so if A is (8,1) and B is (14,9), to find a you do (9-1) and to find b you do (14-8)


ohhh


i got square root 100


what does that simplify to


square root of 10


or 10


yeah


wait is it 10 or square root of 10


okay


so 10 is the straight line distance from A to B


what do we do now


what else does part c ask


i shared my screens


you already found the distance from A to X to Y to B and then you found A to B


so now you compare which is shorter


so take the two distances you found and see which one is smaller


A to B is shorter


yes


now in 1-2 sentences you need to explain why A to X to Y to B is longer than A to B


but why is it longer is it because of the intyersection


yes but why else do you think it would be longer


think about going directly from one place to another in a straight line vs. taking sort of a zig-zag route


why would the straight line be shorter


because there is  o turns


use all of that information to create a short answer on why the intersection route is longer


I have to go now, but you did a great job


good luck!


Hi


Hi Sarah


one moment my images are loading


My problem is question 14


is the correct answer C?


I'll need to enlarge the upload a bit.


okay


I'm reading...


C is correct.


oh nooo


okay thank you


is it because the data points


have the biggest gap


from the mean


Yes. For (C), the data points are the furthest away from the mean. The "spread" is the greatest.


Okay I understand


thank you


that will be all


have a good day :D


You as well.


Hi!


hi


one second


Hey, can you hear me?


yea


OK. Um, OK, so.


first we need to understand the shape of the graph. So the graph is a para uh parabola, right? And the negative sign is just showing that this graph is opening.


downward


upside down you


The coefficient to makes it narrower and steeper, right? So this is just gonna be the original function. We're trying to make it into this Y equals function right here. So now we know that the graph needs to open downward, and the two makes it more steep. The vertex is still going to be at 00. So what we're gonna do is we're going to plug in some X values to get some points. So we have this


equ ation we have 2 x^2, um, can you go ahead and plug in 0 and tell me what you get.


for the X value.


So if we were to replace the X with 0.


I


Um, I'm sorry. I'm kinda confused.


That's OK


OK


OK.


Um, I'm just gonna go ahead and walk you through it, OK? So,


if we have Y equals -2 x^2. Basically we're just plugging in a point to check, oh, if I put in this point, what would I get for the Y value, right? So if I were to do -2


and then I replaced the X with a 0, and I put a square. What is 02? So 0 times 0.


Uh, 0, right?


Yeah, exactly. So it'd just be Y equals 2 times 0, and anything times 0 is just gonna be


0, right?


Yeah


OK, so this is just gonna be 0. So basically what we're saying is when we plug in 0, which is our X, our result is also going to be 0.


Do you understand how I got this coordinate point?


OK, perfect. So now what we're gonna do is on the real graph, we're going to go and put the point at 00.


Mhm.


And the next thing that we're gonna do is we're gonna plug in another point. So let's do, let's plug in one.


OK? So if we were to do Y equals -2.


x 1


2. What is 1 times 1 or 1 squared.


Uh, one


Exactly, so it's just gonna be one. So then what's 2 times just one.


Um


that'd be -2, right?


Yeah, it would be negative too. Perfect. So, now we know that when we plug in one, what would our Y coordinate be?


Here's a hint, you just said it.


Mhm, yeah. So now we know another point, right? 1 and -2.


So now we're gonna do another


um Basically what we're doing is


we can see that the graph up here is, it looks very similar to just Y equals 2 x 2, and we can see the same points, we can see one.


and one is matched up because right here at this point right here, that's 11. This point right here is


2.4. And if we already see a pattern here with one


We can also just see that since it's gonna be the same, a parabola is always gonna be like even, right? It's always or not even, it's always gonna like be symmetric.


So if there's a point here, we need to make it even so on this side of the graph right here, where could I put a point that would match up with this one.


Uh, -1, 2, right?


Mhm. Perfect. Yeah. So that's right. And then


it looks like they want us to, so it says move the red points.


to moving the red points changes the vertical stretch or compression, moving the blue point shifts the function left, right, up or down. So it's, so do you see how like when we have a normal function, we would usually have something like, or not a normal function, but if we're moving left or right, we would usually have like X minus 2 or X + 4.


Mhm.


Yeah, we would have something like that, right? And this function, we don't have that, so we're not moving left or right. And we also don't have like a plus or minus value at the end.


So


basically, all you're really doing is you're just changing the slope to be negative 2.


OK


So, let's plug in another point. Over here they're doing 2 and 4. Let's just go ahead and do 2, OK? So if we were to plug into


so if we were to do Y equals -2.


times 22. What is 22 or 2 times 2?


Mhm, 4, so then we would have Y equals -2 x 4. What's 2 times 4?


Uh, -8, right?


Mhm, yeah, you're right. So it'd be -8. So now when we plug in, what's our output?


Um, it would be.


Remember you just said it


-8, right?


Mhm, yeah, exact


OK.


So it'd be 28, and we could put that as a point on the graph, and where would like the matching point before it?


Uh, 8 or 28.


Mhm. Perfect. So just be right here. And then we could just go ahead and now we can form our parabola and just draw it out. So honestly, all we really did is we plugged in different points.


and we got this. You can plug in any numbers. So we just did 0


1 and 2, but you can do anything. You can do like


preferably you want to plug in like something on the X axis, right? You want to do like -10


all the way up until 10, like any value here. You don't want to do like 32.


You want to do something here and then hopefully it'll match up.


on the graph


All right


Yeah, so let me know if you have any other questions or anything else that I can help you with.


Um


yeah, no, I think I get it now. Thank you.


Yeah, of course


Hi!


Hello


How can I help you today?


just 16 and 17 today


Ok let me see


I need to learn how to make equations today thats my main goal


Yeah so the key here is that you start with setting up letters


So in the last sentence you see how the question says "How many bags of chips 'b'"?


Yes


That's an example. You assign a random letter to things you're not sure about


What else do we not know? In question 16


5 sandwiches and 6$ each and spent 42


So what's the value that we don't know yet?


Oh wait


Sorry yeah we can just solve it from there


Ok


So $6 for each sandwich


If we didn't buy any bags of chips, how much would 5 sandwiches cost?


5x6 right?


Yep


so 30


You got it


But how much did we actually spend? based on the question


Right so keep that number in mind for now


And now let's see how much each bag of chips cost


costs


Can you guess based on the sentence I highlighted?


each sanwich cost 3x as much as bag of chips


Yes and we know that each sandwich costs $6


Yes.


18 per chip


Almost there


But it says each sandwich costs 3x as much as bag of chips, not the other way around


I think you came to 18 by doing 6x3


But actually what we need to do is 6/3


three times? as in mutiplication?


(each chip) x 3 = (each sandwich)


This is what the question was saying


And we know that (each sandwich) = 6


Which gives us (each chip) x 3 = 6


That's why I did 6/3 to get (each chip)


sorry just clarify a bit more


each sandwich costs 3 times a much as a chip


one sandiwch cost 6, and three times as much


Take the word 'costs' as an equal sign


so 6x3, I know your right just i dont understand


and 'as much as' as a multiplication sign


each sandwich "cost" three times "as much as" a bag of chips


If we do that conversion, it turns into


each sandwich = 3 x a bag of chips


ok so 6 divided by 3?


Exactly


So a bag of chips costs?


You got it


So let's go back to the last sentence of the question


You said it would cost 30 if we only get 6 sandwiches right?


But what we actually spent was 42


which means bags of chips cost 42-30 = 12 dollars


Do you get this equation? Or I can also elaborate


whys that there


each sandwich costs 6 right


and we bought 5 sandwiches according to the question


yes


ok and 2xb?


Each bag of chips costs how much?


And for "b," let's check the last sentence one more time


How many bags of chip b did she buy?


So b is the number of bags of chips


b is the unkown


Yep you got it


is there a way to write this without using mutiplication signs


You can just say 2b instead of 2xb


Caught up so far?


Now let's solve this equation


Do you wanna give it a try?


Yup go ahead


Correct


So answer is 6


Got it? Let me know if you have any questions about number 16


Or we can move onto question 17


move on


Ok can I erase everything on the board?


yes


Number 17 - the most important concept here is speed


speed is simply things like mph or miles per minute those kinds of things


this is the hardest one


Well I'm sure you can easily solve it once you get the hang of it


Let's read the first two sentences


So it took Leo 30minutes to ride 3.2 mi right?


so how many miles per minute?


Yep that's correct


thanks


so that's the speed we're looking for


Let's keep reading the question - after the appointment, what time is it?


Right


And then the question says that he rode a bus for 4.8 miles to the soccer field after the appointment right?


But does it directly tell you how many minutes he rode a bus to the soccer field?


no but the speed there


Exactly


So why don't we first set minutes as an unknown "x"?


yes


And you said the speed is 0.106 mi per min


What do you get for x?


wait let me backtrack


Yep what are you confused about?


ok i understand


Sounds good. So what's x?


0.106 x 4.8?


or divison


division


cuz here 'x' is an unknown letter, not a multiplication sign


You sure you did 4.8/0.106?


So roughly 45 minutes right


yeah


And the appointment ended at 5:30pm


so 45 minutes after 5:30pm is what time


Is Leo on time for his 6:30pm soccer practice?


yes he is early


Right? That's it


Thank you alot


Just 2 more simple questions


Ofc go ahead


is number 18 just distributing?


Yeah distribution


and how do you solve 3?


I see you added 8 on each side for the first step


You're actually on a right track


First multiply each side by 4 and show me what you get


is that correct


Yep that's correct


And divide each side by 2?


thats the way my teacher wants


Oh ok that's no problem


You can still divide each side by 2 after distribution


does the left side fully cancel out


and we are only left with right


If we divide both sides by 2, it's gonna give us:


Are you confused with the concept of dividing both sides?


no


Then do you get how I got to r-3 = 161 by dividing both sides by 2?


2 divided by 2r cancled out the 2 just leaving r, 2 divided 6 is 3, 2 divided 232 is 116]


Yep exactly


So can we solve for r now?


164 final answer?


Correct


That's how you solve that question


Mix of multiplication, division, and addition


Thank you


I just realized this is going to be a long year


this is so hard and i just started school


Have a good night


Yeah it's hard cause you're learning a lot of new stuff in algebra 1


But guess what


You're gonna be reusing the same concepts you learned in algebra 1


Which means it's only gonna get easier and easier over time


Thats great


So don't worry it's just one challenge you need to overcome


Thank you for making me feel better, Have a good night!


Alright have a good night!


Hello, Liam! I hope you are doing well. What did you bring with you today?


hello i need help with 8.2 apply properties of rational exponents


Do you have a homework assignment on this? Could you post an example?


yup


give me 5 min


im trying to finding it


Ok no problem


This seems to be a different concept than the rational exponents. Did you want help on the composite functions?


We can do that


yh that


mb


Ok so if we go through this machine analogy it might make more sense


It might be easier if I speak into the mic


Hello, can you hear me?


Mhm


Yeah, I can hear you


Oops


OK. All right. So


I think it would make sense first.


if we


look over what functions are. So, could you fill out


this table


with VFX


So


it says GFX is


3 X


minus 2


and X is uh


well, X can be any real number, I guess, so


It says here -3.


and 2


Do you know how to get the output.


Mhm. I, I know. Simple.


so


and this one,


let me exchange the color


red


Mhm.


It's been -8.


How did you get that?


So


I just put the machine, so in -3 I plugged in for the first one I plugged in -3 + 1.


Oh


which is, I think, for, and then after that, I plugged in the edge of the output and plug in GX, which it, which we can


OK


uh


that's a little bit further ahead. I'm just talking about this one.


I'm not talking about the composite yet.


So this one is


Oh, so


3 x minus 2


I think you have the right idea though.


oh


my bad. Oh


It's OK.


oh, for this 13 times negative, that will equal. That'd be negative 1.


Yeah


So this one is 6 + 2 between 8


Mhm


Mm


other times 3, it'll be 3 X, it'll be -5.


Yup


So 3 times 0 would be 0, so obviously it's going to be negative too. Uh


so 3 times, so this was one.


yeah, positive one cause.


and 3 times plus 6.


will be 4 this one


and then this one, daytime 3 is 99 minus 2 will be 7.


Got it


So the, the point of that is essentially, it's the same idea.


but there's an extra step. So


when we talk about a composite


if we're talking about G


let's see, of F of X.


right here


We're passing through this, this number.


through F of X, that machine you could call it.


So we're getting the output of that machine.


and then we're inputting it into this machine.


So when we talk about the composite,


it's a very similar idea.


So let's see


Let's try 0.


1, and 2


So you, you know how functions work.


so,


essentially what we're doing is


we're going from


the inside


F of X


What shape


and the output of that becomes the input


No


of G of X. So it might help to try, try a couple.


with it.


Mhm.


So just like plugging it in. So I think I got what you mean. So I think says X + 1. So if you put 0,


Yeah.


Mm


uh 0 + 1 which is 1.


Yeah


I see. So what then that means X is 1, so we put G F X


Wait, that means again one?


Wait, no.


Yeah, so she, uh, if you wanna write it out, G of F of 0.


equals G of 1.


and we did that already, or you did it actually.


right? You got one right there.


Oh


Uh


How about you one.


or GFF of 1


OK, so, so one


so one plus 1 is obviously 2.


and then


C X, OK, G X


So 22 times 3 would be 6.


Uh, 6 minus 2 would be 4, that'll be 4.


Yeah, exactly


And then same thing goes as, as another, right?


Mhm


So 2 + 1 is 3, and then


Yeah


so


and then 3 times, 399 x 2 would be 7.


exactly. So if it helps you


you're still just putting the number inside.


Oh


Does this, this expression is just gonna be a number.


and it's gonna look like this table, the first table we made.


So composite functions


Hm


it's um


essentially we're doing a function inside the function or the output of this function you draw a line, right?


We have an output here


It's going to become the input.


of this function


And it, it works actually, um,


from the inside out. So you could just keep doing this if you want. If, for example


how would we do F of


Uh


GFX


How would that be different


Uh, let me see.


So basically


so we solve, you want us to solve it


Wait


if you want, it's the same thing, right?


Mhm. That's the same idea.


Uh, and no matter how it's switched, there's the same idea, right?


Yeah, it's the same idea except


it is a different uh


it would go the other way


I don't know if that makes any sense. Hopefully that makes sense.


Yeah, that's.


I got you


OK


And so for this one, how to explain how the function machine do it just explain how was it, just like what we did right now.


Yeah


Uh, let's see, explain how side by side


yeah


So I don't know if that analogy with the machine.


Hope that makes more sense


But essentially we


we're getting the input, so you have to get F of X first.


and then that


is the value where it becomes the input for the next function.


This could go on, on and on, actually, you could keep


having more functions if you want it.


You have a H right here


OK, so


but that's not, uh, maybe that's too much information.


the armpit, then goes to the 2nd machine GX


GX, which


Moly.


3 and


subtract


so that to me she makes it so.


GFX


Um.


got it. So there's a


OK


Mhm.


Can we do another poem, if you don't mind?


OK.


Um, let's just say here, let me type it up cause I don't, I can't screenshot a lot.


Yeah


FN X


equals


minus 3


+ 4 x.


And she let it be


those 5X


plus 4 eggs


So


there's like


kind of like three problems when it stays like this, hold on, let's do it.


Uh-huh


F


and this is X + G.


X


plus


J X


minus F


and then


minus G


Perfect. Done.


like this


OK.


OK


So how would I do it? Like,


would I


Um


start


I'm not sure what, what is


so what is a teacher


what is this giant F mean


That's a different function


oh


Is that included too


No, oh my, I think I add, oops.


It's a lowercase f. I think my uh capitalize.


Oh, OK. OK


Hm


I, cause that, I thought that was a different one. Does that make sense?


Um.


so


do you know how to add and subtract the


different variables


That's an important thing to understand first.


So let's say we have, let's see.


I, I'll, I'll see.


Mhm.


Let's say we have


uh, where's my pen.


X


uh, squared.


plus


let's see


X cubed


5 XQ plus 3XQ.


That'll be 8SQ.


Perfect.


How about


4 X.


Mhm


+ 4 x 2.


probably 8 x 2.


Yeah.


because the bear was listening


So the idea is


if the exponent is the same.


you can just add the coefficient. So,


What if he chooses me


or add or subtract


Yeah


What if it's different


So


let's say we have 5


X cubed


plus 4 x 2.


What would that be


Mm


Or what's your best guess?


A um


um, to be honest, I'll put 8 XQ 1 A X


squared together


variables


So, the, the thing is it only works when they're the same


It's like


Uh


see


so that means do I add the verbals? That means 3 + 2.


uh no


So


it would be different


So we're just talking about addition and subtraction. It's just, it's totally different if we're talking about multiplication or division.


But that's a different thing entirely. In that case,


you kind of group, group it together.


and then you could add


But


when we're, we're, we're, we're talking about now.


which is just adding and subtracting


You're just trying to find the similar exponents.


And if they're not the same, so I said this one was


uh addition


You can't really simplify it any further.


Um


So that'll be


this is kind of a trick question. It would be 5 X cube


plus 4 x 2.


Now if I had, for example,


5 X cube


+ 4 x 2.


oh.


easy, and I'll be


uh


X


cube


plus


X squared


Yeah, exactly


So make


Oh, so it's different variables, I can't add them, so cause it's


yeah, you, you would just have to leave it alone. So you can't really


uh simplify that


the same goes as subtraction.


Yeah, so let's say uh


let's see, 5 XQ


minus 4 x 2.


uh what would that be?


Uh, same things, uh, 5 X cube minus 4 X squared.


Mhm


It's good. So


you can only really do the operation.


when they're the same


Mm


We have 5 X cubed.


minus 3 X cubed.


what would that be


5 X


oh wait is it Q


Yeah, that's it


Uh, that'll be 2 X cube.


Mhm.


that it


Good job


Yeah, I got the contact


Yeah. So that, that's it, that's, that's the important part to remember.


We're looking at


the similar exponents or the same exponents.


and then we're grouping them together, kind of like


if this helps you


like you put it in front. So this is the X cubed.


5 minus 3.


and then that would be 2 XQ.


Yeah


So this 15.


plus


the


4 + 4.


X to the power of 1/2. And then that's how you got the 8. So


it might help for this problem.


to kind of write it together or see.


Group it together and then see


like kind of like uh


you put F of X here.


This might help you


And then you put GFX there.


and then you see if you can line up the the numbers.


with the right coefficients.


Oh, well, oh yeah, I get you. So I'll be negative.


3 X


Mhm.


and


Yes


Yes.


We'll make this big plus.


and then on the bottom, we change the color.


little dark


because he.


OK, which is 5.


X


have


plus


4 X.


Mhm


So 4 x + 4, so that'll be


do what? OK, 4.


I, mm oh I add them, right? 4x5 plus 4 XF.


What it would be


So that'll be 8 XF.


Yeah.


It's like


you're just taking the X/2.


You'd take it outside. So 4.


+ 4. If that helps you.


All you're doing is really just uh


using the coefficient.


Mm


So -3


um plus 5, that'll be um that'll be 2.


So


X


Mhm.


Yes


plus, which is where he leads to our plus, well, this is the answer.


Yup


and


So now it's very similar with uh these two, but instead of adding them,


let's see.


you would be subtracting them, so you could do another one.


um we try to erase this.


I can raise it for you quickly


OK. Thank you


You're welcome


Here we go.


All right. The next one, G of X minus F of X.


It a similar idea


Yeah.


except


It's nicked


you put GovX at the top.


and then Liam at the bottom.


And you're not adding them


you're subtracting them


Mm


So


5 eggs.


plus


OK, now we do big minus.


and then FS


negative


3 X


uh


Mhm.


so positive for minus 4, so that costs out like that's it.


Yeah


Um


5 X


minus 3. Wait.


How could we wait 5 minus -3, that'll be 8.


Yeah, exactly


P X


Mhm


Yes


No, that's all that's the answer.


It's uh same goes the other one, but


it's a


FN X and then subtraction.


Oh, that's pretty simple


So it's, yeah. It's uh, for the first one, it doesn't matter which one is on top or bottom.


cause you're just adding them


But when you're subtracting, these are two different. If you do this one, you'll get a different answer.


OK.


It's not a


what's the word, communicative.


Oh


oh


I got it


That that's probably more information. You don't need to know.


All right.


OK


so I'll do


negative


The see here.


Well, for Liam.


So, so that'll be boom sub -3 minus


3W9 negative, and then that'll be 8 X.


Mhm


That's


Yup.


Yeah


So I think I uh I think I've got the concept of it.


Yeah. So it's just, this is for addition and subtraction. These are different rules.


when you start talking about


multiplication or division, but


that's not on the your assignment, so


you'll learn about that later


And what if it's like this, Liam


Mhm.


Let me delete this all.


um


it's goes like FG


boom, she


Well if it's like this


So how do I plug it in?


OK, so


this is kind of like what we did.


the previous problem


but it's a little more involved. So it's the same idea. It's not a number


we're not evaluating it. So if, if they ask you to fill out a table


that's how you would do it. You would do GFX first, and then


do F of


GFX, right?


So this is


F


composite of G.


All right? So


when we're asked


to find the actual function,


it's not too complicated. It's the same as just, oh.


change


OK.


Mhm


see


Just erase this


what I wrote


OK, uh


so


if it helps you


what is F of


Y


But you evaluate that


There's no why. So how do I know the way?


So let's just say why is the just the variable Y. There's no uh


I could have, I could say that, but let's just say why is


just why


Well then it's, it's Y. F is Y.


So this would be


Because Y is not


so this would be 2, right? Essentially, where you find the X.


you do 2 Y squared.


minus 3Y.


OK.


If it helps you, let's say Y is 3 X + 2.


So when we say F of G of X


Well, we said


we uh


we say Y is equal to G of X, which is 3 x + 2.


So now essentially where that Y is.


you would plug in


that function. So it'd be 2.


GFX


minus


3GF X.


So then usually when they ask you for this kind of question, they're gonna ask you to finish the whole thing. So,


this is technically true


but what they would want is something like


you plug in


the, the function. So 3 x + 2.


2 times


3 x + 2


Oh, it's a bad 3


supposed to be 3


3 x + 2.


minus 3


times


So this this goes deeper. You can simplify that further, but that's the general idea of how you would solve for it.


Mm


So wherever you see the acts.


right? So F of GFX, you're just gonna plug in


GFX right there. But that, that, that whole thing would be squared.


and that whole thing times.


These are equivalent


OK


So that, that's the, the high level


If you have another one


I wish there was another example, so you could practice it.


But that's how you would approach doing that kind of problem.


Mm.


no


It's, it's the same idea, right? So when we're talking about


we're, we're taking the input


the output of GFX.


and it's gonna become the input to the next function.


And remember that picture?


except we're not using a number


we're just


solving it


or simplifying it


with the, the X


Mm


got it


It might be helpful if there's another, do you have another example, and then you could try doing that one.


Yeah, I do, I do


Hm


So I


X would be X


G X


will be 3 X.


I don't know.


OK, so.


you had


Alright, so.


Liam.


right so


we singing.


at


So I'veMX.


is


uh


honestly


Um, how do I do it


Mhm


So, is that the same problem


Oh yeah


That one?


How would you, what would this equal to?


The X, so it's uh, uh, I square minus 3 X.


right?


Yeah?


OK.


But this is F, so that would be F of X. But so what would F G X be?


Fenyx. You mean GF GF would be 33 X 1 is 2.


Mm


So


Uh, so, wait, I don't get it. I'm sorry.


That's OK. So


No, I


you


no, I would be uh X squared minus 3X. How come it's 3 X? That's why I'm not trying to understand.


OK


that would be


let's see if I can


make up more sense


Now, let me, let me try to ride it out. So F of


G of X


would be F of 3 x minus 2.


right? Cause that's what GFX equals to.


So now, instead of just, so this is what F of X would be.


X squared minus 3 X.


wherever you see the X.


you plug in X or whatever number.


So when


we have 3 x minus 2.


or let's say X + 1.


Wherever you have the X, that's the input.


you would add one to it.


though X + 1


squad


minus 3.


and then that would have to add one too.


So when the input is changed, right, this is the transformation


instead of just X


Now we have 3 x minus 2.


though.


if it makes sense


this is a 3


Wherever we see the X, we have to transform it, so.


if it's


X squared, then it becomes


3 X minus 2


So


if we say X is 1.


then we would transform it to be 3 times 1.


minus 2


but


the way we're doing it, we're using more symbols.


instead of the numbers, but they're the same thing. We put the symbol in place of the number.


So Xs are variable, they call it.


Mm


So how would you do


the next part, minus 3 X. What would that look like?


So you got one.


Mhm.


you plug it out, so there'll be this one, OK.


X


+ 1


Then again, X + 1.


plus


1 in 3 x


plus.


1, and then


based on that, we just solve it.


Yup


So that'll be


so


SS squad


and then one plus.


1 X


1 X again


um plus 2


and then minus


3 X


uh, and then minus.


and then we combine like terms, so.


Uh, I would look at this one again. The last one plus


the last term


it should just


and I


should be just stood because 1 times 1.


So 1 times 1 should be


Hm.


We're doing 2 times 1, that would be.


Not bad


no problem


Oh


Mm


OK


first one. So we combine life term.


Mhm


Um.


so we put X squared first because it's the bigger.


Yeah


minus


3 X. No, wait, no, combined lecture. So,


there's one


1, so there'll be 2 eggs.


Mhm.


uh, 2 minus 3, that'll be negative


1 X


Yup


and then


obviously it would be


wait, is this negative


Oh, never mind. 1 minus 3, so that'll be negative too.


So that's the answer


So that's the answer if Liam is


X + 1. So that, I gave you a different problem cause it might help uh


The first step is just plugging in the expression. So I gave you a different one just because it's easier to solve.


But for this one, you have to plug in.


whatever GFX is. So that was 3 x minus 2.


It was the same idea


right? You would still have to


uh do


distribute or foil.


this would just be a different number inside, so.


it's everything you did


but it would be using this 3 x minus 2.


All right, so let me see if I can erase that.


that was the crucial step. I think you have, you know, the rest of it.


cause you just showed me, um


I see if I can


Oh


trying to erase this


Hm.


So that's the big step you're missing. The first step, actually.


It's just


plugging in


So you seem to know, I think you know how to simplify it.


So it would just be plugging in


So what would the


if GFX is 3 x minus 2.


what would F of GFX be?


I think I did the first part for you


Yes, so that's.


so


I think I got


Oops


I think I got it. Sure.


boom


Wait, wait, 3 times 3.


is 9 and 3 times.


I'm, I'm, am I tripping


3 times 3 is 9.


3 times 2 is not.


not 60


Yep.


6, and plus 4.


no no not 4. What am I getting?


I think I'm getting all


OK, and the natives too, because I'll be 6 against 6.


Mhm


And then it'll be plus


Yeah, that one's +4


and then we plugged in 9X.


And then we combined like two


So


I think this one


Hm


uh


what's -2 x 3.


So I think you, you did this part, right?


this part


we should look at that again


2 times 3 will be negative.


uh that's negative 6.


Yeah.


It's negative


Um, no negative.


since we combined like 21.


X


and then


that's it


That's the answer.


Yeah, that looks right to me. So let me see.


Um.


Yeah


Mm.


Right


12. Yes, that's right.


So that, that would be your final answer if they asked you to solve it.


or to simplify it


then you would have that as your


it would become a different function


essentially, when you do this composite.


but


you put the pieces together.


to make the whole thing


Mhm


so that the important step is, is substitution.


So when, when you see this F of G of X.


you're substituting G


wherever you see X


that whole thing. This could be a very long or different function.


I don't know what it, what it could be, but that's, that's the idea.


If, if they ask you to do


so what would the first step be if they asked you G of F of X


composite of F or G of F of X.


How would that be different


It's just like we switched them all around, that's it. We just switch


right?


Yeah, so what would it


what would it be


That's F of GFX.


cause they might ask you this too, your teacher might put this. She might ask for the other way. So what, what is the other way?


we just switched it, so we, uh, 3 and then 3x minus 2.


or minus 3 x minus 22.


Just switch it up


Uh, could you write it down? Cause I couldn't see.


Yeah, of course.


So measure if it's


can I delete it


Yeah


Right


So if it's up G X


W 3


as I said


and then 3.


minus


we


most


Mhm


And that's it. After that, we just stop it.


Yeah.


That's the most important step, is that


That's probably half of it, I think.


Well, once you know how to do that, then it shouldn't be impossible.


It.


What is the 19 it's my.


So, can you simplify that any further?


No


So that's what we were talking about in the


I forget which problem, but


whenever there are different exponents, you cannot


add or subtract them


Well, that would be the final


final expression


Uh


yeah, that's about it


Did you need help with anything else?


OK. So just keep practicing whatever your teacher gives you.


and then


you should be prepared with the.


with the rest of it


All right


Mhm


OK


Nothing else


No, nothing else


OK. Well, have a good rest of your day.


and I hope you learned something.


OK.


Yeah


Bye.


Hello


hi


what do you think about b?


Hello?


yes


all value of x should equal 0


I am  not sure what you mean. they are asking for which value of x does g(x)=0


can you point to the places where g(x)=0


Yes, that's right. What are the values of x at those two points?


(4,0) and (-4,0)


thats right.


those are the two points. What are the values of x for those two points? thats what they are actually asking.


For the point (4,0), what is the value of x?


yes, and for the point (-4,0), what is the value of x?


right.


so those are the answers for b


for c, they are asking for the intervals of x where g(x) <0.  In other words, for what values of x is the curve below the x axis?


(-4,-5) and (4,-3)


what is the first x value you have circled?


that point with the arrow has an x value of -5


what is the x value for that point?


right, so tht interval is written (-5,-4).  It always goes from left to right.


how do you think you would write the second interval?


what is the x value at the point with the arrow?


and what is the x value for the point where the arrow is now?


right, so what I have written is the x interval for which g(x) <0


since the dots are closed circles at x=-5 and x =5, perhaps better to use brackets for those numbers


ok


Ok, have a good rest of the rest of the day.


did you have a question about this answer?


Hello?


Sorry, but I need to go.


bye


Hi.  How are you?


hi. I'm doing good. how about you?


Good.  How can I help you?


I need help with a homework assignment


Ok


can I have a couple minutes to get it onto the board?


Sure thing


Start with 19?


Do you have any ideas on 19?


so for questions 19-22 I answered in the format "One angle is blank and the other is blank."


I just wanted to make sure that that was the correct format


Sure. Did you solve for the angles?


yes


Ok.  What did you get on 19?


"One angle 30 degrees and the other is 60 degrees."


Right.  Good job.


on 20 does it matter in what order I list the measures


I wouldn't think so, but I don't know for sure.  Mathematically it shouldn't matter.


ok


What did you get on 20?


"One angle 45 degrees and the other is 45 degrees."


Very good.


I was pretty sure that that was the format for answering 20-21 but I just was unsure if that was the format for 21-22


The directions say two answers for each problem.  Again, it shouldn't matter as to the order.  Mathematically anyway.


so as long as I have the 2 measures it doesn't matter how I phrase my answer?


I assume you are inputting answers to a computer of some sort.  I can't guarantee what that software does.  But, in my opinion, you are to provide 2 answers and order shouldn't matter.


I'm writing it down


so it doesn't matter how I phrase my answer as long as I have the 2 measures


right


What are your answers for 21?


I agree


"One angle is 81 degrees and the other is 9 degrees."


Right


Input 9 degrees first, then 81 degrees


so if I already wrote down my answer I should rewrite it?


No.  Order shouldn't matter.


ok


so that answer is good?


In my opinion.  I can't know what the system you are using will do.  Mathematically, it doesn't matter what order the angles are.  You have answered the question correctly, in my opinion.


and does the way I phrased it make sense?


Very much so!


What are your answers for 22?


"One angle is 72 degrees and the other is 18 degrees."


Correct.


so am I good to move on from 19-22?


Yes


Write and solve an algebraic equation to find the measure of each angle based on the given description.


The measure of an angle is 6 degrees less than the measure of its complement.


I need help with that one


Ok


Let's let x be the measure of the angle we are finding.


What would be an expression for the complement of the angle x


The complement would be (90-x)


ok


So.  Consider this


x + 6 = 90 - x


If the angle x is 6 degrees less than it's complement, we simply add 6 degrees to the angle to make it equal to it's complement]


Do you see why that is the equation we need?


so the equation would be "x+6=90-x"?


Give me a minute


Do you understand the logic of it?


yes


Go ahead and solve it to get our answers


so once I write the equation and write what x equals am I done?


Solve the equation for x.  Let me know if you need help with that.


Great.


What is the complement of 42 degrees?


Those are your answers!


You can see that one is 6 degrees different from the other


I have to go do something. Can you stay on the line and  I will come back when I am done?


How long will you be?


I'm not sure


Well.  I can wait 15 minutes. Otherwise, you can put in another request.


ok


I will let you know once I am back


Ok.  If it's longer than 15 minutes, just put in another request.


I'm back


so does x only equal 1 value or 2?


x is only 1 value, but the other angle 90-x is also answer to the question.


x = 42, 90 - x = 48


so would I just write "x+6=90-x" and then write "42 degrees and 48 degrees"?


I would write "x+6=90-x" and the angle x is 42 degrees and it's complement is 48 degrees.


write this?:"x=42"


and then this?"One angle is 42 degrees and the other is 48 degrees."


That would be fine.


Don't forget to write the equation x + 6 = 90 - x as the equation asked for in the question


so I should have those 3 things?


When you first put the problem to me a few minutes ago


you said both the equation needed to be one answer\


and the answers (two of them) would be needed as well.


That's three things:


x + 6 = 90 - x


x = 42 degrees


and it's complement is 48 degrees


so "x+6=90-x", "x=42", "One angle is 42 degrees and the other is 48 degrees."?


Yes.  That should be fine


ok


The measure of an angle is 12 degrees more than twice the measure of its complement.


Would the equation be 90-x=12+(2x)


You have made a nice attempt, but it is a bit off


Let me walk you through it


The measure of an angle is


can be represented by x =


The measure of it's complement is 90-x


That make sense so far?


yes


Putting the rest of the verbiage together look like this


x = 2(90-x) + 12


The measure of an angle is 12 degrees more than twice it's complement


Do you see the difference between this and what you tried (valiantly)?


It take practice to learn to translate from words to algebraic equations.


Jamie,  go ahead and solve this okay?


so the equation is "x = 2(90-x)+12"?


Yes.  Do you see that it is nicely translated as "an angle is 12 degrees more than twice it's complement'?


When you have solved for x that will be the only answer to this problem.


Why did the other one have 2 but this one only has 1?


They are really only asking for the one angle in this problem, at least the wording you gave to me.


They are looking for the measure of the angle that satisfies this condiition


the wording to me looks the same as the last question


I have to go do something. Can you stay on the line and I will come back when I am done?


You can answer it as you see fit.  If you need to provide the complement, by all means do so.


Again, as long as it is about 10 minutes, ok.


If you need more help after that, just put in a request.


ok. I will let you know once I am back


Jamie.  I need to go now.  You should get 64 degrees for the solution to the equation for the last problem.  Please put in another request if you need more help.  Thanks.


Hello How are you?


good


i was wondering how to do a certain question


ill upload it


OK


on the exams method points are a good percent so id also like to know a pretty standard way of going at the problem


i found the inverse and go


t


OK I will copy to 2nd screen pls wait


OK go ahead


however i do not know what it is asking for when it says in the domain [0,1]


or what mutual inverses means


let me think


did u get this by replacing x with 'y' and then solving for y?


yup


OK let us assume that is ok


Now suppos x = 2


is this function defined?


i mean the inverse


its not real


I agree


because its the square root of something less than 1


i mean 0


That is why I *think* they have restricted the domain. Seee what I mean?


yea


Does that help?


i mean i understand that but i still dont really know what its asking of me


OK


let's try this


what is f(-1) (not the invers but f)


yes and what is 1/2) ?


good


so its even


now have you heard of the horiz line test?


yes


see if the domain included both -1 and 1 we could not really have an inverse!


Maybe that helps with the domain?


i mean


i can upload what the textbook says the answer is


OK pls do


but that book is also notorious for being wrong


Ohhhh OK


well I have lots of experince so we will see


wow it is confusing let me think


i see that they plugged inverse into the original


i guess its to see if they get x


OK yes that is to show that they are mutual inverses


we did not get to the yet


what does mutual inverses mean?


that they are inverses of eachother?


I think it means that if you take the inverse of the invers you get back to where you started


yes


ohh ok


btw I look at my kbd a lot so sometimes I miss your msg for a minute or so


I will cirlce


on the bd


There they are plugging in our "new" y for the old x


yea


so theyre just trying to pretty much say


that these functions are equal to eachother in the given domain?


well not equal


not exactly


i mean inverses


but they are showing that if you take the inverse of the inverse you get back to x


Yes


Also I will circle


They can I *think* take abs vlaue becuase of the domain


Otherwise they might need to say plus or minu x


ohhhh


where I circled in blue


ok that makes sense


good


IMHO this ques is a bit confusing


it is


but then again thats ib for you


ib ?


international baccalaureate program


OK I see Ok


Do they tend to be confusing?


VERY


and our teacher has never taught the class before, and our previous teacher that taught for 40 years just retired last year


I see


well mayb the questions make morfe sense to studentds in London


LOL


i mean i guess


theres just not many good resources for the class


well pls be kind to you tchr


and im not very good at math in the first place


Teaching a new course is a challneg


i am, i know she's trying


good :)


and you have Sarah too


yea ive been on here for like 2 hours a day for the past month


ohhh I see


OK do u have another ques now?


nope, that was it


i finished all other questions in the review chapter


thanks for helping!


You are welcome


u seem to catch on quickly


i do


Hope to "see" you again. BYE BYE


hey


how would i solve this?


because


normally these kinds of problems would have 2 cases but this one has 4 because both sides are abs value


i get x<= 1/3


but i get x<=-3 instead of x>=-3


ok let me work it out quickly and ill take a look


ok


or do you want to write your work on the board and i can tell you where you went wrong


i think that would be more productive


that's what i did


hmm that should work


i feel like i must have missed a step to flip the sign


because after checking my work i found that x is supposed to be >=-3


oh i see what it is


this is an extraneous solution


if you plug in -3, all is good. however, if you plug in another value that is less than -3, say -4, the equation is no longer satisfied


i'll write it on the board


oh but


how would i know its supposed to be greater than -3 instead?


did you solve in all four cases?


wait how do i do that?


i was only taught to do 2


that is what i was explaining at the beginning. because there is an abs value on both sides, you have two cases for each of them so there are 4 cases. I'll show on the board


you dont have to solve for all 4


its ok im assuming itll be


right?


no


yes for the +/- but not for the other


it's always >=


huh


just showing what signs i will be putting for each side


so it is always >=


so


and what other 2?


it is just shorthand so i don't have to rewrite the equation so many times


i was just writing those little things to make it clearer. they are not a part of the problem. don't get confused by them


no it actually does make sense


ok


good


it makes more sense because thats how i was taught the first 2


but the teacher who made all of our notes no longer teaches so if some pages go missing we just have to do without them


oh no. that's annoying. i'm sorry that you have to deal with that


its ok i feel like im still doing fairly decently


that's good


you seem to know a lot


the important thing here is to check for extraneous solutions


you will see here that x = -1 and x = 2 are actually both extraneous. that is how you get the correct answer


ohhh ok


theres 1 more question im confused on


mostly just because i dont know what its asking from me


i'm sorry but i have to go in 5 mins.


we can work on it until then though


oh ok


no its fine because its a longer one


thanks for helping


of course


hi how can i help you today


hello! I'm confused with this problem


ok


is that all that the question asks?


yes


did thye give any other info?


the directions say to solve


solve for x?


no like determine at what points the inequality is true


in interval notation


oh i see


well then we can just look at the graph. it is asking where the green line is less than or equal to the blue curve


and you look at the y values


for example, which one is greater at x=0


actually that is hard to tell


try when x=1


they are actually equal at this point


now at x=2


so here the green line is greater than the blue


same at x =2


i mean x=3


can you do the rest?


Hello Jamie! How can I help you today?


I need help preparing for a unit test and I have practice problems I need help with


the first ? is up


how r u today


Alright!


I'm great! How about you?


doing good


Alright, it looks like you already concluded that the law of cosines is needed to solve this problem, which is correct.


How do you think the measure of angle B can be found?


M<B = 9mm / cos(56deg)


Correct!


wait actually!?


No wait, I'm sorry, I made a mistake. First we need to solve for side a.


oh


After finding the measure of side a we can find the measure of the other angles.


ok


so M<A = a/cos(56deg)


Correct! But it should be 66 degrees, not 56.


oh it looked like 56


Not quite. We need to use the law of cosines formula to solve for a.


Are you familiar with what the formula is?


isn't it A^2 + B^2 = C^2?


That is the pythagorean theorem. I'll write out the formula for the law of cosines.


got it


b and c represent the two other sides, 9mm and 5mm


a = sqrt( 9mm^2 + 5mm^2 - 2(9)(5) cos (A)


Well done! Now, how can we solve this equation?


yes


a = sqrt(106mm^2-90mm^2cos(A)


is what I got


Good! But it can be simplified further. cos(66) can be substituted in for cos(A)


take two


Correct! Great job.


Now we can solve for the measure of angle b! How do you think we would do this?


not sure


No worries! Since we have side a and the measure of the angle opposite to it, we can use the law of sines.


ok


a / sin(A)  = b/sin(B) = c/sin(C)


That's a good start! What can be substituted into that equation?


8.331/sin(66deg) = 9mm/sin(B) = 5mm/sin(C)


Right! Let's ignore the 5mm/sin(C) for now since we are only solving for angle B right now.


How do you think we solve for angle B?


8.331/sin(66deg) = 9mm/sin(B)


That is correct! Angle B would be 80.73 degrees, which would be 80.7 since we are rounding.


What about angle C?


8.331/sin(66deg) = 5mm/sin(C)


Great! And that gives us?


Well done!


And since we already solved for side a, we finished this problem!


Do you have any more problems you'd like to go over?


yes


Alright! Feel free to add it to the board.


it says that they are all wrong


That is strange. Did you round them correctly?


it only gives me one attempt on the practice quiz but it says I can try a similar question


Alright, we can do the similar question if you want.


ok


This one is similar to the last one, we have to solve for side a first to find the other angle measures.


What would the equation look like to solve for side a?


a = sqrt (7mm^2 + 6mm^2 - 2(7)(6) cos(72deg)


Great job! That is correct.


How do you think we will find the measure of angle B?


7.684/ cos(72deg) = 7mm/cos(B)


7.684/ cos(72deg) = 6mm/cos(C)


Correct! Well done, and now you can solve for angle c.


Great job! This should be right, let me know if it says it's correct or not.


its correct


k next question if ur down


Alright! I can do one more question and then I have to leave in about 20 minutes.


its similar to the last two


Okay. Which of the three do you think we should solve for first?


a


Actually, we can't solve for side a first because the measure of the angle opposite to it is not given.


oh


This also means we can't solve for angle A since it has the same problem, the measure of the opposite side is not given. The only thing  we can solve for now is angle C.


ok


how will we do that


The measure of the side opposite to angle C is given. Another pair of an opposite side and opposite angle is also given. This means we can use the law of sines.


18/sin(44deg) = 13/sin(C)?


Yes, that's right!


30.11 deg


is that right


Yes, that's correct! We can round this to 30.1 degrees.


Now, what do you think we can solve for next? Angle A or side a?


a?


Not quite. If we have the measures of two other angles, we can find the third one (A). Do you know how we can do this?


no


That's okay! The Angle Sum theorem states that all angles of a triangle add up 180 degrees. Using this theorem, how can we solve for angle A?


A+B+c= 180deg    Which means  A + 44deg + 30.1deg = 180 deg


That's right! So what would the measure of angle A be?


but that sounds like too big of an angle


105.9 degrees is correct!


ok


Now all that's left is to solve for side a!


How do you want to approach this? There are multiple different ways.


any is fine


Alright! What do you think one of the ways we can do this is?


idk


One way we can solve it is by using the law of sines.


Do you know what the equation would be to set it up?


a / sin(105.9) = 18/sin(44deg)


Right! And what does this get us?


is that correct


Yes, that looks correct!


awesome!!! thank u for ur help today


No problem! I'm going to end the session now, have a nice day!


Hello How are you?


hi I'm good and u?


I am fine ynx. How can I help?


may you please help me with my homework


OK Shall we start with what is on the board?


the question


Yes OK


Can u tell me what "domain" menas for a function?


x values


Yes all possible x values


so what go you think the domain is for this function?


do*


-4 to 4


Yes very good


Now, in ur course, to u use interval notation?


ok


Can u write the domain in interval notation?


OK I see


I was looking at my keybd


That is fine


Now how about the range?


-4 to infinity


I disagree


oh


what is the defintion of range?


y vaules


Yes


now what the the allowed vlaues on this grpah (f0r y)?


idk


OK well what is the smallest y value that is on the red curve?


I disagee


I think 4 is the *largest  y vlaue


now what is the smallest


- infinity


Remember y is the *vertical* axis


Yes 0 is the snmallest


and 4 is the l;rgest So can u write the rnage in interval notation?


good !!!


what Abt the f(0)


OK


I forgot that !  LOL


what vlaue of x do we sue to get f(x))?


lollll


use*


I disagree


we have f(x) as a function


so for f(0)) what is x?


idk


OK well y = f(x) and for f(0)) we replace x with 0


so 0


yes so x = 0


and now what is the y vlaue (from the grpah) when x = 0?


pls look carefully at the grpah


idk sorry


OK well start at x - 0 (at the origina) at then move *up* unitl you hit the red graph I mean straight up along the y-axis


y-axis


I hit 4


Yes good! so f(0))  = 4


ok next one


thank you !


OK]


I will copy to 2nd screen Pls wait


ok


OK what do you think about this one?


I don't even know


OK First I have a comment


I think we need to assume that the blut one continues up the right forever OK?


blue*


yea


and the red one up to the lleft forever OK?


OK So what does that tell us about the possible values of x?


infinity


how about some signs ( -  and + )


If x strtas all the way at the left what will be the sing there?


positive


I think left is negative


oh sorry no


so -inf on the left


how about on the right?


positive is on the right


Good


Now can u write the domain in interval notation?


excellent


how about the range?


4 to infinity


my eyes are bad but I htink -3


pls look again


oh ok sorry Abt that


No problem


pls use interval notation now


BTW are u using a stylus to write on the board?


yes


yes it looks quite nice is it an Apple Pencil?


no its with a Chromebook that the school provided


Oh OK


it works nicely


Now this time I will not forget f(0)


yes it's really good


What do u think about f(0))?


Yes excellent


I added confetti


yess I loveeee


OK can u tell me whay f(0)) is NOT +2 ?


bc its an open circle


Yes very good


I have 3 more


OK If I run out of time I will tell you but let's keep going


ok


OK I will copy pls wait


es


yes


OK


Now I am not sure what they mean by "algebraically" Do you know from your class?


no


like solve it algebraically


maybe they mean not graphically


Yes maybe but there really is not solution


for the first one maybe they mean break it into two cases one wehre x + 3  >= 0 and one where x + 3 < 0


See what I mean?


yea can u do it for me


OK I will type on board


I want to stree taht  an ot sure htis what they want OK?


can u see what I type?


yess


do u understnad why that comes from the abs value?


kind


kinda


you see if x + 3 is pos we do not need the abs vlaue


But if it is neg, we need to change its sign


got it


And this one confuses me. I think the domain is (-inf, inf) since we can plug in any x


sse waht I mean?


sorry I have too go


OK One hint in 24 you cannot take sq root of neg nbr OK?


thank you so much for today


You are welcome u did very well


oh ok thank you


BYE BYE


Maria


Hi Alice. I see the problem on the board do you need help with it?


Yes


ill try to attempt it


ok, if ur stuck or have an answer jus type in the chat


Got it


Is this how it should be labeled?


almost, remember that 95% wil be 2 standard deviations away from the mean both ways


so the 2 and 4 should be two tick marks away from 3


good, so what would the standard deviation be?


yes! good job


Great


Percent?


no, just 0.5


standard deviation doesn't have units


Ohh got it yeah i remember now


Give me a minute im gonna write this out in my homework real quick


ok


Thank you


are you going to try to solve this or do you need help?


I need some help


i dont get what it means by normal


normal distribution is like a bell curve, this ditrb=itbution looks like a normal curve


Oh cuz its like this


yes exactly


Got it


How do i explain that do i just say the histogram displays an approximately jormal distribution because it is bell shaped?


yes, and the standard deviation is equally spaced


and approximately 68% of the datav falls in the first standard deviation


How can i tell that 68 percent falls in the first std!


its just an approximation


just by eyeballing you can tell


Between here and here?


yeah


Alright


Letd move on


alright just put it up


It looks right skewed


For 12


yes good


its not normal because it is not bell curve shaped


and the standard deviation is symmetrical on both sides of the mean


Wait how can i see if the std is symmetrical on both sides?


or how can i identify that based on this histogram?


the mean is approx where i drew the line


do you see how more data is on the left than the right


Yes


so its not symmetrical?


exactly


do u need help on 13 as well?


so for 12 id say something like


The distribution of the percentage of foreign born residents in the 50 states is not approximately normal because it isnt bell shaped and shows a right skew and a cluster of data between 0 and 10 percent foreign born residents


yes thats perfect


Great


How can I figure out if its normal or not for 13?


use the SD to see if the min and max are 3 sds out of the mean


If its 3 sds out of the mean does that mean it isnt bell shaped?


it means it is


iusually the min and max are 3 sds out


So do i gotta add and subtract 8049 3 times by 10614¿?


yes


Ok


I got 34761 for adding


and -13533


so i dont think its bell vurved


So if it’s bell curved it stays within min and max?


But if it exceeds the minimum and max its not a normal distribution


exactly


Got it


Noted


Ill write it out by hand at the bottom of 13 and you tell me if it sounds good


ok


How’s that


perfect


Great


Is the answer e do you think


not quite, a histogram is the best


a stemplot and a dotplot can't give a bell curve


Ill pick stemplot


Cuz in a dotplot at least you see a bit clearer


no, histogram is the best option, al the other choices are hard\


to see the distribution


Yeah but since it said least helpful i had to pick 1


Shall i move on


ohh sorry it would then be a stemplot you're right


Yesh


yes


Youre good


for this one draw the bell curve and label all the marks


Got it


nice, so at what number does the weight go under 9?


or what tick


i would use 9.02


since your looking for the first number thats greater than 9.02


now you now everything between 9.02 and 9.22 os 95%, so what is everything outside 9.02 and 9.22 equal to in percent form?


Is it 5 percrnt?


but thats for both sides, so you must divide by 2 to get just one side


2.5 percent


exactly


so approx 2.5% is below 9


And this is likely to pose a problem for the company because people arent getting the right amount of chips in their bag which will cause their company to lose money?


And therefore they wont be able to produce chips?


well only 2.5%, so I don't think it will be a big problem


Ohhh ok


also no one is going to realize the difference between 9 and 8.97


so the opposite of what i said


got it


but if it was like 75 percent


then that would mean what i said


then yes it would be a problem


Ok


its very subjective so it depends on wha tyou think


Yeah


I have about 5 more and im done


Is that fine?


i can probably stay for 1 or 2, but I have to go after that


Alright thanks


you can always end this session and join a new one with a new instructor


Actually i have to go now


is that ok


thanks for your help


Hello


Hello :)


How are you?


I’m good, are you in need of assistance?


I see your picture, are you in need of help with both problems?


Would you like to start with 1?


yes


Ok :)


So, do you know what domain and range are?


domain is range of x values


range is range of y values


Good :)


Wow, very good. All of that looks absolutely correct


Thank you


Do you happen to have a mic or nah


I am now allowed mic access I do apologize


Not*


oh


np


I believe it is this websites policy


so 2. is a quadratic right


can't you just click the microphone button?


Yes 2 would be quadratic to the look of it :)


I can however it says that it disallows me mic access


So would there be any limiting factors on the domain of this function?


um


yes


wait


Yes?


Where would that be if any?


domain no


range yes


Good :)


is this right?


Very good :) that looks absolutely correct


I see no flaws in any of your work, you seem to be very good at this


thank you


Are you looking for any more help with the subject?


Ok, would you like a practice problem?


Oh I see there is more problems


So in the square root, what would the limiting factor be?


For question 3


ok


Very good :)


Do you know what numbers would be the easiest to plug in?


Though you could plug in anything


That fits the domain


Those are the numbers I would have picked


And now we just look at question number 4


What would the limiting factor be there?


At X-2 can you tell me what type of discontinuity it is?


hole


Close, because it’s in a denominator and it doesn’t cancel out at the top, it would actually be a vertical asymptote


Meaning as it gets closer to -2, it would go infinitely up as it approaches from the left, and then goes towards the negative when it comes from the right


i feel like


my drawing is inaccurate


Because as it grows closer to -2 like -1.999 then it would be 1 over a very small number, growing towards infinity


Yes, because it has a certical asymptote and not a hole, would you like me to demonstrate?


Vertical Asymptote*


Yes good :)


Oh wait a second


No yes you’re right my bad


Very good :)


I believe you have this concept down very well!


Is there anything else you are looking for help with?


yes


Anything specific?


Ah I see


So would there be any restrictions on this problem?


hmm


nah


Good :)


That looks very good to me :)


Would number 4 have any limiting factors?


Sorry, 6


um


i dont think so


Nothing in the denominators, no radicals, etc


is this like lineary


wait is this justl iner


lol


Linear? Yes


Because no quadratics, nothing else etc :)


Very good :) everything seems right once more !


Any more problems ?


yes


Alright :)


You seem to be doing a very good job so far!


cause of ur great teaching


I don’t believe I’ve been helping at all, but thank you :)


It seems you’ve been having it down to a lock, I’ve just been here to be saying good job


Ok, I see what’s happening, you know what a parent function is?


perhaps


Very good :)


Wait a minute


Would it be going to the left ?


no


The 1st question


Good :)


wait how do i say it


that its -2x like longer


Well, the negative and the 2 would be 2 separate ones


If it’s negative it would be a reflection over the X axis


If it’s multiplied by 2, that would be a vertical stretch by 3


Sorry, by 2


Also don’t forget the reflection over the X axis for #3


wdym


I’ll also say that it would just be 6 to the left, because we’re going direction we won’t need to give a sign


Because h(x) = -2 the negative in the front means that it’s a reflection over the X axis as a transformation


um


is everything right?


And everything else looks good :)


W


Do you need any help with these problems? You’ve been doing well so far :)


wait


i dont have to solve all these right


Yes?


how can i tell just be looking


by*


Well they are the same as transformations


so like 7


oh wait


Like 7, what would the transformation be?


i think i get it


so i think its better if i just look at the graphs


so for a


it's


f(x) = (x+1)^2


Yes :)


so 7. is A


Correct :)


Because (X+1) is the same as saying one to the left


So for D, we are looking for 1 to the right and 1 up


Which would that be?


B. is f(x) = -(x-1)^2


I would look again for B


Good :)


C. is f(x) = (x-1)^2 - 1


You were right just write it in the wrong box


D. is f(x) = (x-1)^2 + 1


F is f(x) = (x-1)^2 - 1


wait


then


c is wrong


I would look at C again yes


C is left 1 down 1


If it’s going left what would it have to be ?


ima just restart


That’s alright, I believe you got this


ok so A. f(x) = (x+1)^2


B. f(x) = -(x-1)^2


C. f(x) = (x+1)^2 - 1


Yes doing well so far :)


D. f(x) = (x-1)^2 + 1


Yes :)


E. f(x) = x^2


Good


F. f(x) = (x-1)^2 - 1


Very good :)


G. f(x) = -(x+1)^2


Now you’re doing it really fast


Hokd :)


Good * :)


H.


f(x) = (x+1)^2 + 1


Good :)


I.


f(x) = x^2 + 1


Very good, the last one checks out :)


You did very well once again, definitely hit the hang of it :)


all thanks to ur help


No problem :)


I’m glad you asked for it


Is that all?


no


lol


That’s alright :)


hmm


is 14. correct


Looks good to me :)


Oh wiat


Maybe -3 because it seems it is going by 2


it does?


it looks like its going 1


Oh yes, more like it looks like it’s under -2


You see that 14 is more -3 than -2


Everything else looks very good though :)


wait whats wrong


oh i see


For question 14


There we go


sorry i thought u meant like


the


No problem, everything looks good now :)


wat do u call it


like strecthing


strech


No problem


Any other problems you need?


yes


Wow you get a lot of homewoek


it's like a week worth of hw


That’s no problem as long as you are doing it


i had already done it but like


You seem to be doing well


not really cause the teacher was out so


i kinda did it but


well i did the first couple problems of it


So we are just finding when it’s continuous


ok so would that be like


I believe you can do this


(1, 2


or


continuous is that it keeps goign right


You would be everywhere that isn’t discontinuous


(-infinity, 1]


Single -


So it would be ( - infinity, -1) U, infinity


why -1


Good :) but remember not to include -1


Oh sorry, just 1


ok and why is it not bracket


i thought a closed dot meant breacket


Because it can’t be continuous at -1, because it is a jump discontinuity there


then the closed dot is for intrevals only?


Because those brackets mean it’s included


But -1 can’t be included because it’s discontinuous there


2 is right though :)


3 is close


what is it


oh i see


But there’s also a jump discontinuity at -1


Good :)


I think you should look at 3 again


Just name the X coordinates where the discontinuities are


Okay


*to start


Ok let me stop you there for a sec


You don’t need to stop it at 0


You can just go from (-1, 2)


why


Because it’s continuous throughout all of that


See how there is no break at 0?


I would make it parenthesis at 2


Because it’s discontinued at 2


You can probably put the brackets at the end though


bracket where?


You did -1, 2]


nah


Good :)


wait


is it -3, -1


or -infinity


, -1


Because that’s where it starts :)


But it can be [-3


Cause it is continuous there


i thought u cant have brackets


on continous


You can :) at least I think you can, you just need parenthesis where it is discontinousv


But at the start it should still be continuous


And then I would make it 4] not infinity just because it doesn’t show an arrow


At the end


hmm


Very good :)


so according to that logic


why for 1.


is it not (-infinity , 1]


Because for 1 it’s discontinuous, if we included 1 it would be saying it’s continuous at 1


hhmm


i see


Yes we wanna exclude 1 :)


Same logic for 2


Hey i think im doing hw for tmrw


Ok :)


i think i did the hw i was supposed to


Good :)


cause idk types of discontinuity


If you need any more help I normally do more 2-4 on week days I had a good time helping you :)


Thank you very much!


Thank you :)


hello


i see the problem on the board


Casey


im on 1


alright


do you need help wiht it?


I'm assuming yes


yes


how can i determine what type of trandformation it is?


alright I get what you mean


let me first ask do you know


what vertical and horizantal stretch mean


nope


ok


lets start with that


ok horizantal stretch


means


let me draw a graph realquick


do you see what I have


yeah


is that at the origin


a horizantal stretch would look like the red line let me show you


do you see how


it moves down?


wait let me redraw


it's still at the orgin


but its less steep


does that kind of make sense


for now we don't have to worry about specific points


is there a rule for it


yeah but lets get the basics of what a stretch and shrink do


okaay


alright so a stretch makes it towards the y axis


oops


mean closer to the x axis


if that makes any sense e


it gets like pulled towards the x axis


do you kinda see how


oh cuz its horizontal


howd you know which way it was gonna go


yeah


well think of it like a string


you know when its all like messy


it looks like this


but when you stretch it out


it becomes straight like the x axis


does that kind of make sense


what about the way it tips?


sorry what do you mean by tips like how do i know it doesn't become like this


you moved the top right down why didnt you move bottom left up closer to x axis instead


i moved both closer to the x axis


oh okay


would vertical lead it away then


yes in a way


how


here let me show an example


scroll down a bit Ill draw it tghere


do you see the orginal line(blue)


crossing through at (0,-2)


you here?


sorry checking something


i see it


oh that's alright


so a horizantal stretch would be like this in red


it becomes more like a horizantal line


so now you asked


or vertical right


a vertical stretch would be a bit more different


you are right in thinking it would go away from the y-axis


i mean x axis


but theres one more difference


whereas the cross through point for  a horizontal shift won't change where it crosses through


a vertical stretch would


in green is what it would look like


oh okay so it leans towards y axis


i know i just wrote ea lot


yeah


your getting the picture


is there a fotmula


yes


let me write it for you


g(x)=f(bx)


huh


b = the factor


yeah its a bit weird


ohh


wait


before you do anything that's the formula for the horizantal shifts


x is just the x right no y includedz/


g(x)=b⋅f(x)


yeah x is just the x


do you understand what f(x) means?


and this is vertical stretch?


yeah for vertical stretch or strink


f(x) is the function right


yeah


lets erase this board I'll teach you how to use this formula to solve


and repaste


the problem


alrighty all these variables are confusing Mr. Smith


yeah thats fine I'll teach you to use it


sorry can you repast the problem


it gets delted when I erase the board


alrighty lets first test the horizantal formula


do you see how in the orginal f(x) = 2x-4


yes


can you tell me the equation


of the line


thats been transformed


oh sit


u good


if you can tell me that it gets a lot easier


i meant to say wait not that whoops


i don't really care if you curse


uhhh


i can help if you want


yes pls


alright


so to find an equaiton for a line


we need the slope and the y intercept


so what's the y intercept


that's where


the line crosses the y axis


clsoe


it would be (0,-2)


do you see the pink


oh yeah whoops


oh ok


so we have the y intercept


do you know how to find slope?


rise over run


yup


good job


so the equation of the new line


is y= x-2


alright now lets apply the formula


g(x) btw is the new line


let me simplfy that a bit for you


ok let me tell you what I did


so the orginal formula is g(x) = f(bx)


right


yes for horizontal stretch


we know g(x) = x-2


as g(x) is the new line


so i replaced the left side of the equation with x-2


and f(x) = 2x-4


but because b is inside the f(bx)


it only affects the x


so it becomes bx-4


does that sorta make sense


uhh kinda


are you confused on the right side of the equation and how i did that?


yea


yeah i kinda understand


uhh for now just bare with me on the horizantal stretch


lets try A it says it stretchs by a factor


of 2


which means b is 2


let me rewrite it for you i sorta messed up


scroll down


can you see it?


yep


so for a


we see the scale factor of 2


plug in 2 to b


and tell me what the right side of the equaiton looks like


-4 is right btw


did you see what I did there


yes i just got confused


since it tells us for a b = 2


oh that's alright


so what that look like


if you simplfy only the right side


yup


and that doesn't match the x-2


right


yeah so the goal is to match the right side to the left side


so the left side should end up as x-2


oh wait were trying to gt it to equal oh okay


yeah


now lets try b


we are told the factor is 1/2


tell me what the right side equation would look like


now simplfy the right side a bit more


this one is wrong


so it has nothing to do with a horizantal stretch or shrinl


so lets look at the vertical stuff


the formula is g(x) = bf(x)


do you get how i came up with that equation


scale factor times function


yup


so lets try c


scale factor of 2


tell me the final equation


on the right side


yup and it doesn't match right


nope


we pretty much know it's d now


so the answer is d


okay alright


yeah


do you need help on 2?


isnt it 10 < x <15


yeah don't forget the -


on the 10


but yeah


okay yay


anything else?


i thinkkkk i got it


alright then Ill cya then


goodnight!


u too


I need help from#2 and down


Is there an accompanying graph or something for this problem?


no


thats just all thats on the paper


Ok I see


Do you need help starting or with one of the steps?


everything


I want to do all the problems as after doing these I can do the homework


Ok


I’m sorry I accidentally erased some of the picture can you insert it again


yeah no problem at all!!!


Ok for number 2 I think we should start by drawing a graph for 1/x


ok ok


From 1-5


can we do it on the board since I am aslo writing this on my paper


Yea sure do you need help with graphing or can I just snip it from online


Cause this question isn’t really about graphing but it’s helpful


uh if we could do both that would be wonderful


Do you know the shape of 1/x we don’t need exact values for this question


no i dont


Ok well just by plugging in values from 1 to 5 we can graph it


So it will look like this


what is that


Something like that


Yea that’s good


Now from 1-5 we can create our 4 sub intervals


Can you draw them as a right reimann sum


like that?


Sorry give me a second I don’t see anything


I can’t see whatever you added to the board right now


But I will add the intervals and you can check with what you did


Can you see what I did?


what is that ovedr the 1/2 on the y axis


We don’t need to worry about the y values on the graphs because in our equation we will just plug in the values


Can you write the equation for the reimann sum now?


how is that done


Do you me to do the equation as an example?


huh


Do you know how to write a reimann sum?


is it the sum sign


Yes basically


like sigma


Yes lemme show you


Oh wait you already did can you finish the equation?


is it that


Not exactly


oh


should I write that on my paper


Yes but instead of f(x) substitute that for 1/x


ok ok


did it


Ok now we write the equation for each interval


Ok the equation for a reimann sum interval is the height times width


oh...


And we already know the width of each rectangle is 1


how do we know


we never talked about this


The way we figure out the width is by taking the total interval and dividing it by the number of sub intervals


So in this case it would be (5-1)/4


ok but how do i do that this is my first time in this class i dont know anything


Did you teacher not teach you how to solve a reimann sum?


no he got sick and llefy\


Liam I don’t have the time to teach you everything unfortunately


its okayyy


It the basic equation for the interval of a reimann sum is (b-a)/n


oh


So in this case the problem tells us the start and end of the interval is 1 and 5


Hi, sorry you got cut off.


What would you like to work on?


OK, I see you're supposed to put these into categories. The first one is the checking account.


1,450 ?


Yes


ok


What about savings, etc.


ohh i added 170+45


It looks like she has a savings account 0f 3500


OK, that part is probably what she puts into her savings each month, not sure.


"Savings allocation"


So I would put savings allocation into the second line.


Does she have life insurance?


i only see car insurance


Car insurance would go under expenses.


Looks like my last message got lost.


We have to look at the 4 different sections:
Assets
Liabilities
Income
Expenses.


Right now we're only dealing with assets, money & stuff she already has.


Does that make sense?


yeah


i dont see life ins.


Right, she doesn't have any so we leave it blank


So the worksheet should show the total liquid assets, 1450 + 3500 = 4950


yes


LIQUID assets are those that it very easy and fast to convert to cash.


Now her household assets are things that have value but can't be immediately converted


She doesn't have a home, apparently, but does have a car, computer and ipad, so put those in


For what?


Oh, the total, yes


it says its incorrect


What line did you put it on?


an error on my part i enter a 4500 instead 4950


OK, and I wrote it wrong too. So we're finished with assets.


I did the rest


besides the credit card and charge acct


Looks like the connection is spotty.


So you filled in the other pages?


What course is this for?


personal finance


i started this one


i cant fill in the blank ones


No, some categories will be blank.


But the total expenses should add up to the total in the list.


oh okay


and idk what to put for the saving amounts


What would you say for "Regular savings" - would you put it under Financial goal savings or Other savings? Probably either would be OK


other


OK


Any more questions?


yes im still stuck on it


On what?


other savings


Can't you just take the $175 regular savings and put it there?


no


it says incorrect


Then put it into financial goal savings


i did


Does it show you what part is incorrect or could it be anything on this page?


its the other savings part


its 20 for emergency


175 for finanical


Maybe they want you to use up the whole "surplus" amount.


Because if she has a surplus balance every month, it has to go somewhere.


nope


So you tried putting 750 - 195 = 555?


its ok its fine


i just need help wth thoses to wrong answers


i got the first one right


i just need help with emergency fund


actual i got that right


Why did you change it?


OK, you got it all right now?


idk i over looked it


yes


last question is this one


OK, let me know what you have trouble answering


is the current $15000?


But I think you might need to multiply by 4 for the years.


It's not clear from the calculator.


61,200.00 would be the inflation cost?


Well, without inflation it would be 4 x 15K = 60,000, so I think it has to be more after inflation for 18 years


so it would be 60,000 x 18


im confused


Not at all. The current cost would be 60,000 so put that into the top line. Then it should show you the projected future cost.


i did


What does it show ?


nothing for projected future cost.


So you're supposed to calculate it yourself, you can enter a number there?


Have you learned about compound interest?


no


I don't know how they expect you do to this if you haven't learned that, though.


Each year inflation is 2% which means the cost goes up by 2%. So in 18 years the cost will have gone up by 1.02^18


1.02 multiplied by itself 18 times.


So on the calculator you can type 1.02^18 x 60000


You may have used 1.2 instead of 1.02


what do you get for 1.02^18?


Are you using the power key like xʸ It is not multiplication.


That's right. That's how much the cost will grow from $1 in 18 years, what's $1 now will cost $1.43.


Multiply that by 60,000


That's actually a simplification because the cost over 4 years will be a bit more each year. But hopefully they'll take that.


I get 85,695 but maybe you rounded before finishing.


yeah


The rest involves financial formulas I don't know. I'd use an online calculator, because you have to figure out how much to save every year, at an interest rate of 10%, to yield 85,695 at the end of 18 years.


It should be in the material you covered.


this class is not teach by a teacher


I guess we need a business and finance section since it's not really part of algebra.


yesss


that would be great


If you're self learning, then you have to be able to find the material yourself, which can be harder. But surely it's in the course you're taking.


You can also ask any AI agent not for the answer but to explain how to work it out.


We even have one here, the little green space man


You can see that ours is rather limited.


Thats good to know


BUt is would be a snap in Gemini for example.


oh ok


OK, I've got to go as it's 8:00 but good luck.


thank you


hi Lily


Hello


how can I help you


Um


do you think you can explain to me what is like an irrational number. It's like rationals and irrational.


sure


Lily got you


OK.


So


rational numbers, it's just numbers that can be written as a fraction. I'm just going to rate it for you.


OK


We could do


this


or we could do 7/1.


Rational numbers can also be decimals


and


both


OK. Can they be like any decimals or does it matter?


decimals it matters actually.


so


for example, irrational numbers. I'm getting into that.


like pie, it's a never ending decimal and it will make you vomit.


Hm


So I just remember it like the.


and the square root of 2, it keeps on going.


You can see the value of um pie and square root of 2.


and you will get me.


OK


The decimals which are terminating.


they are um


rational because they have an end like 0.25 or 0.3 or 0.75 because they can be written as a fraction, 25/100, 3/10, 75/100. And then you can simplify it more.


Oh, OK. So do, um, like


So, would you like to give me some questions which we could go over or you're good, Lily?


Oh yeah, one question, so like square roots like I'm just writing one for example, like, could that, is that or irrational or rational?


OK, you need to figure out the value of it. Put it in your calculator.


and then just write whatever you figure out.


So then it would be a rational because it's like not one that.


Did you round it? Like how many digits were after it.


Oh


it's like


a lot of digits.


OK, just put like I don't know, I'm just gonna put it in my calculator, wait a second.


Hi


Hi!


ok


let's start with statement A.


what do you think?


i want to say its true but it should go to 7


you are right


but the statement is also true because it says between 3 and 6 what happens to the function


as long as this is true, then the statement is true


okay


it doesn't say anything about 7


but doesn't the line reach to 7?, so maybe an error in the writing


no


as long as what it says is true, then it is true


statement B is true


so how about statement C?


good


its true too


because it faces up


yes


again we only care about what happens between 3 and 6


mhm


how about statement D?


thats false because even though it decrease its not facing down.


exactly


it is still concave up


any other question?


yes two more ill post it, but im getting a hang of it


great


let me clear the board.


wow this one is interesting


lol ik


how about statement E?


how do you find p(x)<0?


these two pieces. right?


because they are below the x-axis


rightt


so what do you think?


ummm i think true


you are right!


ok great


let's move on to statement F?


wait it increases


and then decrease


x > 0 means to the right of the y-axis


oh lemme jot that down


gimme a sec


ok


okay so statement G is true bc it is decreasing


yes!


now statement H?


clearly false but lemme develop my reason


so thats false bc its decreasing and concave down?


x<0 is which region?


below the x axis?


that's for p(x)


x<0 is to the left of y-axis


ohh


so what do you think about statement I?


so its decreasing and concave down on the left side of the y axis?


it is increasing right?


oh yes


good


wait so how is it false


now the part on concave down


would it be concave up/


piece of it is concave up


so statement J is wrong.


okay it is wrong because piece of the graph is concave up and not fully down


exactly


alr js one more thank you


sure


what do you think of statement K?


hmm seems false because its concave up and then down


like a 6 7 haha


yes!


you got it


how about statement L?


its got it


yes


how about statement M?


statement N is true bc you go from -2 to a positive 6


well done!!!


perfecttt! thank you sooo muchh!


it makes so much sense


you are very welcome.


have a great day!:)))


you to


Hello! How are you?


am well thank you, how are you


I'm doing great! What can I help you with today?


today I need help with some math questions I will be pasting them on the board ok


here is the first question that I need help with


Alright, so let's start with a process of elimination. Are there any answers that you feel that you can eliminate right off the bat?


option 1


And out of curiosity, why do you think option 1 is incorrect?


I think because at the top is says ABD and DBC are complementary and option one says supplementary


The question asks about proving that ABF is 180 degrees*. So it's certainly possible for ABD and DBC to be complementary (which means they add up to 90*)


And it's possible for ABD and ABF to also be supplementary (which means they add up to 180 degrees)


Does that make sense, or is that a bit confusing?


it makes sense


In that case, I realize that I may have accidently hinted at the answer to you


is it option 2


or option 1


If you had to pick a correct answer out of those two, which one would you pick?


I think option 2


Not exactly. The trick here is that option 2 is technically a true statement, but it can't be used to justify why ABF is 180 degrees*


So the correct answer ends up being option 1


oh ok


Does my picture help clear things up a bit? Since we know that there's a straight line, it means that the angles on top of that line add up to 180 degrees


yes


Since ABD and ABF are both on the line, they have to add up to 180 degrees


Ah alright, I'm glad that it helped. This question is certainly a bit oddly worded!


yup, thank you next question


Alright, so this question is certainly less wordy than the last question! Just for clarification, does your question want you to fill in all three of the boxes, or just the box labeled #2?


it just wants to justify statement 4


Ah, alright. Do you have any ideas on where to start?


but I think its the transitive property


no but I think its the transitive property


Yep, that seems right to me!


Well done!


thank you next question


here is the question


I think that's its the last option


So let's start with a bit of clarification. What does the two lines on point S mean?


a vertex


Sorry, yes, it is the last option!


ok thank you next question


To be quite honest with you, I don't understand this question at all! I'm sorry!


no worries, next question


Same situation, in all my years of doing math, I've never had questions that ask about the technique of using a compass, so I'm not sure if I can can help on this question either. I'm sorry!


no worries it's okay thank you so much for helping me with the other questions.


bye have a nice day


Bye! Have a great day!


Hi Sarah


hi


what can I help you with today?


welp I need help


ok


does my graph make sense?


yes


do you want to give a try on the domain of V?


using my graph


basically what values can x take


that's the part I'm struggling with like how to get there, and what steps to use


no problem


do you think x can be greater 21?


no?


no


why no?


bc the numbers we have are a lot less then that


exactly


you see 2x must be less than 21


there is no way we can get a x such that 2x >=21


because 2x is just a part of 21


ok ok so is that the reasonable domain?


it makes sense right?


as long as 2x<21, we can do the cutting


because the other dimension is wider


okkkkk that makes sense


can you solve this inequality?


being honest, probably not


how about this: can you solve the equation 2x = 21?


is it 11?... or


how did you get it? you are very close


I divided both sides by 2


well don. Sorry the inequality is the same


we want to isolate x on one side


to do that we divide both sides by 2


so I got it right?


yes


I'm cooking


yes you are


divide both sides by 2, we will get x< 10.5


thank u Mr. Mr. Davis for tutoring me I'll be sure to give you 5 stars


can x be negative?


thank you


no I don't think


so the domain will be (0, 10.5)


does that make sense?


yes bc none our numbers are negative right?


Hi


Hello, Alex! What can I help you with?


I need help with a percentage problem


Of course!


Could you paste the problem on the white board or put it in the chat?


I need to find the discounted price without subtracting the discounted price with the original


Okay! If you could send through the exact question that would be very helpful. We can work through it together!


Alright, just give me one second to work through the problem!


Ok


Okay, just to be clear, you need to explain the process of solving this problem?


Alex, are you there?


Yes


Yes I need to explain the process of solving this


Without using subtraction


Alright, perfect!


So, you're first sentence looks good. We need to confirm that $12 is 100% of the price.


Now, instead of using subtraction to solve this, here's what we can do: First, tell me, what 100% - 15%?


Perfect!


Therefore, we know that taking 15% away from $12 is the SAME as finding 85% of $12.


Does this make sense?


So, we just need to find 85% of 12. Do you know how to do that?


Multiply 0.85 with 12


Yup! Tell me what you get!


I got 10.20


That's the correct answer! $10.20!


Are you able to explain the process we just did, or do you need some help?


First, subtract 15% from 100%, which is 85%, then, I find 85% % by multiplying 0.85 with 12. That would lead to 10.20, which is the answer


Beautiful explanation!


You're all done!


Do you need anymore help before I end the session?


Nah, i think i might be good


Great! You did an amazing job!


Bye!


Afternoon


hi


i am very confused with this


I see the problem


DW it's simple


ok


You know how to expand (a+b)^2


no


i am not sure


Okay it's simple


We use foil to expand the expression


That means First, Outside, Inside, Last


Wanna try?


its says a+b


so how would i expand this expression


ohh


Now you wanna try? :)


This will be useful for solving the problem


then b b?


Yes, but not yet


What is a*b?


ohh ok


Wanna solve it now?


Oh, and here's a hint


I'll give you some time to solve it, okay?


ok


your asking how to simplify it?


We want to find out what (5+i)^2 is, and given that (a+b)^2 and i^2=-1


I'll give until 4:30 to figure it out


And if you still need help, I'll walk you through it


ok?


is that what you mean


Close but not quite


I made changes


Now solve (5+i)^2


Let's go over this


Given that (a+b)^2 and i^2=-1, here's how we solve it


You got taht?


Hello?


hi yes


i think this is


I solved it for you


so you multiplied 2x5


For 2ab, yes


Hi Alex


Hi there.  Am I able to set up a session like on Sunday to review my study guide etc?


I am new to this


What time is it in your time zone now?


Almost 8


OK. Maybe can you show me the first page of your study guide to give me an idea?


Oh I wanted to set up a session for Sunday not yodau


Not today


Yes, I understand. When would be a good time for you on Sunday?


Like 11 am?


I get my study guide on friday


Give me a sec to check my schedule.


Thank you so much


Noon or 1 pm would be better. Would that work for you?


Yes thank you so much!!! Noon is great


Will you send me a link ? Do I just log in?


Just log in to Ben. I'll be online at noon on Sunday.


Ben you so much!


You're welcome. We can end the session for now. Have a good evening.


Hi again. I think there was a tech issue. 🥲


Yes, I think so


Ok, I need help completing #21.


sure!


I’m not sure if the work I did so far is right. And I need help graphing it on a number line.


ok! let me check


Thank you!


The work looks right


good job!


ok so to graph, you first draw the number line and then draw a circle over the two numbers you got


Do you understand so far?


No rush, but are you still there?


yep!


Hello Chloe, how can I help you today?


hello


my stuff on the boatr i need to find the quotient


if you're dividing 6 by 2/3, you need to flip the 2/3 to make it 3/2 and then multiply


ok


what do u do now with that


if you flip the fraction it becomes multiplication instead of division


and remember that everyone whole number (like 6) can be represented as itself divided by 1


can you show me i need a visual


ohhhh


do you know what to do from here?


i got 9/1


yes nice job


but remember any number divided by one is itself


so that's really just 9


oh ok


do you have any other questions you want to work on


i can do next one on my own


ima stillm be here just in case confused


ok let me know if you need my help


next i have 3 9/10 and 2 6/7


i frgot how to do this


it says divided it but dont we do multiply


can you draw it on the screen for me


my drawing not working i dknt know why


is it like what I drew


yes


ok so for these you have to turn it into an improper fraction first where the numerator is bigger than the denominator


do you know how to do that?


ok


no


you want to multiply the denominator of the fraction by the whole part so on the left you do 3 x 10 and then you add the numerator


ohhhhhhhhhhhhh


then we do it for the other


can you try with the fraction on the right?


yes good job


so now you have this


what's the next step?


multiply right


what do you have to do before that?


umm flip it


um


what do you get now


good job


ok what next


that's the answer


Follow these steps when dividing mixed numbers.
1)  Write the mixed numbers as improper fractions.
2)  Multiply by the reciprocal of the second fraction.
3)  Multiply numerators and multiply denominators.


says incorrect


ok, let's try to find where we made the mistake


maybe it wants a mixed number as the answer?


try 1 and 73/200


how you get that


because 273/200 200/200 + 73/200


but a number divided by itself is 1


so it's 1 + 73/200 which is 1 and 73/200


one sec


i gave the wrong numbers oops hold on


now it saying


You've done a great job for the past 50 minutes, unfortunately I have to go but it's been a pleasure working with you. I hope you can finish your homeowkr!


Hi


How are you doing?


Hello im okay


Checking an answer for algebra


Hi! Marcus, how can I help you today?


Of course, I am here to help


Did you put the question on the board?


I tried not sure how to send


No problem, can you put it in the text box?


X-c/2 =d


What is the question asking?


To find a variable?


Solve for x


Ok, let's start!


So first, tell me what you think we should do forst


first*


I times 2/1 by x-c/2 and also by d


ok let's walk through together


step 1


Multiply both sides by 2


so you get 2(x-c/2)=2*d


make sense?


let me know if you have questions before moving on


step 2-Distribute on the left


Then my two 2s cancel out and I am left with x-c=2d


Yes, exactly


Multiply both sides by 2/1 (which is just 2)


The 2’s cancel on the left


Any questions?


Then I added c to both sides and came up with x=c+2d


Awesome, exactly


Any others?


HI! I am glad I was able to help. Let me know if you have any other questions and we can set a time to meet. Have a nice day


Hi


hi


I have a math assignment that I haven’t finished yet and I need help to get the answer to the first section to finish the rest of the Assignment


Alright


Can you check my answers?


Yeah for sure


Can you see the picture i uploaded


I dont see it


Ok now


On the number line i marked a star for the answer but i dont think thats right


Well what steps did you take to get the solution?


Which one


The number line


Oh i just guessed


Oh ok so you want me to show you how to do it?


Yes please


Can you see that?


Yeah


Thats how you do it


Ok


are My answers on the other questions correct


Yeah they all seem right


My teacher checked the first one and she said it was correct so I kind of just Copied the steps for all of the


Rest


Yeah it looks good


So do I mark -2 on the number line


Anything else you need help with?


One of the questions says solve the equation so Do I mark Jay as -2 and solve with the equation that you showed me?


J*


Yeah, if it says solve the equation then take the steps I did


They just want you to isolate J


I don’t know if that’s the way my teacher wants me to set it up though


Oh nvm


I mean solving the equation is exactly what I showed you


So if I didn’t know the J when I’m solving it, it would’ve just been one


What do you mean?


Because I don’t know what the variable Number is I just use the number one to get my answer?


No, you just do the exact steps I did


Ok


Using the equation, you isolate the variable on one side and that's your answer


Ok thank you thats it


Okay no problem :)


hi could you ckeck my answer for this problem?


i got 17/2


I see lots of correct work here. Let me ask a few questions. Have you been taught how to use horizontal slices (horizontal rectangles)?


yea in terms of x


i just did this with y because there's no sqrt


so no +-


is it correct?


Oops my previous message didn't send. I said "Hi Jamie! I'd be glad to help."


I would recommend horizontal slices to avoid the square root. But


But both ways should work! Let me continue looking at it.


ok


Ok! Lots of very good work here!


Let me ask what you meant by the green and yellow areas.


green shaded and yellow shaded regions


in the graph


is my final answer correct?


Oh I see now. I didn’t see the yellow part. Let me look over that.


Alright. I get the same result! It is correct! Good job!


It looks like you started to do vertical rectangles but switched to horizontal ones. Both would probably work, but horizontal is easier here. Good job on that!


Is this a homework assignment?


yay thanks


it is


Great! Would you like to go on to the next problem or ask for help when you need it?


this is all i have actually :))


thanks so much for checking for me


Oh OK! Great working with you!


Hi! I need help with the formula to solvin this


Hey! How are you doing todya?


*today


I'm good, yourself?


very well


Can you elaborate the question? you need help with what part?


like this whole thing, can you see it on the whiteboard?


yes i can


okay, so let's start with 'a'


can you tell me what will come here?


k


idk bc idk the formula idk what to do


okay no worries, let me help you here


it says a purchase increases the unpaid balance and a payment decreases it


look at line 1 and line 2