


OK


He, um, OK, we might just have to rewrite it. I kind of remember that, uh, the equation.


H


parenthesis B + C.


needs to.


Well, I guess an easier way to think about it is just


no, no, just divide it by one half, but


also because it's a fraction


what should we multiply one half by for it to equal 1.


Uh


Yeah, yeah, 2


Yep.


So, actually if you want, cause we're dealing with a fraction, we can uh we can just multiply both sides by 2.


So, if we multiply both sides by 2


do you wanna uh write out the equation


Uh, yes.


You can write it down with a pencil here.


Yeah, you can write it on your paper. I'll just use the whiteboard.


just a song, there you go, here.


You can just type it in as well. Here you want, or you want to type here just so you can do it here. OK.


So that you can just write it


Write it with me or with a pencil.


Oh, no worries


Write it here.


Yeah, I don't know why the platform is being really glitchy right now.


Yeah.


So what would you get on the other side if you multiply it times 2?


8 times 28 times 2.


So


What kind of 2 is that?


Yeah, I don't know. I, it's a little hard to draw on the board.


Yeah


So.


But I see, I see what you're writing. So just 2 A.


Uh-huh.


Mm


And then you multiply the uh the other two X's on the other side, that would apply the parentheses.


I'll also


OK


just for like a rule of thumb


Mhm. Listen


Stop


Let's say you have like Y equals A times B C.


When you multiply like both sides by 2.


you'll get 2y equals


just 2 times A times.


E times C. cause I've seen like other people try to like distribute the two to like each variable when really


Um


you know just


just be like one more multi uh


multiplication, so like, add on to everything that's being multiplied.


So it's not gonna be like equals to ax 2B


Mhm


Alright.


Just making sure. All right


So what should we have on this side of the equation now that we multiplied


everything by x 2


So it's the one half H will, will that


will that can the one half will cancel out?


Yeah, it'll cancel out the one half.


You.


Yeah, right? OK, cause you multiply it on the other end. OK.


half


Let's just rewrite it together. So we multiply both sides by 2.


So just you know 2 times 1/2.


times each


times whatever's.


OK


and um


we can see at this part at like at the front, 2 times 1/2.


You already know that equals 1, right


Yeah


So we can rewrite it again to just be 1 times H times


uh


B plus C.


And then that's all gonna equal to a.


But the times 1 is insignificant because


I mean, it doesn't really change anything, so we can just like cross it out. So it just equal


H times


B + C.


Uh, does everything make sense? If not, then I can be.


Yeah, that's fine


All right.


You gotta understand


OK.


I


I, you know, keeps on glitching.


Oh yeah, just, we just want to cancel everything that's being multiplied to H.


So


So we have H times B + C.


And we want to get, we want to make H alone, right?


So like um


Don't copy it. Wait.


uh, like what we did, uh, with the One Health.


and a way to take this away and put it to the other side of the equation.


OK


So we're using multiplication, right?


Yes


We're gonna wanna do the inverse of multiplication or like the opposite of multiplication.


using B + C.


so we can get it away


All right


So what uh what operation should we use to get uh to get rid of this.


The vision


Yeah, we should use the vision


And what should we divide both sides by?


uh, the bee and the other B.


OK, so we're gonna divide both sides by B


C.


in parentheses


We're gonna do that to the to the other side too, so it's equal.


Um


So when we rewrite this, we're just gonna get


2 A


divided by


B plus C.


OK


And we're just gonna get that fraction, like we had before


since the new and the denominator are the same. It's just gonna equal one.


So it's just gonna be H times 1, which is just gonna equal each.


So we have our


equation of when we solve for each.


So H equals 2A over B + C.


OK, OK


Thank you so much. He does have another one. Do you mind helping him with it, please?


Yeah, of course


I think it's better, I think it's easier to do more practice for this, so like.


yeah of course


Yeah, appreciate it. How do you, oh, how do you, OK. So I guess we can take a picture. How do you take a picture? Take a picture. You don't know how to use technology. OK then, take a picture. Do you know how to?


You don't need to take a picture of.


just on


If not, if you uh read it out to me, I can just, I can just uh draw it


OK, so we did


oh


it's um this one A eagle. It's OK.


equals to BXT + C.


And we're looking for tea.


BXC + C


A equals BXT + C salt for tea.


OK


Oh, OK, plus C.


OK, I, I wrote it all the way at the top. I don't know if you can see it. Wait, let me read all the ink because it looks a little wonky.


Does it look like this, or I guess maybe lowercase a.


Yes


I'm gonna get a


All right, OK, nice


I'm gonna get a result


OK.


Hi do we get any er? I, can I have a razor?


I call for tea.


so


just


or


it


tea


All right


So, um,


we basically, OK, yeah, we want to isolate tea, and by isolating tea, we're going to get all of these other variables onto the other side where A is, right?


No


So we can just leave tea on um


you know, on its own


So we can see that tea being multiplied by B and X.


and then they're also um


don't write yet. Just listen.


adding a C


Don't, don't


So


like listen.


it's fine


So which variable do you think is gonna be the easiest to get to the other side right now.


Uh


sing


Yup, see, you definitely want to do, you definitely want to get rid of like any multiplication, sorry, not multiplication, oh my gosh, addition or subtraction before you like mul like divide or multiply aside.


Oh my gosh


I feel like some people like try to divide first, but if you were to divide both sides by B, then you would also have to divide C by B, so it makes it harder. So yep, we're gonna, we're gonna try to move C to the other side. So what operations should we use?


subtraction.


Yep subtraction, uh, what should we subtract?


Go check it out


Uh, what should we subtract from both sides.


Um


just tell her your best just let's seed from both sides.


Yes, perfect. So,


on the left side, we're gonna have A minus C.


equals BXT


plus C minus C.


And that's just gonna equal 0.


Mm


You're gonna just cross it out.


So we're just gonna have A minus C.


equals BXT.


Now that we have that


um


what, what do you think our next step should be?


uh just like


to divide the uh, the BNX.


divide, OK, sorry, my thing keeps on cutting out. So,


OK


Say it again. It's OK


say what? Repeat what you were saying to uh get rid of the BNX.


yeah, yeah, exactly, and we should um


yes, he said divide. I do remember you saying that. OK, so we're gonna divide both sides by


BNX


exactly. So,


the right side, we're gonna have BXT.


divided by


EX


On the other side, we're gonna have a minus C divided by BX.


And then since BNX


she's gonna cancel out


We're just gonna be left with


A minus C


B X


equals T and then amazing.


I don't even really have to help you that time. So


He's writing stuff down now.


Thank you. Thank you.


yeah, I don't know why my upkeep is so glitchy.


All right, but amazing


Can we do a couple more, please


Yeah, of course.


Thank you so much, Mia


Yeah, no problem. He's already seeming like a pro, honestly.


Thank you.


me a very long time to understand how to do these. And I was also just teaching one of my classmates.


my


people from my school


So yeah, it's, it's a hard topic. It's


OK


but you know, you, so don't worry.


Thank you


You I was fine with these two.


It says, OK, here you got.


All right, so you want to tell her what's the next one? Um


just let her know and just read it online. It's why


Mhm.


minus 2 x equals 6 and we.


solid for once.


OK, Y minus 2 x equals 6.


I


to


OK.


And what are we solving for?


Uh, why


Oh, OK, OK. All right


I don't need, OK, if you don't need help, then what is the next step?


Uh


adding 2 X to both sides.


Yeah, exactly. Honestly, that's the only stuff you gotta do.


All right.


Yeah, I keep on glitching. Oh my gosh.


So why


minus 2 X


+ 2 X


equals 6


But we know it's -2 X and this + 2 x just equals 0.


So we're gonna cross that out


And yeah, you have Y equals 6 + 2 X.


as your final


your final thing


Thank you. So, the 6 + 2 X, will that be 8X?


Oh, is it 6 sacks


Oh, no, no, yeah, it's it's, oh no, that's


just


Is it, uh, is a 6 by itself? If it has an X after it, then yeah.


this is just 6. It's just sexy.


OK, OK


Yeah, so Liam uh then it's just uh 6 + 2 X.


OK, wait, hold on, my family back home. Hi.


So what would that be


OK, my bad. Oh


She will help us


So is that the final answer? Y equals 6 + 2 x?


yep, Y equals 6 + 2 x because um we can't simplify anything further.


OK


but doesn't have a variable, like it's just a constant while two has a very too, I mean Liam oh my gosh.


Yes, OK


What


And all right, thank you. And can we do just one last one, please?


Yeah, let's do another one


OK. The only reason, maybe that's fine.


Let her know what it is. It's 2 x minus 3Y equals 6 and sulfur X.


3 Y equals 6


Yeah


All right.


Yep.


OK, so wait wait it's all for X


Uh, yes.


we


We're solving for x


um, I mean, what should our first step be to just get X by itself.


uh, adding CY to to both.


Yes, exactly


right


my aunt.


Uh 3Y


Yeah, and we're just gonna get 2 X equals


OK, 6 + 3Y.


And then


uh what step should we do next?


Um, dividing by two on both sides.


Mm, yup


So we're gonna cancel out that too. That's on the X.


We're gonna have 6 + 3Y over 2.


All right.


This one's a little tricky cause


uh when we get this answer at the end, we're gonna think that um


we can actually simplify this further. The 3.


I guess it depends on what your teacher wants.


Can you simplify the 6 and the 2?


Yeah


Mhm


you can either keep it this way, cause I realized the other one isn't, like it'll still be a fraction.


Right


Uh we can split this up


So when you're adding stuff in the numerator.


Let's say you have A + B divided by


3, for instance


You can uh turn this into a divided by 3.


plus um be divided by 3.


So if we wanted to apply this, this is all because they have like a common denominator, technically.


So, if we want to apply this to the answer we just got right now.


Could you split it up into two


Um


divide by 2 plus.


3 Y divided by 2.


62, 62.


All right, yes


6 divided by 2.


6 divided by 2 + 31.


Mhm


Because this will be the A, I don't know if you can see my cursor.


OK


OK.


Yeah, this would be counted as the A.


This would be counted as the B


Yeah, the two different variables. So now that we've uh wrote this out.


Uh, which, which one looks like it could be simplified?


6 and 2


Yes, exactly. The 6th and the 2. So what can we simplify this to?


1 and 3, three and 1.


and 1


3, the 6 divided by 2 is just equal to 3, right?


Yes


Right.


So


we'll have 3, and then I'll bus, it'll it'll be, oh my gosh, it'll be.


equal to 3 divided 3 divided by 2.


Mm


If you want to, you can put the fraction on the outside and just make it 3 divided by 2 times Y, or you can just leave it as 3y divide by 2.


So,


OK


you have um two different ways you could put it. You could put it as 6 + 3 Y divided by 2, but some people like it more when it's just uh made into 3+.


3 divide uh 3 divided by 2 Y.


So yeah, you have your


final answer


OK, what do you say? Thank you, that's very well.


David, I can't say his full name.


David


Thank you my blushing. Oh, of course.


You learn, you learn very quickly


I had, I had to explain this to my friend for like ages, so


uh you're very fast learner


So you got this


Thank you


your studies


are


Thank you, Ms. Mia. Yes, thank you.


All right


Have a great day


OK.


Hello how are you?


I am good.


That's always nice to hear.


What is it that you are concerned about?


How can I know where i place the dot on a grid


Like if it is (7,2)


Well, one thing we must know is that every coordinate is set up as (x,y).


X is the horizontal or flat line while the Y is the tall or vertical line


Oh ok


So when given (7,2) you would want to go 7 squares to the right on the flate line


Flat line*


While going up 2 squares in the tall line.


However one thing you must note is that if the X is negative you go left and if the Y is negative you go down


So what do you think you should do when given (-7-2)?


I think you go down 2 and left 7 because they are not positive number


Nice work!


Oh ok thank you i just had that for a question.


Bye


Goodbye!


hi


hey


i am here to help.


ok give me a sec


k


good work


yay


yay!


i know for sure that <4 and <12 is


right


1 and 3


2 and 4


lots of corresponding angles


1 and 4?


no


these are my options


are 12 and 16 corresponding?


yes


they are vertical angles


oh


6 and 4 ?


one thing about corresponding angles.


one will be interior and one will be exterior.


6 and 4 are both exterior.


they are alternate exterior.


not corresponding angles.


ah


also corresponding angles are congruent.


8 and 2 are alternate interios


but 4 and 12 ar both exterior


12 is interior.


it is between the parallel lines.


oh 15 would be exterior


yes ti 15 being exterior


correct?


let's look at 5 and 7


theyre both interior


if we use the blue lines, 5 is interior


yes


its between parallel linees tho


there are two sets of parallel lines in this picture.


the blue lines and the yellow lines.


12 is interior for the yellow lines, but it is exterior for the blue lines.


og i get it


great!


these would be qual to each other?


why?


because they are congruent?


why


what is their special name?


corresponging


are they alternate interior or corresponding>


right!


are the angles alternate exterior angles?


no


do both angles appear to be acute?


is one acute and one obtuse?


yes'


so they are not equal.


what would they equal to then?


angles in parallel lines are either congruent or they are supplementary.


theyre supplementary


right


what is supplementary?


90 degrees


good


1 and 6 are alternate interior angles right


correct!


so they would be equal to each other


yellow?


are the questions getting easier?


a little yes


im on question 15 out of 20


but some of them i can do on my own


kk


it would also help


yes


alternate exterior angles


I just remembered an errand.


last one please


I need to sign off now.


you are doing well.


just this oneeee


yes, slope is 2


pleaseee


got to go.


Ok.


it is for my neighbor.


i just needf to get the equation


I will stay signed on and come back.


yesss


ok


thank you


coming right back.


2 is the slope for perpendicular


slope is -1/2.


flip and change the sign for perpendicular slope.


im finished


Liam


Hey Liam!


How can I help you today?


hi


I need help with math


Any problem in particular?


decimal


math


Do you have a problem you are working on or would you like to to come up with an example?


yes


there


Okay which part should we solve first?


the first one


What is the order of operations?


the 1 then the 2


Well the two is squared so we need to solve all exponents first


alr


What is two squared?


Hello John


Hi Sarah! I have a quiz tommorow and i have been struggling with these questions!


okay let's review together on board


start with a?


I will guide on board


okay!


vertial angles


exactly


so they are set equal to eachother?


yes


k


use board to solve for X


should i add 20


subtract 20


oh my days


i am legit hald asleep


thank you


right?


so now do i subtract-35 to get Y?


not quite


oh wait i plug in


i gyatt this


yeah


super!


ayyyyy


the second one looks scary tho


similar concepts


okay


go for it


I color coded the vertical angles


so now i make an equation?


yes


because they are vertical?


exactly


wait so now what?


right?


good


so do i do 56+16 to get the full angle


find y


how would you do it?


i fear i am lost


angle of straight line =?


so would it be-56-16


because they are given on that line


perfect


ah ha


good work!


wait i am cooking rn


keep it up!


color code the way I did it in a and b


so wait this one was hecka confusing


remove the black markings it will become more clear


oh okay


undo


I will adjust


do my markings make sense?


yes


so start creating your equations


wait would it be y+10 = 90


see board


oh wait we need to add the x to match it up


i see


one more equation


dont tell me i need to do elimination


sorry


no 90


oh k


oh i get it


get rid of y


right


use board to solve


I will guide on board


arrange all the terms first


oh


i am so lost


I walk you through it


Emily


clear what I did for X?


yes


cool


Now find Y by subbing x


oh lawd


y=?


solve for y


clear what I did


mb i was in another world


Good work!


Continue your efforts!!!


Need to sign off now. Good luck with your quiz!


yuhhh


word


Hi Liam, how can I help you tonight?


Hello! I need help understanding how  to do these fraction questions! :D


Can you teach me step by step