Exactly so now you do you want me to show you how to write the answer


sure


So now what does -5x1x and 3x x


Does that make sense


no


Step 1:
Multiply the first number and the last number:
3 × –5 = –15
Step 2:
Find two numbers that multiply to –15 and add to –2 (the middle number).
That’s –5 and +3


yes i  got that


Ok then you just want to fit the numbers in a spot


so you said -5+3=-2


So if I multiply -5x1 and 3x x I would end up with -5x+3x= -2x which was originally our b value


does that make more sense


yea


ok so now you should try #2


Then I’ll correct you if needed


im confused


i dont see what number to use


What do you mean for number 2


yes


The equation you have to factor out is 3n^2 -8n +4


no number 2


Oh just do number 3 for now tyen


Then*


i dont know


Ok where are you getting stuck so I know ere to start explaining from


i cant see where it multiples to four and adds to -8


Ok so if you add 6-+-2 what you get


exactly so why is 6/3


What*


Exactly o how do you think you can put 2 in the equation twice


Like what is your best guess


by multiplying i have no idea


Ok if you know (3x-?)(x-?) then what do you think you can sub if for the blanks to get the original equation


Like what value did you find earlier


im sorry i genuinely have no idea whats happening right now 😭 its not your fault i just dont understand algebra


maybe i can try with easier questions


No don’t worry I understand this is not a very easy topic to explain when not in person


Have you ever learned the area model


yeah


Cause many students understand using that method more than the one I’ve been explaining


but it was awhile ago so i might need to relearn


Ok do you know how the area model works


That’s completely fine but show em what you know so far


I can give you an easier question if you want


Exactly so what eqaution do you think that factored


4x^2 + 10x +6


Exactly so do you think you could use that method to solve the earlier question we had


ill try 😓


Don’t worry if you get stuck I’ll help


Ok so for the squares with 4x are not correct try doing multiplication and find the right number


But you were very close


Do you need help


yes


Ok so first list out what pairs can multiply to 12


Ok so which pair do you think we can automatically rule out


1 and 12


Yes now theres one more pair so what do you think


3 and 4


yes so now try plugging 6 and 2 in the open boxes and then tell me if when you multiply it out do you get the same equation


i have to go


thanks for the help


Of course have a good day


Hi again Mia


oh heyyy


so I need help with preparing for my test soon


OK, do you have some sample problems?


umm sorta we are learning about shapes and stuff let me draw a refrance


that's one of the questions


OK. Does it say that the triangles are similar? What is it asking?


You can upload it if you want


its asking whats similar and we could round to the nearest 10 if we need to


Can you upload it?


I think some information is missing


yeah one sec


I gotta go can we talk later


OK


Bye


byeeeeee


Hello!


Hi Ben!


How can I help you?


So I want to rework on the problems that I did in class with my teacher because I am still confused on them and I am very terrible with some of these problems. I am kinda familiar with the concept but not really. Can you go over the same problems like in order from the pdf that I did in class. I am currently on page 2 problem 9! Can you help me with reworking the same problem and then create one from scratch just like it but with different numbers & vairables. I want to do it in order from the second page. Here's the pdf link to access it: https://mathdocs.org/algebra_problems.pdf


I am on the pdf!


Ok!


You did problem 9 correctly. Would you like me to give you another problem with grouping?


I did it in class with the teacher thats why its correct I want to redo the problem and then have a problem just like that one w diff numbers


ok


Let's go through this problem again.


x+2 is the gcf


This problem is a special case because we actually want to group the first three terms together and then leave the last one by itself because that one is already an easy perfect square


oh nvm i didnt have the prompt so i forgot


Yes, and we do this specifically to get two perfect squares


Nice! So the first group simplifies to (x-2)^2


And what does the second group simplify to?


umm uhh


the middle number is a -4 not pos


Yes, but that still works because we are using -2, and -2-2 = -4 like you mentioned before


oh right


Sarah!!


How can I help you todayy


We are learning about probability and I am doing my homework assignment


okayyy do you need help on specific questions or like a concept you need??


Yes do you want me to tell you the question on my homework?


suree we can learn from there


Wait I think I got it


Sorry


Thanks for helping


no problemm if you got more questions just make another requestt


have a good dayy!! byee


Ok thank you


Afternoon


Hello, how are you doing today?


I feel like I'm about to crash out tbh. But for your sake, I won't get into details.


Well I hope things get better


I doubt it, but I appreciate the sentiment


You want to solve this?


Sure, I'll try


I already the work for you. Just set each part of this equal to 0.


Okay, but the part that I was confused about was setting up this step


care to solve now?


Congrats. You found the roots of the equation.


I was saying that I know how to find the roots from that second step. I'm not sure how to factor the equation to that second step though.


Oh


Well, we need two numbers that have a sum of -5 and a product of 6


and since there's a negative, we also need to consider the possibility of negative numbers


Okay


Want to try it?


Sure


I'm not sure if that would be right


no


try again


dingding


Youre on the right track


Okay, great!


Now continue


Sorry that took so long. I think I understand now.


There


How did you get the second expression? Did you factor out a 2?


yes


Okay, got it.


Thank you for your help.


Any more?


No, that will be all.


Okay


Before we go, I want to ask you something


Have you ever had your heart set on a big event, only to find out that due to circumstances beyond your control, you might not get to participate in it?


I'm sure that I definitely have experienced that before. It can be very disappointing, but if you think about the fact that you could have many opportunities in the future, that can make it less disappointing.


Nah, this is a once in a lifetime event.


I'm talking about one of the biggest movies of the year, one that I'm pretty sure you're too young to see, and it won't hit streaming until 2027.


Oh okay, unfortunately, that is a part of like sometimes. Try not to focus too much on it (even though it will not be easy). Try and do other things to take your mind off of it.


I'll try. But my birthday was two days ago, and I really wanted to see that movie.


That makes sense, but like you said, some things are beyond our control. Even though you really wanted to see that movie, you can't, and you can't really do anything about that. So instead of focusing on that, maybe try and find another movie?


Movies suck these days


And this is something I suffered the entire year thus far for.


Well, that happens sometimes, it will get better even if it seems like it is the end of the world right now. 👍


If movies aren't good, try to find another hobby. There are many things you could do.


I'll see what I can do. I'll let you go now.


Okay, I hope you find something :). Have a great day, bye!


Hey Alex!


Hi!!!


What topic for 8th grade math do we want to work on today?


And also is it for homework, studying, or just questions


Ratios. My teacher says there is a quiz coming up but we didn't really go over it. I don't understand it at all.


Sure! I can definetely help you


I'm going to go ahead and pull up some practice problems for you and we can work through it together


Thank you!


Just to clarify, are we talking about simplifying and converting ratios or finding ratios from word problems


Unit ratios


Is it fine with you if I turn my mic on


Yes please!


Hey there, Alex, can you let me know if you can hear me, please?


Just checking in with you. I wanna make sure you hear, uh, you can hear me, so that way I can explain the problems to you. If you can't hear me, can you please let me know?


Hey Alex, since I haven’t heard back, I’m going to wrap up for now. If you still need help with ratios or anything else, I think this chat will still be open even after I close it. Have a great day!


1. Part-to-Part Ratio
This compares two parts of a whole.

Example:
A fruit bowl has 12 apples and 8 oranges. Ratio of apples to oranges =
12:8

Simplify by dividing both numbers by their GCF (greatest common factor), which is 4:

12÷4=3,8÷4=2
✅ Simplified ratio: 3:2

2. Part-to-Whole Ratio
This compares one part to the total.

Example:
Same fruit bowl: 12 apples + 8 oranges = 20 fruits Ratio of apples to total fruit = 12:20

Simplify:

12÷4=3,20÷4=5
✅ Simplified ratio: 3:5

 3. Part-to-Part-to-Whole Ratio
This compares each part to the whole, showing all relationships.

Example:
12 apples, 8 oranges → total = 20 fruits Ratio of apples to oranges to total =
12:8:20

Simplify all three by dividing by 4:

12÷4=3,8÷4=2,20÷4=5
✅ Simplified ratio: 3:2:5


Hey Alex! This is your tutor. I haven't heard back from you so I'm going to close the session. Here are some helpful tips for ratoios:


1. Part-to-Part Ratio
This compares two parts of a whole.

Example:
A fruit bowl has 12 apples and 8 oranges. Ratio of apples to oranges =
12:8

Simplify by dividing both numbers by their GCF (greatest common factor), which is 4:

12÷4=3,8÷4=2
✅ Simplified ratio: 3:2

2. Part-to-Whole Ratio
This compares one part to the total.

Example:
Same fruit bowl: 12 apples + 8 oranges = 20 fruits Ratio of apples to total fruit = 12:20

Simplify:

12÷4=3,20÷4=5
✅ Simplified ratio: 3:5

3. Part-to-Part-to-Whole Ratio
This compares each part to the whole, showing all relationships.

Example:
12 apples, 8 oranges → total = 20 fruits Ratio of apples to oranges to total =
12:8:20

Simplify all three by dividing by 4:

12÷4=3,8÷4=2,20÷4=5
✅ Simplified ratio: 3:2:5


Here are some helpful tips


Hi Alice


Welcome to Tutor Provider. How may I help you?


I need to find the derivative of x/sqrtx^2+1


OK. I'll write it on the board. Did you learn the "quotient rule" ?


Yes


Is that the function you want to differentiate?


I'll write the quotient rule on the board. Then we'll apply it to your problem.


OK so far?


The derivative of u is du/dx or u' = 1. What is the derivative of v = v' = ?


That’s what I have do far


So far


I'm checking your answer...


I’m not done yet I dont know what to do after that


Your calculation is correct so far. All you need to do is simplify a bit more.


Idk how


I'll show you the next step.


On the numerator, we want to add two fractions. We look for the common denominator.


Can you continue?


I don’t understand that


Can you circle the part you don't understand on the board? Then I'll add more details to explain.


OK.


If you look at the line above, the square root and the square (^2) cancel out, correct? See the pink color.


Yes


Oh oh I get it


Awesome!


You multiplied by the reciprocal


Got it


Correct.


I'll continue lower on the board.


I get it now


I didn’t know I need to do all that fraction stuff


There's a lot of algebra in calculus!


Yes well thank you so much


You're welcome. We can end the session. Have a great day!


You too


Hello, what can I help you with?


I'm new to Tutor Provider, and I just want to learn something


Amazing! What would you like to learn?


anything really I just want to learn to help me in school


Sounds good! In 9th grade, a concept that really helped me was learning about slope, and about lines. Have you started learning about that?


yeah we have and I dont full understand it


Okay then I will help you understand it!


Do you know what a graph is, like where the x and y axis are?


Actually I have to go I'm sorry but thaink you for your time and for trying to help me.


Okay!


Bye


bye


hi


can u help


Hi Alex. How can I help you?


my ixl is hard


Go ahead. What's the problem


there


Let me take a look


OK. So here it is talking about the cupcakes and the profit. So if she makes 47 cupcakes, she makes $15 profit, right?


ye


Right. So, what is the, uh, so they are asking us according to the values on the table, do X and Y have proportional relationship, proportional means that their ratio is the same.


ik


So the ratio in the first record is 47 by 15.


right?


yes


So the ratio in the second record is 49 by 23.


yeah


So what we have to see is, is 49 by 23, same as 47 by 15.


/uhhh


/ok


Yeah, you can use your calculator also, but this ratio is not the same.


ok


So 47 by


47/15 != 49/23


15 is not equal to 49 by 23, and same way you can look at the ratio.


for the other records, which is not the same as 54 by 43, and it is not


equal to 60 by 67.


So, but they're saying is our x and y proportion they do they have proportional relationships. They are asking, is the ratio between x and y the same? Does that make sense?


I know


I just couldn't find out if they were the same


Yeah, so, uh, see this, uh, these numbers are not too straightforward. So you can use your calculator. So if you say 47 divide by 15 on a calculator. What do you get?


Right. So now let's do 49 divide by 23.


right? So 3.13 is not the same as 2.13, right?


yea


So they are not proportional.


Anything else, Alex


uhh


yeah one more


Go ahead


Hello. Hey, I think you give me 10 minutes, I'll call you back.


ok


OK, OK


oops


I broke it


OK. Sorry about that. I got another call.


OK, yeah. So we were talking about that uh problem, right? So now the second problem is similar to the first one.


You are there, right, Alex


Alex, are you there


yes


OK. Yeah, so this is similar to the previous problem. Here the table shows the relationship between the number of school days, the driver has been driving the bus, and the total number of miles the bus has been driven, right?


Alex


yummy cupcake


So now the first row says in one day,


a he wrote 33 miles.


So the ratio is 1 by 33, right?


Right. So the next uh record shows in 2 days, uh, he, uh, drove 46 miles, so 2 by 46, can you simplify 2 by 46?


yeah


Try dividing both numerator and denominator by 2.


my wifi is bad rn cuz hotspot


No problem


Let me know if you want me to repeat it.


ok


Right. So can you simplify 2 by 46?


Go ahead


What does it simplify to?


Right. So 1 by 23.


2/46 = 1/23


yea


So 1 by 23 is not the same as 1 by 33.


yes


I agre


Do you agree? In the first record, the ratio was 1 by 33 in the second one, the ratio is 1 by 23.


So again, the answer is no. The X and Y are not proportional in this case either.


oh Alex


OK.


well


that's all


We can continue with the next ones also, but just the first two don't match. This means we, the answer is no.


OK, that's it. Perfect.


All the best for tomorrow.


ITS CHRISTMAS


bye


Bye.


hiii


what can i help you today


I need help setting up and equation form points in a graph


okok do you have any question from school like hw or classwork


so i can explain to you


My question is write the equation of the line that passes through (-6,3) and (2,-1).


Okay so we have two points now


we can find slope


do you know the formula for slope


y=mx+b


thats equation


slope


is m


in equation


i showed the formula on the board


can you try to put two points in formula and find the slope


the number in parentheses means one point


yess


so we know slope now, means we know m


and we need to find b


So do I plug it into the equation I told you about


there are two ways you can do


one is you put two points in the equation you showed


another one is what i wrote on the board


i showed both way on the board


can you get it


Yea so you used point slope formula also


What if you have a point and that point is perpendicular to two other points


yeah okay perpendicular means the slope will change


we use this quesion for example


first we need to flip the fraction


and then change the sign


if we wanna check is when they multiply, it will be -1


I don’t understand the last part you said


we can do another number


for example, we have slope -3/5


the perpendicular slope


so we get +5/3


ohhh I get it now


Can you help me on another problem for my hw


yeah ofc


The question is to write the equation of the line that passes through (5,-1) and is perpendicular to the line that passes through (-3, -13) and (6,2)


first we find the slope of the line that passes through two points


can you try on the board


use slope formula


Okayy


okay and then we know is perpendicualr


so we can find another line's slope


yess


and then put number in equation y=mx+b


you can find b and equation


put 5,-1


or the way i wrote, which one do you preferred


What do I do now after I plug in the values


x is 5


yeah and now b is the only number you dont know


do you get it


Yes so when I have an equation like that I find the slope of the two points then plug in the slope and one of the points into the y=mx+b


i can give you a similar question if you wanna practice more


Yes please


The question is to write the equation of the line that passes through (4,7) and is perpendicular to the line that passes through (1,2) and (5,10)


you forgot something


it is perpendicualr


perpendicular


so the slope is not 2


Okay I fixed it


yess


you got it


What equation do I plug it in now


you replace b and m


so you can get whole equation


Okayy


one more practice?


or you have other qeustions


I have another question


okay no problem


The question it to show thag -a/b is the slope of the graph of ax+by+c=0


so we know slope is the number before x


so we try to change equation to like y at the left


and all other at the right


do we subtract everything to the right


yeah except y


What do we do now


How did you move the b value


so both sides divide b


Ohhh got it thank you so much


ofc!!


Hi! how can I help you today?


hi


Hello


so


I need to help with my math work.


Ok! Is there a problem you want me to help you solve?


Yes


Do you want to put it on the board?


I can send it to you and you could put it to the board.


Ok!


OK


There you go. It's on the board now.


Che check


Ok thank you!


Could you zoom in a little, please?


yes


So it seems like for every number, 2 is being raised to the power of that number


Does that make sense?


yes i think so


Ok, so for example, could you write an expression to represent the 10th stage?


On the board or


Sure!


I just wanna make sure


Or you could say it out loud, either way works!


Oh sorry!


I'm


it's like


I want to


like say 10 to the 10 to 3.


So I wanted for the, for the 3 to be smaller.


Ok, I understand!


Yeah, that's.


That's close, but not quite right


I'll do it out with you for stage 5!


So we know that each time, 2 is being raised to the power of (the number of that stage)


So in stage 1, it's 2^1


In stage 2, its 2^2


in stage 3, it's 2^3


In stage 5, it's 2^5


In stage 10, it's 2^10


So what would it be in stage 20?


Hello, are you there?


Yes, I, I was just thinking.


Ok!


Do you have any questions?


um


Don't be afraid to ask!


yeah


I know that like the power meaning to like to to multiply certain numbers.


Is that right


Yeah, that's right. So, when you


So,


my what


Yeah


So if you raise, for example, if you raise 2 to the power of 1, that would be just 2.


And if you raise 2 to the power 2, it would be 2 times 2. So there's like, there's 2 2s. Does that make sense?


Uh-huh


So then


the question here is, um


write an expression for stage 20. And at stage 2, it would just be to to the power of 20.


Oh, OK


Yeah, does that make sense


OK, do you have any other questions?


No


OK. Glad I could help.


No.


Thank you


No problem


put on


What?


nothing


Ok, unless you have any other questions, I'll end the session now?


thank you


Hi Alice! How are you today. What are you looking for help with?


Hi! I'm doing good thank you for asking!


I'm studying for my precalculus test do you mind if I ask you some questions from my study guide?


Sounds good!


Is this problem you have up on the whiteboard one of your problems?


Yes, this is the first problem.


Ok great. So we have an equation with a single variable, and we're looking to solve for x.


What are some things we can do to try and make it so that we only have x on one side??


we can subtract the 6x


to the other side?


Be careful! Is the left side 6x+(x-1)?


Or is (x-1) being multiplied by 6x?


oh its being multiplied do we distribute?


Exactly!


You had 6x(x-1) on the left side there


is that correct?


Yep, so the left side is equal to 6x^2-6x


Now we have an x^2 in our equation, do you know what we call an equation with an x^2 in it?


quadratic equation


Right!


And usually, to solve a quadratic equation, what do we want to have on one side?


Perfect! So what can we do to try and get 1 side to 0 now?


add the x from the right side to the left side


Yep!


Ok so now we're closer to having one side be 0, what now?


we subtract the 12 to the other side


exactly


So now we have a quadratic equation that is equal to 0.


There are a few different ways to solve these, what are you familiar with?


I know a bit of factoring and using the quadratic formula


What conditions do we need in order to factor a quadratic equation?


mm would it be using the 6 and -12 and finding out what it would multiply with and subtract wi the 2 numbers?


So when we factor, we need a to be 1. (Which could be done by dividing the equation by 6)


and then we find two numbers that add add up to b, and multiply to equal c


However, we'd have b = -5/6 and c = -2.


And that would be very difficult to do


oh I see we would have to turn the x squared into 1 Infront instead of ^ rihgt


Right, you'd want it to be a 1 instead of a 6.


would I always have to do this for any problem like this to get it correct?


If you want to use factoring, yes


ok


But you don't need to if you use the quadratic formula


okay so I divide the whole equation by 6?


yeah, lets try that


wait but it wouldn't go into -5x


Well it doesn't divide evenly, but we can use fractions


So if we want to factor, we would then try and think of two numbers, such that they add up to -5/6, and they multiply to -2.


But that seems pretty hard, doesn't it?


yes


Sometimes, you'll have an equation where the factors are pretty obvious.

Say, for example, x^2 + 3x + 2


What are two numbers that add up to 3 and multiply to 2?


2 and 1


Right. So we could express x^2+3x+2 as (x+2)(x+1)


However, we can't really do that with this example


So instead, we use the quadratic formula.


oh okay so if I come across this on the test I would use the quadratic formula?


Yes


Usually it's worth seeing if you can factor first, because it's faster if you can


But if you can't then use the quadratic formula


ok


So your quadratic equation is very close to right, but you're missing one thing


There you go


So now we can plug in our values for a, b, and c, and get our answers


You don't need the x next to the 5 for b.


a, b, and c are just the numbers next to the x's


6, -5, and -12


oh sorry


All good!


And then what do we do to the -5 inside the square root?


solve it to equal 25


Yep, now it's all just simplifying


Be careful, can we subtract before multiplying inside the square root?


Remember order of operations


im confused


So inside the square root, we have


do I take out the 25 from the square root as 5


We can't take out the 25 yet, since it's being added, not multiplied


We want to get what's inside the square root to a single number


ok so 25-24 is 1 then 1 x -12


is -12


Do we do 25-24 first?


Or do we do 24 * -12 first?


we multiply first bc of pemdas


right?


Yep!


So we multiply 24 by -12


Good catch on the +


Since we're subtracting -288, we add


So now we can add the two terms inside the square root


is that right?


Yep.


Now at this point you could call this done, or you could plug sqrt(313) into your calculator and get two decimal numbers


Do you know what you usually do in class?


For problems like these?


we cant use calculators at all


Ok, if you don't use calculators, then this would likely be the answer that your teacher wants


just put an x =


next to it


And that would be the solutions for x.


If you used a calculator you'd get two values roughly equal to 1.89 and -2.72


Do you have another example of a similar problem for some more practice?


Are you still there?


yes sorry i went to get my textbook for another problem


No worries!


Are we trying to simplify this fraction?


yes


and the denominator is supposed to be 2+1?


or should it be 2+i?


yes sorry


Ok, so we have a fraction using the imaginary number i


We have two terms being multiplied together in the numerator


and one term in the denominator


What do you think is the first step in trying to simplify this?


multiplying the top


distrubuting to each


Yep, we can mutliply them together, distributing to get a single term


Let's look back at the last term of your distribution


we have 2i times -i


squared?


Now what can we turn i^2 into??


close, do you remember what i represents?


Right, the square root of -1


so if we square it, we get -1


So instead of -2i^2, we can write +2


So now we have four terms in the top, 3 - i + 6i + 2, can we simplify this more??


yes like terms


So now we have a single complex term in the numerator, and a complex term in the denominator


Do you know how we proceed to get just a single term with no fractions?


bring it up? but there's no negative


Right, so we can't bring it up yet


Have you heard of a complex conjugate?


or multiply 2 +1 to top and bottom?


no I haven't


So a complex number has two parts, a real number and an imaginary number, right? 5+5i is a complex number, and 2+i is a complex number.


The complex conjugate of it is the same real number, but the negative of the imaginary term


So for 5+5i, the conjugate is 5-5i


For 2+i, the conjugate is 2-i


What we do is we multiply both the top and the bottom by the conjugate of the bottom.


So in this case, we multiply both sides by (2-i)


Does that make sense or am I going too fast?


yes I understand


like this?


Not quite. Remember we're multiplying, not adding


And also, the conjugate doesn't just cancel out, we still have to distribute.


When we multiply a complex number by a conjugate though, we always get a real number.


could you show  me pls I'm kind of confused


Yeah. Are you able to hear me?


Sorry I haven't used the mic before, do you hear me directly or does it just send text?


It's okay me either. It just sends texts


Ok, that's fine


So right now we have a fraction, we have a complex term in the top and the bottom


To simplify it, we want to make it so that we only have a complex term on top


and the bottom is a real number


So what we can do is use something called the complex conjugate


So here we have another example, 4+2i.


The complex conjugate of this is 4-2i


We keep the real number the same, and negate the imaginary number


And what's special about this is that when we distribute these terms when we multiply


Is there anything you notice?


When we combine like terms?


they are the same


Right! More specifically, the i's cancel out


So we're just left with 20, a real number


Whenever you multiply a complex number by its conjugate, this is the case


So let's try another example


What's the conjugate of this term, 5-3i?


Yep!


Now try distributing and see what you get


Great work!


So you can see, whenever we multiply a complex number by a conjugate, we'll always just get a real number, the imaginary term cancels out


yes!


So now, if we want to multiply our fraction by something so that the bottom is only a real number, what do you think we'll multiply by?


Referring back to our original problem


Exactly


And since we need to keep the equation the same, we need to do it to both the numerator and the denominator


So now we distribute both


Can you distribute the top and the bottom of the fraction?


yes


Awesome! Now we can combine like terms in both and see what we're left with


And now is there anything else we can do to simplify?


yes divided by 3


simplify


Yep


So what are you left with when you divide both terms by 5?


oh I meant 5 sorry and we would get 3


Yep! And that's the answer. 3+i


Would you want to try another example of the same type of problem?


I have one ready


yes please


Alright, so we have another fraction with a complex term in both the numerator and denominator


What should we do to simplify?


multiply 4+1 to top and bottom and distribute


I *


Good!


I'm going to use the bathroom really quick, I'll let you distribute the top and bottom and I'll be back in just a minute


yes, no worries


I'm back, and that looks good! The only thing is make sure to include the i next to the 3 and 4


Looks like you just forgot to write them


yes I was just seeing that


sorry


All good! No need to apologize it happens. So, now what do we do?


combinelike terms


Yep!


And now, can we simplify further?


no


Right!


Last time we had a denominator that fit into the terms


So we simplified (15 + 5i)/5 to 3+i


But in this case, since it doesn't fit, we're done


Does it make sense how to simplify complex fractions now?


Or do you want to try another example?


yes it does thank you!


Do you have more problem types to work on? Or do you want to try more examples of what we've already practiced?


yes I have a few more if you have time I'm sorryb


No worries! I have plenty of time. As long as you need


Thank you!


Just confirming, this is what it's asking to rationalize?


yes


Alright, so this is somewhat similar to the previous problem. We have an irrational term in the denominator, and we want to make it so that it's a rational term.


What can we multiply sqrt(3) by so that it becomes a rational number?


I'm not sure would have do have 2 and 1 in a square root


How about this, what is the product of these?


sqrt(3) times sqrt(3)?


careful, that's 3x3, what about sqrt(3) times sqrt(3)?


how about if I write it like that?


square root of three, squared?


ok


I'm not sure


would it be 9 with a square root?


It is the square root of 9


But more specifically, what is the square root of 9?


Right, so sqrt(3) times sqrt(3) is just 3


And this applies for any number


oh okay sorrty


sorry*


Since it's a square root, and you multiply it by itself (squaring it), they cancel out


and you're just left with the number under the square root


So we can multiply both the top and bottom by sqrt(3) to rationalize the denominator


Since sqrt(3) times itself is 3, a rational number


Yep, for the top, we just leave it like that. 12sqrt(3)


Now, is there anything else we can do to simplify now?


divided by 3


yep


And that's your answer


So what if I gave you this example?


How would you rationalize this?


exactly


I'll give you one more


This one is a little different


ok


But is mostly done the same way


Awesome! And at that point it's simplified as far as you can go


okay thank you!


You feel confident to move on?


yes


Awesome! Feel free to hit me with the next problem


Alright, so here we're looking to factor a cubic


Often times what we want to do here is split it into two terms


So we can treat it as (9x^3+18x^2) + (-x-2)


So if we look at the left term only, is there anything we can factor out of it?


Good! We can factor out a 9.


Can we factor out anything else?


or would it be 9x^2


9x^2, good!


So if we factor that out what would it look like?


Make sure you keep the factored term outside


We aren't getting rid of it, just taking it outside the parenthesis


ok I didn't know we kept it out thanks for that


So now, we want to make it so that the stuff in the right parenthesis is the same as in the left parenthesis


Is there anything we can multiply (-x-2) by to make it the same as (x+2)


Exactly


So you can write it as 9x^2(x+2) - 1(x+2)


okay what would be the next step?


The second term should be positive now, since we negated it


Instead of + (-x-2) it's - (x+2)


So now we have 9x^2 times (x+2)
                    minus 1 times (x+2)


ook


So now we can combine like terms


do I combine them


is that correct?


Be careful, we don't multiply 9x^2 and -1


We're adding them together


ok 8 and positive?


Nope, just 9x^2 - 1


We have two separate terms, an x^2 and a constant


So we're left with (9x^2 - 1)(x+2)


And that would be your answer. Do you want to try another example?


Sorry I actually have to leave. Thank you so much for your help, I really appreciate it!


I  will save this example so I can practice it later.


Ok, have a good night, and good luck on the test!


Thank you so much! Bye!


goodbye!


hi there


how can I help?


Hi how are you


I'm good,how about you?


Good thank you, I’m having trouble with solving for Literal equations


okay,let me see the question you are solving for it.


okay I see it. please give me a minute to look through it and solve.


Okay ty


you're so welcome!


So given:𝑉=I⋅w⋅h
To isolate 𝑤, divide both sides of the equation by I⋅h:
W=(V/I⋅h)
So the solution is:W=(V/I⋅h)
This tells you how to find the width if you know the volume, length, and height.


do you understand or want me to explain a little more?


Can you please explain a little more


of course!


I have like about 7 more questions about the same topic do you think you’re able to help me with them?


of course🤓!


So given:𝑉=I⋅w⋅h
This is a formula for volume of a rectangular prism, where:
𝑉 = volume
𝑙 = length
𝑤 = width
ℎ = height


Sarah


your welcome!


And the goals is that We want to solve for 𝑤 — that means we want to rewrite the equation so that 𝑤 is by itself on one side.


Okay yes perfect


I added the second equation we have to solve for A


now time for the step by steop explanation
#1:Start with the original equation: V=I⋅w⋅h
#2:To isolate 𝑤, we need to get rid of the other variables multiplying it — which are 𝑙 and ℎ.
#3:Divide both sides of the equation by I⋅ℎ: (V/I⋅ℎ)=(I⋅w⋅h/I⋅h)
#4:On the right side, the I⋅ℎ cancels out:W=(V/I⋅h)


okayy thanks,i'll take a look at time right now.


tell me if you need help with the answer I gave to you.


It helped me so much David!!


your so welcomee🤗


the goal is that:We want to rewrite the equation so that 𝑐 is all by itself on one side. That means we need to
Find all the terms that contain 𝑐
Move everything else to the other side
Factor and divide to isolate 𝑐


so Step 1: Identify terms with 𝑐
The original equation is:𝐴=2𝑎𝑏+2𝑎𝑐+2𝑏𝑐
We factored out the 2𝑐 from 2𝑎𝑐+2𝑏𝑐, to get)


Step 2: Move the non-𝑐 term to the other side
Subtract 2𝑎𝑏 from both sides:
𝐴−2𝑎𝑏=2𝑐(𝑎+𝑏)
Now the right side only has 𝑐, which is what we want.


Step 3: Divide both sides by 2(a+b))
To get 𝑐 by itself:
c=(A-2ab/2(a+b))


Final answer:c=(A-2ab/2(a+b))


you there Sarah?


Yes I’m going over it sorry for taking long


it's okay,please go ahead,I can wait😊


I’ll put the next equation and I’ll go over this one


okay


thank you


A= 1/2h(𝑏1 + 𝑏2 )
This is the formula for the area of a trapezoid, where: 𝐴 = area ℎ = height 𝑏 1 and 𝑏 2 = the two bases Goal: Solve for 𝐴 Lucky for us — it’s already solved for 𝐴 ! That means: 𝐴 = 1 2 ℎ ( 𝑏 1 + 𝑏 2 ) So if you know the height and the two bases, you just plug them in and calculate. Example: Let’s say: ℎ = 6 𝑏 1 = 4 𝑏 2 = 10 Then:𝐴=1/2⋅6⋅(4+10)=1/2⋅6⋅14=3⋅14=42


tell me if I made a mistake on that one


I think that’s perfect I don’t think there’s any mistakes


okayy


yo


Hi Kai! How are you today?


js need ti review for my test


Sure thing!


Can you zoom in the paper?


uh


i try


Also, I need to see the full paper.


my teacher gave it to me like that


is that better


It is better! But the left margin is gone.


I can't see the full paper.


yeah.. my teacher gave me it like that


OK! I will try my best to review!


oh wait


OK!


man i cant


copy the picture


or save it


wait..


Unfortunately! I can't help you with this. Or you just post the last paper.


THERE WE GO


good?


Great! Which question are you interested?


can we uh


do all..


I have 30 minutes for this session! I will review as many as I can. Does this sound OK?


ok


Part 1 looks right to me.


no, thats my teachers copy


So you want to know how to work through the questions?


yes


OK! What have you tried for part 1?


i js know that uh


the first 2 numbers


cant be bigger


i mean


should be bigger


then the alst number


last


given a triangle, any length of a side is greater than the absolute value of the difference of the other two length of sides and is less than the sum of the length of the other two sides.


so uh


would


and 4 work?


since its


10 = 2+8, so fail the condition.


i ment like


answers


and 4


which is


4 <8-2, so fail the condition


7 is right


8-2 <7<8+2


i dont get it


can you let me know why you are confusing this?


ur symbols


let's first check 8-2=6, so the length of the third side must be greater than 6, do you agree?


yes


nice! so we eliminate answer (3) and (4), which are less than or equal to 6.


Next, we check 2+8=10. So the lenght of third side must be less than 10. Do you agree?


So which is the right answer do you think among (1) and (2)?


You got this!


yay


The second question of part 1 uses the same idea.


It is left for you to check for saving time, is this OK?


is it 2


YES! (2) 8 is the right answer.


yippie


Let's move to part 2?


sure


Have you tried this already?


no


ion get it


OK! No worries!.


First, what is the sum of interior angles of a triangle?


TRUE!


so angle A + angle B + angle ACB =180, do you agree?


yes


Next, for two supplementary angles, what is the sum of the two angles?


mk is 15


so


is uh


ml also 15


since there's supposed to be 2 equal sides


do you see the graph?


i do now


OK ! AB is a line


O is a point in between A and B


O is on line AB


OC is a ray


what is the angle AOC + abgle BOC?


Teacher imma be dead honest with you


angle*


i have no idea what u js said


OK! No worries! Have you ever heard of supplimentary angles?


yes but i forgot it


Two angles are supplementary angles if the sum of them equals 180 degrees.


OHHH


Please refer to my example, AOC and BOC are supplementary angles because the sum of them equals 180 degrees.


do you agree with this?


uhh


yeah


Nice. Let's go back to the question is part 2.


ok


ACB and BCD are supplementary angles as well because the sum of them equals 180 degrees


do you agree?


yes


Nice! Now we can obtain an equation that A + B + ACB=ACB+BCD


Do you agree?


Cool! So we cancel out ACB for both sides of the equation, what we can get?


i have to eat..


OK! See you! You have made a progress!


thank you


see you!


Hiii


Hi, I'm Sarah, how are you?


Hi Sarah im fine how are you?


I'm doing great, what can I help you with today?


Thats good,  I need help with finding a point on a line segment that splits the line into a certain ratio


Okay! Line partitions, perfect, do you have a specific problem you want to do or you want to just make some up and practice


Any is fine


I just want to know how to do it better like i have a quiz coming up


If you have a specific problem you want to try, feel free to just draw on the white board.


Okay


Are you able to see what I am drawing right now?


Yes


Ok, so, if this line is 10 blocks long, how long would it be if you split the line into 2 parts?


That are equally long


Yes, so you just cut it in half and the line is now split in two equal parts


Ohhh


Now, how long is each line that you just made?


So, both lines are now 5 blocks long, which means we can write the ratio between them as 5:5


Do you know what that ratio can be simplified to?


Not exactly, when you see a ratio like 5:5 or 1:2, think of it as a fraction or a division problem.


5:5 just means 5/5
1:2 just means 1/2


So, 5 divided by 5 is..?


Exactly


But remember to always keep your answer as a fraction


So, we would have it as 1 / 1


Which just means we have a ratio of 1:1


You could also think of it like this, if both parts are 5 blocks long, then they are 1-to-1  with each other.


Ohhh i think im starting to get it


Now, look at the new line I drew, how long is each part?


Oh 2/10?


Almost, h9wo long is the short side exactly now?


Great! And the long side?


its 8


so 2/8?


Exactly!, The ratio between these two parts is 2-to-8 or 2:8


ohhhhh


Do you know how we can simplify this ratio?


Remember, a ratio is just another way to write a fraction basically, so simplifying a ratio is the same as simplifying a fraction.


Yes, exactly, so would you write that as a ratio?


Perfect!


Now, how long would each part be if I told you to split it into a ratio of 4:6?


Exactly! Now, how long would each part be in terms of blocks?


Almost, if their ratio originally is 4:6 . This would mean that one side is 4 blocks long and the other is 6 blocks long.


Giving us our 4 blocks to 6 blocks ratio


Ohhh I was thinking of that but I wasnt sure


Sarah can i have one more practice question I have to go


Yes, of course!


Now, If I want to split this line into a ratio of 3:2


How long would each part be?


Not exactly. One way we could approach this is by first dividing how long the line is by the amount of parts we have.


So how long is the line in total?


How many blocks long is the entire line?


Great! Now, to find the amount of parts we have, we just have to add the numbers of our ratio together.


Since our ratio was 3:2. The amount of parts we have is equal to 3 + 2


Yes, so we have 5 parts in total.


Remember, to find how long each part is, we can just divide how long it is by how many parts we have.


So each part is 10 divided 5, blocks long


Great!


So, essentially we are just splitting the line into blocks of 2


Now, the line is split into 5 parts of  2 blocks exactly.


Remember, the ratio we wanted to find originally was 3:2


So, one side will be 3 of these parts long, and the other will be 2 of these parts long.


Do you want me to clarify anything so far?


Ohhh


I think i get it now, but unfortunately i have to go Sarah:(


Thank you for teaching me how to do this i really appreciate it


That's okay, to answer one last question before you go. How long would each of the new parts be if one is 3 parts long and the other is 2 parts long?


Of course, anytime!


Close, how long is each of the smaller 5 parts on the line


How many blocks long?


That's our ratio. Take a look at the line again. Each of the parts is 2 blocks long right?


Exactly, each is 2 blocks long


Yes, the ratio of our parts is 6 blocks long to 4 blocks long!


If you need to leave as well, feel free to end or leave this session whenever.


Oh okay!! It was really nice to meet then Sarah thanks a lot!


It was nice to meet you too, anytime!


Hello


Afternoon


I need help with this homework assignment, would you mind taking a look at it?


Fire away


Here is the first question! there is only three.


I am slightly confused, I neutrally understand this.


Can you make it bigger?


Yes


Here you go!


Okay let me copy it onto a notebook


Okay! also I might have to go soon because of class.


Oh


Okay so


So you set it equal to zero right?


yes


Thank you so much, I sadly have to go.


I'm only speeding up because of time constraints on your end


Yes thank you.


There aer your ansers


Thank you I got a better understanding.


hi


how are you doing?


need some help in math?


yup😐


can you post the problem to the board?


yup


i started this with someone else but they barely helped me


I can help


I like these kind of questions


do you see the triangle with the dotted lines


yea


it's a right angle triangle


yes!


so we can use a special formula to find the sides and angles


soa cah toa


it's called SOH CAH TOA


do you know what the letters mean?


yes


let's start with the H


hypotenuse


what is that?


yes! good job


and in our diagram which one is the hypothenuse?


yes! across from the right angles


angle


you got it


sin/hyp


cah = cos = adj/hyp


and which one is opposite to the angle 37?


wait


hm


don't forget what we are trying to find


wait what are we trying to find ? the cos ?


we are trying to find the distance BC


WHAT!?


the other guy told me CB


or is it the same?


iit's the same


oh ok😐


now is BC adjacent or opposite to the angle 37?


adj


yes!


so which one will we use Sin or Cos ?


cos ?


yes! excellent


so what we did was cos (37) = CB/2.1


so now cross multiply to find CB


oki


great!


so the 2.1s cancel on the right


yup


do you have a calculator?


yea


let me know what you get for CB


okay i got 1.67713 so on 😐


that's it exactly


so i have to round it


now can you round to the nearest hundredth?


yes


to 2 Dec pl


so 1.70 ?


not quite


the hundredth is the 2nd Dec pl\


so 1.67 or 1.68


oh oki😐


look at the next number (a 7 right)


so will it be 1.67 or 1.68


uh 1.68


yes! because the 7 is > 5


excellent work


you're doing great!


any more or is that it for now?


i have some more


ok


want to clear the board first?


sure


oki


ok thanks I see it


so again we have a right angle so we can use SOH CAH TOA


what is H this time?


hyp = 7


yes!


and the opp is 3 ?


and the side of length 3 is adjacent or opposite to the angle at B ?


opp ?


oh


nvm


it's the angle at B we are trying to find


so 3 is adj


yes! excellent


so we use ?


cos


yes! cos again


can you do it on the board?


oki


excellent!


so put 3/7 in your calculator


but don't round


then you have to use 2nd (or inverse) button


so find the inverse cosine


can you find that button?


? so the csc?


no


2nd button then COS


it should say cos^-1


oh oki


tell me what you get


so 64.62


so on


yes! and you rounded correctly


good job!


see, these questions are fun right?


not rlly lol


yeah, that was a stretch!


but you're getting it


want to try one more?


somewhat 🤣


oki we can do another


ok, last one then I gotta go


oki👍


ok, this one is a bit different


yea


do you know what cot means?


yea cotangent


right!


its adj/opp


yes! exactly


so looking at angle A


which is adj ?


adj is 6


yes!


and opp is?


yes


so cot A = ?


excellent


now can you simplify this 6/8 ?


to get it in lowest terms


you got it!


good job


thxs👍


keep up the good work!


have a great day!


👍 u too


thanks


bye


Hello


How are you?


Hey what’s up?


I’m good, you?


Same


Do you need any help with anything?


im just styding for a quiz


Cool, what are you guys learning?


so this is parent functions and transformations


wait so what does intercepts mean


The y intercept is where the function intersects with the y-axis, and the X intercept is where the function intersects with the X axis


so like 0,2


or


Yeah that would be a y intercept


so x intercept: none


y intercept: (0,2)


Sorry dude I gotta go now but good luck on your quiz!


oh ok


thanks


Hi Emily: How are you today?


Hi I'm good thanks


What's up in Precalc?


well I'm in ib analysis so idk if that's in the same area?


Hmmm, if you can post a problem, I'll let you know if I can help with it.


Ok


This is the proble


I don't see a post yet


where do you post?


There it is, give me a sec plz


OK, looks like you are studying functions


Yeah


OK, for (a), you want the output value (or f(x)) of the function when x = 3


OK


Understand what to do?


yes


Let me set up (b) on the board


ok


What you do here is plug in the f(x) function in place of x in the g(x) function.  Your answer will be an equation, not a value.


Ohh Ok


Make sense?


Yes


OK, for (c), start by switching the x and y values and rewriting the equation underneath


Ok


Plz show your work


Good, now solve for y


You might want to graph x - 3 and x + 3 on Desmos to see what a given linear func and its inverse look like!


Anything else today?


that's it for now, but thank you so much


My pleasure, have a great rest of your day.


Thank you, you too


Hello


Hi Ben


So for a i got


6 is correct.


I dont get b tho


How would it be incorrect isnt it correct since the majority is imaging


For "imaging" to be the majority, the frequency would have to be at least 50% (0.50), correct?


I dont get it


ohh do you mean if imaging was more than 50 percent?


Yes.


Yeah it would be that


How would I answer that


You can say: "Although 'imaging" accounts for the greatest frequency of all missions (0.34), the statement is incorrect because the frequency is less than 0.50"


Ohh so therefore it doesnt count for the majority


Got it


Awesome!


For 8 i put D


And for 9 i picked A


8(d) would be my choice, too.


So when it asked for individuals it means this?


Yes. The "individuals" are the objects being studied. In this case, it's homes.


I'm checking your answer for question 9...


Did you consider "zip code" to be categorical?


Yes because isnt it numbers?


Do variables mean numerical data?


And categorical is like names


Yes. "categorical" would include names.


The question is tricky. Did you include the home's address as a variable?


No categorical


Oh wait i mean variable


It's difficult to decide between 7 or 8 variables. Some people consider "home address" to be a variable, and others don't.


Yeah ill ask my teacher about that


But the other categorical variables would be: zip code, building material and whether there's a pool.


Isnt zip code numerical though?


Wouldnt it be a variable?


Zip code is a variable. The question is if the variable is categorial or quantitative. If you Google: "is zip code categorical or quantitative?", it will say "Categorical".


Ohh ok got it thanks


Alright then i also think B is the answer


(b) seems best. But I can't say that (e) is wrong, if we include "home address" as categorical variable.


Yeah


alright thanks


You could check with your teacher.


Yep


Have a good day bye


You as well.


Thanks


Hello!


hi


hello


how are you?


good, you?


im doing well


how can i help?


Im trying to get ready for my sat but I dont think im the strongest in gemetry can you please help me?


Sure have you taken any SAT practice tests yet?


yeah a few


my highest was only a 1050


what score do you want to have?


1350 or higher


nothing below


Oh ok and how much time do you have


what grade are you in?


i have a good hour and im in 11th


so you're applying to colleges soon


what colleges are you interested in?


yes


State University


thats a good list, whats your current gpa?


Wow thats impressive


are there any concepts you want to go over?


probably circles alot but i would like to go over general stuff too


back


what type of questions on sat math do you struggle with?


hi


Hello!


How can I help?


with scientific notation


Do you want me to provide questions or do you have your own questions you want to prepare on?


you porvidwe


provide


ty


No problem! give me one second to think of a few problems


ok


Ok it is on the board


write this in standard form


Is your answer 0.0048?


yes


Yes very good ok next question


I will make them more and more difficult


as we go on


Yes


Very good!


Convert 0.0007476 to scientific notation


good luck!


Very difficult


i'm i right


Yes very good!


7.476 x 10^-4


is that like the caculator type


Alex


this sign "^" means to the power of


so ten to the power of -4


7.476 times ten to the power of negative four


check on the board


Very Good!


Ok I will give you questions


ok


5.2 x 10^4  or 3.9 x 10^5


which one is larger


A (the 1st one) or B(second one)


Close why do you think it is A?


A the 1st one


No the correct answer is actually 3.9x10^5


ohh


expand each one and you will see B is bigger and then I am going to show you a trick


because look even though 5.2 is slightly bigger then 3.9


10^5 is wayyyy bigger then 10^4


thats why B is correc


correct


expand both A and B just for you to see


put them in standard form and compare


now i understand


Ok hmm one second let me find new questions


you are good you understand everything though


ok which one is larger


trick question


a or b


(1st or second)


a


Yes very good


because the most important thing is the exponent of ten


not the decimals (8.1, 9.5)


and we know -2 is bigger then -3


meaning A is right


good job


yeah i did'nt know that


It is ok let me think of new questions


ok


ok add these two things


3.45 x 10^3 and 2.1x10^2


i don't have a caculator


its ok these are small numbers


i'll try


i did them small


2wiat sorry


sorry


do those


am i right


close but no


ohh


heres how you do it


Ohhhh wait


ok I think you subtracted


add them not subtract


but yes very good


try adding them though and then you are done


ok


Yes very good but just one thing when adding, see how they were both 10^3


that means you keep it at 10 to the power of 3


yes


dont add both 3's to six


its look keeping the denominator of the fraction the same when adding


you still keep the three


dont add the threes and make a six


but yes good job though


you mean keep the number after the ten


understand?


i circled the mistake on the board in green


Very good!


I think you are ready


for


Oh one more way to do the problem


for your test


ohh


one more way to do this problem


convert both of these into standard form


try really quick


and then we are done


just to make sure you really have this


ok


done


good then add both those numbers up


which would give you


and then you can convert it back into scientific notation


into 5.55 x 10 ^3


same thing


thats another cool method you can do


so yeah just so you know


do you get everything?


yes


Great! I think you are ready!


Do you want more or is that enough?


where is it


Where is what?


You want more questions?


the question


ok here


i can't see them


want a pretty difficult question?


some


Ok here subtract these


actually


add these


ok


dont subtract jsut add these


Ok one problem so with these


if the exponents on the tens arent the same


then you cant add the decimal


see how like one is 10^4 and one is 10^3


yes?


so i got it right


No but close


but look see how the numbers after the ten are different


yes


that means you can not add the decmials up


its the same thing in fraction you can only add if th denominator is the same


so how to do this is


convert 4.5x10^4 so that it has 10^3


so you know that 45x10^3 is the same as 4.5x10^4 right?


so yeah rewrite the top part to 45x10^3 THEN do your method


and then itll work


and remember dont add up the numbers after ten they stay the same


so it 3


yes very good


ok so now redo the question but instead of 4.5x10^4 change it to 45x10^3


like this


almost but make the ten to the power of 3


ohh


yesss now add them up and itll be easy


so does that mean the answer is going to be 86x10^3


very close if you look closely its 3.1 not 31


so dont do 45+31


its 45+3.1


so yes the answer is 48.1


very good ok now just some scientific notation practice


so all i did there was just convert


the 4.5x10^4 to 45x10^3


that way we can add the two numbers up because the numbers after ten have to be the same


now i understand


Yes very good ok Im going to give you easy questions now


Yes sorry


yes very good!


Ok which number is larger


this might be  a little of a trick


be verrry careful


very simple but lets see if it tricks you


a or b


if it helps put both of them in stnadard form and see which one is bigger


A


wait let me see


very good


now which one is bigger


B


A is clearly bigger


i was gonna say a


guess i was too late


but at least you expanded rightbut  after expanding we should know 7.4x10^6>7.35x10^6


so be careful


yeh i wasn't really looking good


ok


i'll be careful


True or false: The number 52,300 is the same as 5.23x10^3


false


wait


is that your final answer?


yes


yes very good


next question


0.0048 is the same as 4.8x10^-3


true or false?


true


very good is 55x10^2 the same as 5.5x10^3?


yes or no


no


wrong


are you sure? these are the exact same


make sure


55x10^2 and 5.5x10^#


expand them both


put them both in standard form and you will see


these are the exact same


5.5x10^3 55x10^2


Yes very good see how they are the same?


good so try these


4.7x10^-2 is the same as 470x10^-4


true or false


false


close check again


this the last question check really closely


it does'nt look the same


try both of them and write it close to the text


ok


last try and then If you need help i will solve it in front of you


wait see


you did a mistake


u brought it over 3 times


u were only supposed to bring it over twice


ohhhhhhh i see what you did


for the first one


its not 4.70


its four hundred seventy


as .0


right


so how you would do the first one is this


look


did you see what I just did


i idid'nt really get that


ok wait just 470 x 10^-4


I want to see your mistake


Ohhh i see your mistake


remember you keep treating it as if its 4.70 x 10^-4


look at the board


ok i put a decimal point


now try it


this time i specified wher the decmial point it


is


yes now put 470x10^-4


like this


yes


my chrombook is dying


Oh ok its fine


but ok last question


for negative numbers after ten


do you move the decimal to the left or right


i have 30 more minute left tho


ok but this is the last question anyways so then you just move the decimal four spots to the left


do you understand everything?


kind of


Ok is there anything you are confused about


the question you just give


it has a power of -4


yes good


so why was a going right


nono you dont go right


look for  470


because its in the hundreds


the decimal point already starts 470.00


ohh


and then you move it to the left


now i see


but because its a bignumber it already starts far out


yes ok


any questions before I leave?


i'm ok


Ok sounds great!


thank you


No problem!


Have a good day and Merry Christmas!


you too


Hello, how is it going?


What can I help you with today?


How does your tutoring service work?


It's going good thanks for asking


We offer 1:1-on-1.


I see, would you be able to help me with homewlrk


Of course. Could you please put it on the board?


Yes


Do I take a picture or type the problem?


Either works.


Ok


I am logging into my school portal to get the question


No worries, take your time.


Okay, the first to simplfiying is to first expand the expression "-2(k+1)". How can we do that?


Oops I meant to put terms instead of forms.  But I am not sure


No worries, still the same method.


So, what is -2(k+1) expanded?


Hmm I don't know


We need to use the distributive property to do so.


When we do it, we get the following:


-2(k+1) = -2k-2.


Ohhhh okay


Yeah.


So the expression we have now is the following:


Can we still simplify?


Yes?


Yes we can. What can we simplify?


I'm not sure


The "k" terms.


So, we get -8k-2.


If we wanted to simplify this expression further, we can do -2(4k+1).


Since both the terms -8k and -2 share a common factor of -2.


That can be taken out.


Ohhhh okay I see


Yes.


That makes sense


I'm glad.


I was a little confused on that specific topic but I appreciate you for explaining


Of course.


Is there anything else that I can help you with today?


Hi


Hi, uh,


I'm gonna be uploading


some new material.


uh like, uh, uh, if


right.


I


ok


I upload this.


OK


I want you to make something uh similar to this because


we have a major crisis.


I need help with Geometry


Hi whatdc


hi what can i help with?


I am struggling to understand concepts in geometry


okay give me one that youre struggling with and I can help you!


I'm going to try and upload a picture of a problem


okay


Here are a few


okay we can start with y=-2x+9


I really don't understand at all. and am struggling in class


its okay!


the -2x is your slope


that's your rise over run


so basically you go up 2 and run 1 on the graph


but in this case its negative! so you go down 2 run 1.


the 9 is your y-intercept. this is the point where the line crosses the y axis, the line crossing down the middle


so you go up 2 over 1?


down 2 over 1! the 2 is negative in this problem :)


can you please slow down?


I just need a sec to take notes


yes what part are you confused on?


ohh Liam!


sorry


we start at 0 axis and go down 2?


no, I would suggest you plot the y-intercept first, which is 9!


then go down 2 over 1!


are the y and x axis always the same each time. Meaning they don't change


Ok, got it. start at 9, go down 2 over 1


yep pretty much!


do you want to try one of the other problems on your own to see if you understand?


that's the answer?


like the graphing?


I'm sorry, I don't understand. I"m not sure I can learn via the chat.


Is there any video sessions


I'm actually not too sure but I'm sure I can find a quick video for you to watch to get a better grasp of this concept!


ok, great


this youtuber is really handy for math


hello?


I'll end the session now!


hi


hello


how can i help you today


Also i do have to leave reallly soon just to let you know so I apologize in advance


ok


Figure A no, Figure B yes, Figure C no, Figure D yes, Figure E yes, Figure F no


for Figure A its because both points on the top share same y values


Figure B is a straight line with positive slope


Figure C is a downward parabola


Figure D has no same y values


Figure E every y corresponds with a x value


Figure F this is a wave


sorry i need to leave now but i hope this helped you understand


Hello


Hi Lily! What do you need help with today?


Are you able to use. Your mic


I'm sorry, I cannot right now because I am in a loud environment.


But you can use your mic if you want to.


No it’s ok I just need help with a question from my notes it’s about dialations in my notes


Ohh ok, can you take a picture and upload it onto the whiteboard?


Ok got it!


Ok, so what is the question asking you to do?


Find the value of the missing  x using the formulas


Sure!


Ok, so we know that <B is equal to <N because the triangles add up similar triangles right?


Yea


So you see how <M and <C are equal and <N and <B are equal?


Yes


We can say that NC/AB=CM/AC


hello


Um, can you help me with a question?


OK, what is your question?


It's question 26.


Oh God, this is a thing.


Oh God


it.


It's what


How many ounces are there in a pound?


Oh


Oh, my boy.


That


I did not mean to say that


So we set up a ratio of lbs to ounces


we want the lbs to cancel out, so we put lbs in the denominator


Do you see how I set that up?


Yes


point


Yeah


I'm not saying this.


Um, hello


Are you all set with this?


You just need to multiply 8.3 times 16


OK


uh


I got 32.8


I


Yes,  132.8


Is that just it


are you all set now/


Yes, thank you.


Mm


You are welcome.


OK.


Have a good week.


bye


My, have a nice day.


Hello


hi


ill upload the question one sec pls


sure


im struggling on 51 and 55


will i do it completely or should i do the whole step


can u do it step by step if possible


how did u get the 2x times 3 square root of x


just multiply the constants and leave x as it is


ohhhh gotcha


get it


yess it makes sense now, just writing it down thank u


any more doubt?


nope that was all


thank u!!


want to try something on your free time?


maybe next time im kinds rushed to finish my assignment


Hello!


Hello


i’m having some trouble with some homework could you help me out?


Yes :)


i’m working on solving system of equations by graphing and substituting


okay


the first problem is asking me to solve by graphing and it’s -x+3y=6


my bad the other one is 2x-y=8


so those two equations are for the same problem


When graphing the equations, you want to put each equation into slope intercept form


Because graphing calculators have y = ...


Do you know how to do that


i don’t


i also don’t have a graphing calculator i have a graph on paper


oh okay


Do you understand how I got each equation?


on the second one how did you get the y on the other side of the equal sign


I just flipped it around


Let


Let's graph the y = 2x + 8 first


The 8 is the y-intercept, or what y equals when x = 0


gotcha


The slope, 2, says how steep the line is (2 up for every 1 right)


right


The solution of a system of equations is where the two lines intersect


Oh no


I messed up the second equation


its 2x - 8 = y


Sorry


it’s okay i’m still kinda confused though


With what


how do i graph the first equations also in class we worked with a partner to solve problems an the answer to this one is (6,4) and i’m not how sure how we get to there


There's two ways to solve it, like you said


by graphing it and seeing where the two lines intercept


or by substituting and solving for x and y


Let's try substituting


ohh okay


Because both equations are equal to y, we can set them equal to each other


If you're substituting you don't have to use slope-intercept form


i’m still kind of lost


let me send my hw sheet i think that would be easier


Ok :)


Do you still want to work on question 3?


i do


By graphing or by substitution?


let’s do graphing because that group of questions ask for it


When graphing, you want equations to be in this form:

y = mx + b


right


because m tells you how steep the line is and b tells you where to start


Do you understand how I turned each equation into this form


i do with the first equation but not the second one


I first added y to both sides then subtracted 8


2x - 8 = y is the same as y = 2x - 8


gotcha gotcha


Now, you graph each lines


The point where they meet is the answer because that makes each equation correct


how would i graph the first equation


i see i see


You first start at 2


when x = 0, the equation becomes y = 0 + 2 = 2


The steepness of the line is determined by the slope, 1/3


Have you heard of rise over run?


yes i have


so you would go up 1 and to the right 3?


Correct!


and we start from 2 at the y-intercept?


Yep


okay i got it


The second equation is the same wa


way


it starts at -8


and goes up 2, and left 1


right


yes i’ve gotten that graphed


Nice


so it would look like this


yes


i’m using each point by counting by 2s btw


ok


If you're going by 2's, the bottom line would go 1/2 a square right and 1 square up


The top square would go 1.5 squares right and 1/2 square up


what do you mean?


*top line


sorry


so like this?


Yes, for the top line


Because you didn't make a scale, it should look the same as if the squares were by 1


sorry could you show me?


ohh i see what i did wrong


looks good!


so it would look like that


okay great!


be sure to label the point where they intercept


right


okay we can move on to 5


5 uses substitution


yes


It's an easier question because it directly tells you what y is equal to


and if we could could we just ignore the answer that’s just to check my work


We can plug in, substitute, y into the first equation


so solving with only the equations


oh okay


Now we can solve for x


okay i got it now


Great!


i should be able to finish the paper by myself now


Nice


okay thanks a ton!


No problem :)


Hi there!


Hi Alex.


Hey Alex!  I’m here to help with 8th grade math—are we working on homework, studying for a test, or just reviewing? Let me know what topic you’re on


I'm working on homework. I think I know what to do with the problem. I just need to double check


sure


The problem is: Each bus can hold 48 students. 570 students are going on  the trip, how many buses are needed?


Thanks for sharing the problem! Do you want to walk through it together, or do you already have an answer you’d like to double-check?


We can walk through it together


Sure!


Is it fine if I turn on my microphone


yes


High winter, this is David. Can you let me know if you can hear me?


I can hear you


OK. So the question is asking each bus can hold 48 students 570 students are going on the trip. How many buses are needed. So what um what um


type of math do you think we should do, um,


let me rephrase that. Do you think we should do addition, subtraction, multiplication, or division to help us find the answer.


Division


Yeah, that's correct. So we're gonna go ahead and divide


48, 1 sec, let me draw. 48


570 because there 570 students, and each of us can only hold 48.


So in this situation, we're gonna go ahead and


we're gonna go ahead and um solve this. So how many times can 48 go into 57?


What, yeah, that's right. So we can put a one here and then 48 times 1 would be 48. So we're gonna get, go ahead and put that here.


and just subtract that.


And then 57 minus 48 would be what?


11. I see the way you're thinking there, but, but you're so close. You should retry that one, but you're doing really good so far.


Yep, that's correct. So I'm gonna put a 9 here and then we're gonna drop down to 0. Also, while I'm doing this, if you have any questions, just feel free to ask me. Don't be afraid.


OK, and how many times can


48 go into 90


One time, right? So we're gonna go ahead and put a one here and then 48 times 1 would be 48 again. And what is 90 minus 48.


Yup, that's correct. 42. So we're gonna go ahead and put a 42 here. Now over here we have 48 into 42. Now that's not gonna work out and we're gonna need extra, extra decimal spaces. Do you know how to add decimals in here?


Yes. Add one at the top


Yup. So we're gonna go ahead and add here. and then send 50s, 570 is basically the same thing students.


you know, cause 570 students, that's not adding anything. So we're gonna go ahead and drop this back down.


Put the 0 here, and how many times can 4 uh 48 going 420.


OK. So 40 420. It's, I see you're, you're on the right track, but it's not exactly um too cause see we're in the hundreds place. 420 divided by 48.


8 So I'm just gonna give you that, that would be 8, but the question is, is asking, um, how many


sorry, I'm gonna pull it up


buses, are you gonna


got 11.8, but you can't have 11.8 buses. You can't have 4/5 of a bus, can you?


no


So what do you think we should buses are we gonna need?


12, exactly, cause we're rounding up the answer for the problem would be 12 buses. Does that make sense?


yes


OK, cool.


Do you wanna go over some more problems maybe that


your homework or good.


no that was the last one


No, that's all. OK. Perfect. If you have any questions, like if you don't understand anything, just feel free to ask me. I'm not scary, I promise.


thank you.


You're welcome


goodbye


Bye!


Hi Sarah, what's up


Hi I am new here and just practicing this platform


Oh, OK. Is there any questions about the platform that I can answer?


OK


I'm tutoring, so.


Yeah


pick up. OK. Do you want to just do, uh


chili? Yeah, yeah, that would be


a good thing. OK, see you when we get back.


oops was talking with my wife...


any questions I can help you with?


oh ok sorry goodbye how do I end session and thank you for your time


up top, says End Session


I will do on my end


thank you


What is the best way to order rational numbers.


Okay, to start what do u already know about rational numbers?


they contain fractions, decimals and integers


Yes!


The best way is to look at the number with the most value first, and work you’re way down from there


Like 7.79 and 6.79


ok


We know that 7 is greater than 6, so that comes first


We can do that with the tenths place too


Try ordering 5.4


And 5.7!


Are they 5.7,5.4 and 5.2 if I order them from greatest to least.


Yessss!!


Do u wanna try adding in the hundredths place too?


No I think I got it!


Okay greatttt


Anything else or ru good to go?


I am good


Okay great


Have a nice day!!


hello again! I forgot a question!


OK.


Can, can you see it?


Yeah


mostly


I see


OK, cool


So, um


you want to know


Uh, I


I tried doing it, but I got all of the like dobe vertical to holes and all that. I got it wrong except I did get that there were no holes, but


other than that, I think.


Oh, I see


it all wrong


Mhm


The white is what is the wrong answers scribbled out.


OK


give me a second, OK


So the domain


what, what's, what's your answer for domain?


I put


uh


all real numbers, which is wrong.


For units, OK. So, um


so for the, uh, the nominator cannot be zero, right?


Yes


So to


times x^2 minus 25 cannot be zero.


So do I set it equal to 0 and see where it comes out.


Mhm yeah


Mm


is it


yeah


These are the X values that I got.


one second


Where um


where is these two come from?


Oh, wait, wait. Oh, yeah, yeah, yeah, they're right.


Yes, so, because the domain just the X value, so just 5 and 5.


So X cannot be


file a negative


OK.


Mhm


And the, the


the vertical


asy has to be awarded those, so


would it be


because that is what gets 0.


Uh, let's see.


So the value is 5, yeah, mhm.


OK


5 and


and 5, yeah


0, 5802?


Oh, OK, OK


And then


I


I couldn't get it uh


reduced. So how do I find the X and Y.


I couldn't figured out what to reduce.


I mean intercept inter intersect.


Yeah, yeah, yeah. Intercept


OK, so in order to find the X intercept, you need to let Y equals 0.


Do I do that


after I try to, don't I have to do that after I make a reduced form though?


Um


like what, what, what, what do you mean like?


Like, uh, I thought the only way you could


find it is you can't use the original, you have to use.


like.


F reduced form of


X.


Um, I don't


Oh, but, uh, yeah.


I, I think there's too complicated.


OK.


So, because you just need to remember if you need to find X intercept, you just let Y equals 0.


OK


So that will be like


And use the numerator


Mhm


yeah, yeah


the numerator, yeah


And why interceptors let x equals 0 and see what you get.


Uh, I get a


negative undersquare root.


negatives


Oh, wait, wait, over what?


Uh, would it be


uh positive to it a negative too.


Yes, for um


as intercept, yeah


OK.


And why I make them 0?


00 wait, wait, wait, wait, wait, wait.


You, you get um


work for X intercept.


Ex I get you I'll write it.


Where should I


Uh


that's what I, can you see it?


Oh, I see. So,


but let's try. You, you, you try x^2 + 4 is 0, right?


Yes


Is this possible?


well, the first time I did, I got.


Mhm mhm


which that's


doesn't, that can't


Yeah, so it just


non-solut


So there is no exitrocept?


because, uh, a route number cannot be uh 0.


But sorry, cannot be negative.


But there is a why, intercept, right?


OK, OK.


Mhm, mhm. If you put extra 0 and you can find what's the uh one.


That's good. So for


Uh, let's see, for


All right


this


Oh, you, yeah, so you forget that.


yeah, you can, uh, divide by two of both. Oh, and negative, you forgot the negative.


because it's 0 minus 25.


Yes


Mhm. So 2/25, correct.


Mhm. That is the


the correct answer


Mhm


And then


I tried to get the horizontal asceto, but I think it's wrong.


I got


one half


One half.


I don't think that's right.


One half uh.


Yeah.


that would


I think it's correct


You do


Oh.


15, right? Uh.


Because isn't it the coefficient of the.


uh the like the highest powers, it's the coefficient.


ratio of the coefficients


Mhm


OK, so, uh


yeah, yeah, 1/2 is correct.


OK


And then I don't know what to do for symmetry. I don't know what that.


I don't.


I've forgot that


Oh, so symmetry just check this one. let me write it down.


Uh, this will become um


this will become a


so that's what you need to check.


Oh


Uh.


it's even, right


is even I, I didn't try it yet.


Sorry


Yeah, it should be even.


So that's why I would write just even.


Mhm, yeah, just even, because if you put negatives to FX that will be the uh the output will be same, so yeah.


And uh


do you see how I drew my


Mhm.


he said it was awful point for that. How, what did I, what did I do wrong?


right


So you find the X intercept and right intercept, right?


And that is the true point you have to put in there.


That's the first step


Mm, but since there are no excepts, can't it not cross the


X-axis


Mhm, yes


So


would I look here I


or like


uh


Why the sound like I just, you put it right here.


what


Oh no, never mind


Like


like this


No.


Mhm, yeah.


except


uh this is the


The VA


that light


because those are a cro cause there's a Y intercept.


but


the Y intercept is negative.


yeah, it's negative, so


How well then, would it cross the X-axis?


that


hm, interesting.


Let me think


Give me a second


That's weird


Oh, I see.


So, uh, there you go.


Let me drop another graph for you.


We know the uh the V, the asymptote is X equals 5 or -5, right?


Yes, 5 and 5.


Mhm


So


when it become


5, you can see uh


uh the uh denominator when there will be uh a very, very small, right?


Uh


because that's uh


something like uh


you can see when X equals 5, like uh approached by the denominator will be very, very small.


OK.


because here is approach to zero, right?


x^2 minus 25 approach to zero. So the number will be very, very small.


OK


that will become uh infinity.


state


Good


So it will look like


this.


And it does not cross the x-axis.


Mhm, yeah, because uh we know there is not X intercept and when X becomes very, very large.


This


function will be very, very small, right?


The output will be very, very small.


Uh, yes


So it will like uh approach to


zero at some point, but never


become zero. So we'll be like something like this.


Uh, so there are 3 separate lines. There's one in the middle too, so I can get the why.


And you know why in the service, like a negative.


Yes


Yeah, yeah, that is it


2/25, I forget, but yeah, yeah. And also we know


uh this one is like uh event, so that is symmetric.


So is the parabola a U?


Yes, correct


Mhm


So it does technically cross the y-axis. I mean, the X-axis.


At the x-axis, like, uh, what do you mean like excesses?


What would you make the


point, it crosses.


doesn't it?


Because, because Y goes negative to over 25.


Doesn't it go like, like uh


That this point


does it go like this?


Oh, sorry


Like


does it go like


that?


Hm


that in


Or does it go


some


that is something you need to check.


If you put like, I mean you can try one, right?


huh


Hmm yeah


it will be go like this way


Oh,


You good, you good


So


but doesn't that make it odd?


yeah


You


that's even


because it goes opposite ways.


because so um


if the graph looks like um


this is


or some somehow like this.


The left side is equal to the right side.


But the graph


So this even.


yeah, but the graph if it looks like this one.


that is


just odd


because um


yeah.


The pieces go opposite ways?


Yes, yes


But if there are 3 pieces and 2 go the same way, but 1 goes the other way. Does that make the whole thing odd?


No, did, um, so if you, you want to see that even, you just need to check the left and the right.


The left side is right here.


Oh, OK, OK.


The right is right here. So left


is right


equal uh the left side is the right side, that means that's even.


So the, it is even


Yeah, it's so simple. Don't overthink it.


Just left side, X, right side, that even.


OK


or you can add the formula I just put down where I uh top.


At the top


right here


Uh.


Let me show you how to do that


Uh, we put F X


where + 4.


negative X


2 minus 25.


is exactly


same as the original one.


you see


uh


It's just affects.


So I don't think uh


look at the graph is a good way, but


that's one way, but um


the most efficient way is


to what


what I did, right, right here.


OK.


that


so it can guarantee you


you will get it right.


I think that is it. I think


OK


now I still have any more questions.


Uh, then I just end this session.


Uh, yes. Bye


bye


Hello!


hii, Alex


I want to practice and study objectives 11 and 12. I kind of understand the concepts, but I get confused sometimes, so I need to improve in certain areas.


I’d like to go over the problems from the PDFs in order, starting with the Objective 11 PDF.


I want to work through the problems from the first page onward. Could you also create new problems that are exactly like the original ones—same concept but with different numbers—and make two versions for each problem so I can get more familiar with them? https://example.com


do you have a screenshot or anything


I can't open the pdf but you could try to upload a screenshot of it on here


You have to click the link twice


and copy and paste


okay, I think that works


so do you want to go over those questions


Yes in order but diff numbers etc but exactly like the problem


okay, I could try to find problems similar to those


you can use chatgpt


okay I got some


Ok


lmk when you've put them on th board


ok


ok thanks


do you wanna do them together


Yes


so I have to find what equals 15 but gets you 2


yea


so its (x+5)(x-3)?


yeah, exactly, good job!


do you wanna do them one by one?


ill do #8 since i only want to do 2 of each for the problm


okay


exactly, you really understand this topic :)


lets skip to page 3


number 25


give me a sec


Ok


okay I got them


do you want examples


thanks


is that enough


ok


or should I get some more


yep


is enough


so we do a tims c?


what's that again


wait wiat no


you could use the board if you need


I need help


i cant find three numbers that get u 48


with which one


okay, let me explain


48 is the sum of the numbers after u multiply and add, right?


so it doesn't just have to be the multiples of it


with factoring trinomials u find 3 numbers that equal the middle #


so lets break it down first


k


so if it is 9, the constant would have to be what?


nvm i get it now


oh okay


next one


the one on the right?


okay


mhm


you sure it would be +?


minus


yeah, good job!


now 26


actually no


lets go to page 4 problem 15


do you want examples on that?


do you understand the questions?


I'm gonna be back, give me a sec


ok


yep


just write the answers when you are done :)


Ok


I need help


for the gcf


2 for the first one?


yea, exactly


but idk about the second one


the second could be by itslef


x?


it has to match tho


oh nvm


you could make put -1


just tryna make sure you understand the problem :)


does it all make sense?


isthis right?


yeah, that's right, great job!


alright, next one!


okay


next page?


No i'm doing the 4x problem


ohh okay


so its 4x^2+4x+7x+7?


you can clear the board if you want


is 4x and 7x positive tho?


yeah


oh no its a neg 11


yeah, so it would be negative


is this right?


yea


make it -1?


yea, just like the previous one


lets do page 6


yea, good job!


give me a sec k?


yep!


I'm back


ok


let me go to page 6


okay, I have to get some examples


Ok


did u understand the problem


Oh now I can see the problem


oh okay


just tell me if you need anything


or don't understand


sorry, I think the problem has a problem


does it have a mistake, or am I mistaken


I don't think so


Are you talking about the first one?


yeah it may


yea


were u able to solve it?


No


make sure chatgpt knows what kind of problem it is


its factor by using subtitution


yeah, it does, but i think it was tweaking a little


so lets just skip the first one


Ok


so far its: 2b+1b+10b+5 right?


yeah, that's right


kk


yeah, exactly


now you have to do the substitution


is the answer (x-4)(5x+6)?


not quiet


oh


can u show it on the whiteboard then


this?


yeah


so that would be x + 6 right?


mhm


what about the bottom part


can I ask where u got the 5 from


on the second line


oh nvm


its 2


just make sure to pay attention to that next time, other than that, there are no other mistakes


yeah, that's it


ok another one


okay let me get some


i can do the 4(w^2


problem


yeah, okay


is it 4x-4x-1x+1


ok


need help w th gcf


of which ones


the 4x-4x-1x+1


so for the first two, you could put 4x, right?


ohh i see


that would make it x-1


but the 1 infront is negative and the 4 is pos


see


so the first one would be 4x(x-1) as we said


and for the second one, you could make it -1 like the previous ones


oh i see


okay


no we have to substitute


would it be (w-1+4x-1)?


no it would be (4(w^2-1) -1)


ohhh ok


you get what I did right?


yeah


would i distribute?


and then subtract the one at the ned


end*


wait write this on the whiteboard so i can solve it on there


which one


the substitution part u just typed in chat


is that good


ok


this?


try not to forget the squares


that should be right


what about the other part


so let me write it on the whiteboard


the last problem had squares and we didnt square the final answer


oh nvm thats bc it was on the outside


now the (1x-1)


okay


now you can simplify that expression


yeah


so the final answer is (4w^2-5)(w^2-2)


yeah thats it


good job!


now we can work on objective 12


the one that i am struggling with


give me one sec to get the link


here it is


okay ,give me a sec to open it


kk


okay I opened it


kk!


okay so do you want me to give you examples about the first page


mhm


thanks


do you want some mor


more*


or will that be enough


its good


okay


so 81 becomes 9


yeah


yeah, that's it


yep


so (10p-7)(10p+7)?


yess, good job!


now a problem like 3 & 4


okayy


thank you


you're welcome :)


i will brb!


kk


back


so 8y becomes (2y)^3


yea


yupp


but its difference of cubes, so wouldn't that be different?


This is the stuff that confuses me lol


so hold on, let me try to explain it


ok


so the formula for difference of cubes is (a−b)(a^2+ab+b^2)


and the form of this problem is a^3 - b^3


does that make sense?


can you show this on the board


oh yeah i forgot


yeah you're right


wait and these are problems from 3&4 page 1?


yeah


oh problems 3 and 4?


on page 1?


yeahh


lol


ohh I thought you meant the page number


so sorry


its ok! lol yeah i figured


let me find ones for those problems


Ok!


I'm gonna brb, is that okay?


yes!


kk


kinda need help  this one


when you come back


I'm back


which one again


the firsy pn


that one


give me a sec


okay so you see how both of them are divisible by 5?


yes


you could take five out of both of them and then simplify


does that help?


Wait can u show this on the board


okay


did you get it?


I need to see it solved on the board


I just wrote how it goes on the board


let me refresh


kk


still dno't


it might be my wifi lagging


I can just type it in here if you want


should I?


Sure


(45/5y^2-5/5) is what you get when you divide them both by 5


you can try simplifying it


ok


so it becomes 9y^2-1


yeah and then we could just put 5 out of the parenthesis right?


mhm


so we only put the number on the outside if we used it to divide?


by the same number 2 for the binomials


thats what you could do if the first coefficient doesn't have a gcf


yeah basically


you know differences of squares right?


it changes to 3?


and not rlly


yeeh


yeah


because the formula is (a^2-b^2)


so its 5(3y-1)(3y+1)


exactly


do you get the concept?


ok next one


okay


but the power of the first one is 4


instead of 2


i thought it changes to 2 since its divisable by that


even if you divide it, it becomes 2, because like 81, we don't just say 3^2 right?


I don't know if that makes sense


right


like its supposed to equal the original term, and (5x)^2 doesn't equal 25x^4, does it?


yeah, but it would be 25x^2, not ^4


ohh ok


so its 5x^4


yeah


and (9)^2 or 4 as well?


okay so for the first term, it would be (5x^2)^2


why two 2's


cause when you distribute the powers will add up


and that would make ^4


oh ok


and then the 9 is (9)^2?


yupp, that's exactly it!


yeah i think the exponnet part is what trips me up too


now 5 & 6


okay


problems, right?


mhm


kk


can u give me one like #4 since its a fraction


problem 4 on page 1


Thanks


so that one becomes 2/3x^2-1/4y^2


yeah


but you wouldn't keep the powers cause we already eliminated them by square rooting


I know


yah


so its (2/3x+1/4y)(2/3x-1/4y)?


yupp


now the other ones


I think this one was easy for you, right?


Yeah kinda


mmk


so the first one becomes


yup, that's right!


now the second one


yea


gonna use the bathroom one moment


kk


ok sorry about the wait i'm back


so does it become 4^3-5^3?


no ur good


you could say that, or you could square root them


ok


like (8a^3)^2


ill do that, it makes sense


yeah


and for 25 i can do (5^2)^2?


wait no ^4 and ^2?


you could do (5b^4)^2


yeah,


yupp


so it becomes


yupp, exactly


I have a random question


sure


do you like kpop or BTS by any chance?


I like R&B lol


but i know who they are


oh okayy


I mean who doesn't atp lol


loll yeah theyre worldwide


i have a friend who listens to them


BTS or kpop


kpop


i actually never heard of BTS


which groups


i searched them up and they remind me of fifth hrmony


with the diversity


do you know gnarly, the trending song


yes


yeah lol


i listen to SZA


yeah they are the artists that made gnarly


i have a friend who listens BTS


ohh i didn't even know they made that song


and yeah i love BTS


anyways, we got off track lol, lets continue with page 2


lol yep


so one like #7


kk


#7 and 8


Gonna get some water and then ill be back to work on these problems


back


so find the gcf


we can continue with the questions


is it b>


what


for gcf


oh yeah its b


is it 2?


for the second one


wait, so you would put a^2 out of the parenthesis


for the first one


ok


yep


for the second one, is 36 divisible by 4


yes


then you could use 4 as the divisor


kk


is this correct


ohh we take out a^2


not b


but i thought u take the smallest exponent out


for the first one, you should put a^2 out of the parenthesis, instead of b


you get it? cause we have to make them equal


yepp that's the answer


ok next one


yea okay


ok soo


what can you take out of the first one


make the gcf 9 for 36


wait no


that's the second one


ok


first one would be 1


and that would be -9


nvm


you sure it would be 1?


im tryna get them to match


cause you can also take out variables


oh x


x is basically 1


so you could write the first one as (4x


bro I cant typee


sorry


lol its fine so x would be on the outside


yeah its on the outside


so does that equalize the sides?


36/9 is 4


yeah


so how would u write it?


(x-9) cause the 9 is negative


oh right


so problem 9 now?


yes


kk


one or two problems


we can do one


okayy


gcf is 3


oh wait no


for which one


its a^2+3a+9


so what's the result


so it'd be a^2+3a+3a+9+4b^2?


but yeah


wait can u write this on the board


sure


so basically find the gcf excluding 4


and what would be the factor of the first three terms


yeah that's what it is


ok


is this right?


you could divide the first two terms by a


not only 1


you don't have to write the 1 if its in front of a variable


so its 1a(a+3)+3(a+3)?


yeah


and what would it be when simplified


yeah and you can remove the 1


now page 4


and that would make it (a+3)^2, right?


waitt what


now im confused lol


oh yeah i forgot about the 4b


cause look, if you remove the one, it would become (a+3)(a+3), right?


you could put that as


wait can u rewrite it out with the 4b^2


kk


can u see it


mhm


ohh i se makes sense so thats how the answer?


the answer, you could write it like this


yep


ok now page 5


two questions for this page?


okayy


so the answer is


yepp


can you tell me how you got it


just simply


u do 4 times 4 since its squared


and then 4 times for a(b) and then 1 times 1 since its just c times itself


yeah


now the next one


so it'd just be (m)^9?


what is the gcf of 9 and 12


so (m^3)^9?


no, you would divide both of the powers by three


so its just m


n becomes 4


no it would be m^3 and 6n^4


do you want me to explain how


uh yeah


yeah i said that


so we are trying to put 3 out of the parenthesis, if we do that, m would be to the third power, and because 216=6^3, it would become 6, and n would be to the fourth power


so its( m^3-6)


yep


mhm


oh right its 4


you know the difference of cubes formula?


yes


can you type it out for me


so its m-6


and then m times m is just m^2


we need the formula to solve the problem


is it this?


not really


oh


does this explain it


yeah


and then that is the next step


oh.. this looks diff


it is because it is not simplified yet, and we are using the formula


ohhh ok makes sense


so its m^6


so how would u write the final result after the last step


when you distribute all the terms are multiplied


like in the first one it is m^6 right?


Alex can u write it out on the whiteboard


kk


soo


can you complete them for me


So would it be 6nm^12


no because they are not the same variables


it would be 6m^3n^4


because we are just putting them together


do you get it?


ohh ok


can you complete them now


on the white board


umm im kinda confusing


on which part


like all of it


so first, you know how its a^3-b^3


we are tryna get a-b, and that's why we divided both sides by 3


wait can u write it out simplified and then ill see if i get it


based off of the formula


the final result?


yes


okay


the red one is the answer


ok let me look


i thought it'd be 3n^2


oh nvm


which one


oh okay


ok this makes sense


did you understand it better now?


yeah


so are we good for this question?


okay, then lets go to the next one


kk


oh wait so which question are we doing next


we are doing 12 & 13


mmk


one for each?


mhm


if im confused then 2


so what's a and b


yeah that's the a+b part


actually I have to go, I'm going to get in the shower. I will do this problem when I get back on. Thank you so much for your help!


i will favorite you as a coach


so you can see ifi request


thank you for listening and paying attention too


hi Alex what can I help you with today?


How do you solve 2m=-6n-5


are you sure you typed that in correctly?


Fully sure. i dont think we are solving but rewriting to solve for m


oh ok, i was confusing because there are two different variables haha


confused*


to solve for m


divide both sides by 2


since 2m is already isolated we dont need to move things to the oter side?


correct!


the m term is all by itself on one side


therefore all we have to do is divide


can we leave the answer like that?


yes, but keep in mind that it can be broken down into two different terms


is it nesscearoy because my teacher left it like that for other equations


if your teacher left it like that, then it is definitely not necessary


both are correct answer at the end of the day


answers*


ok now 4n-6m=-2


so this time, we need to isolate the m term, so we need to subtract 4n from both sides


next, to solve for m, we need to isolate m just like we did earlier, so we divide by -6


in this one, the solution can be simplified even more by dividing every term by -2, and although i am not sure if you're teacher wants that, the numbers are just smaller and look more simple


ok now 10m+6n=12


last one


of course


you should do this one with me


what do we do first?


good so far?


nice job, just don't forget to add -6n on the left side


right*


sorry


now isolate m


good job man


you could simplify it just like the previous problem, but that is also correct


do you have any other questions?


is it ok if you repeat a problem that i forgot to write down


sure thing


what's the problem?


did it!


ok thats all thank you


no problem man


any time


have a great day


goodbye


you too, bye!


Hello Anna


Ben , sorry I’m in this geometry chat because I really need help with drawing/ labeling a pie chart for my homework and I have been 2 hours waiting in the statistics section and no one has helped me , I was wondering if you would be able to help …


Sure Anna. I can definitely help you with this


Do you have the question?


Yes I can upload the information on the board


White board


Sure, go ahead


That is what I have so far


So, is it the first question right? Drawing the pie chart


Yess I think so


Can you tell me if you are aware of the steps?


I still need to do 4 percent , 22 percent , 26 percent , and 9 percent


Yes I am , it’s just that since I don’t know how to really use the protractor I am having a super hard time labeling the pie chart


But I know how to do everything except that


Ok, so you have flying done which 140 degrees and is correct. So great job there!


Now, for Telepathy what is the degree?


That's right. So, now how would you plot this on the chart?


Im not sure to be honest, that is what I need help with lol 😓


To plot 14 degrees, you can keep the base line of the protractor and make it coincide with any one of the lines you have drawn for the flying portion.


Does this make sense to you?


Not really , can you please demonstrate it to me on the whiteboard if you don’t mind …?


yes - are you able to see?


Yes


So how do I know where 14 is at …


protractor has angles from 0 180 degrees.
there will be markings at intervals of 10 degree with smaller internal marking of each 1 degree


I am drawing below your sheet also. Please check that


Are you there?


Like that ?


Yes, something like that.


So that would be 4 percent right


But can you check for me once if the flying angle 140 degrees on protractor?


It looks slightly more 140 degrees


yes so the 14 degrees for telepathy corresponds to 4%


Oh , I just estimated but I’m not too sure , it’s my first time using a protractor and learning this ….


ok no worries - I understood


Yeah , that is why I need like extra help correcting or learning how to place dots to make the lines equal to the percentages and all


Yes, there might be confusion during first time and that's what we want to learn and I will explain you


Let's start again:

So yeah, using your protractor now try measuring 140 degrees - there will be clear markings for the degrees


It 140 degrees on the big numbers of the protractor


ok fine.