Okay, so open your compass to any length, needle on the R, and intersect your line a at two points


can you do number 2


Did that make sense?


That gives you A and B


ok


Do you know where to go from here?


no


It is the same as the instructions you have


Look at Step 1


You have your A and B now, right?


yeah


Wait, did you understand how did we get A and B?


not really


No problem


were you able to do Step 1?


Were you able to do Step 1?


Not on my own


Okay, do you know how to do it now after someone has helped you?


Okay, no problem


Can you tell me what you are thinking tho? When you look at Step 1, you have the instructions on the left. We can talk thru what is not working, okay?


okay


Okay, so we have the exact instructions on what we need to do, but why are we not able to do it?


I just don't really understand what the words mean


Okay, cool


So, do you know what a perpendicular is?


Is it like a up and down line


Not exactly


Not always


So, for the instructions that we have our line k is a line that goes from left to right, yes?


yeah


Let me know if I stop making sense at any point, okay?


Okay, so for k, when we draw a perpendicular, the perpendicular is indeed and up and down line


okay so for number 2 the line would be left to right no?


Yes


Both these lines are perpendicular to each other


ok


And perpendicular means that they are at 90 degrees to each other


So, they don't have to be up and down or left to right only


They can be diagonal


okay


What is important is the angle between those 2 lines


Cool :)


So, our goal is to draw a perpendicular thru lines a and b in the questions


Okay


Do you have a compass and notebook right now?


yes


Okay, since you have already done Step 1, let us try to do Problem 2 now


Look at step 1, what is not making sense there, and let me know


okay so I would start on point r


Yes, you start at R


Place your compass needle at R


Open your compass to any length, but keep it consistent for every step


As in you can change between steps usually, but not while you are doing one step


So when marking A and B, it needs to stay the same


So, needle on R and mark any 2 points on the line


would it look like that


Not really, those arcs have to be on the line that you are trying to draw the perpendicular on


Try again and let me know, but you are doing good!


okay do I draw the line first


No, you have the line


The pencil marks that you made, they should go on the line


That is it


okay


Let me know when you are done


like that?


Yay! :D


They can be smaller, but this is what we needed


Okay


Okay, do you know where points A and B are?


no


Where our arcs intersect the line, those 2 points are A and B


hi


hello


i


hii


I need to do my math homework


sure


can u put it on the board


ya


u can just type it out its fine


Ok 144 books into 8 equal stacks how many were in each stack


ok soo all u have to is


divide 144 by the 8


can u do that


Ya


ok


There


what did u get as the answer


what


7,remainder 64


thats not right here lemme show u


Ok


the answer is 18


get it


Yes


How much money


whats the question


Is 1\2 of 5.80


Dollars


ok just divide 5.8 by 2


then u have your answer


Hi Maria


hello


can u help me with a hw assignment?


Sure. Can you upload the first question on the board?


We could start with 2(a). Any guess?


Did you learn what "lim" means? If not, I can explain.


In any case, "0" is correct.


yes, I know what lim means, what I'm confused about is for the + and - after the number


The "+" means "limit from the right". "-" means "limit from the left".


In other words, lim x→-3 means the limit of f(x) when you approach x=-3 from the left.


For example, when you look at x=-3.2, -3.1, etc, f(x) gets closer and closer to zero.


Actually, "from the left" or "from the right" only apply when the sign is *after* the number. For example, 2(d) has lim x→-2+, where "+" is from the right.


For 2(a), the negative sign is before the "3". So lim x→-3 simply means the limit as you approach -3 (from any direction). Either way, the limit is zero.


Would you like to try 2(b) ?


DNE right?


Correct. You got it.


2(c) ?


It's below the x-axis, so it should be -5.


oh yea


For 2(d), you approach x=-2 from the right (+), along the curve I drew in pink color.


Exactly.


e. would be -1


Right.


And for 2(f), you approach x=-2 from the left, along the pink curve.


Yes.


would g. be 4 too?


2(g) is tricky. The limit from the left is -1, but from the right is 4. Because the two limits are different, we say the limit does not exist (DNE).


I meant, limit from the left is 1 (not -1). My bad.


oh ok I get it


and the h is 3 and I would 1


Yes and yes.


Did you want to do 3(a) ?


For 3(a), the limit is below the x-axis, so -1.


It's difficult to see, because your graph does not show the negative signs for the y-values.


Sorry. I was looking at the wrong graph. For 3(a), the limit from the right is 1. You were right.


3(b) ?


3(b) DNE is correct.


For 3(c), you look for the limit at the open (white) dot, not the black dot which is f(2).


3(c), "1" is correct.


3(d) DNE. You got it.


3(e) "2" is right.


3(f) is also right.


3(g) is tricky, because the limit does exist. The limits as x→0 from the left and from the right are both "1" (open white dot).


3(h), 0 is correct.


Now it's all correct.


Anything else I can help you with?


can u check this one


OK. I'm checking...


I'll put blue checkmarks next to correct answers.


1(i) DNE is correct.


At x=2, the limit from the right is 1, but there's no limit from the left. Because the two limits are different, we say the "limit" DNE.


can u help me with one more thing?


Sure.


I see question 5. I'm reading...


Any guess for 5(d) ?


I don't know how to do d and e


For 5(d), we want g(x) to increase on -5<x<-3. I'll show you.


Where g(x) increases will be shown in blue, and where it decreases in red.


As you can see, g(x) increases on -5<x<-3, and also on x>1 (blue color).


oh I get it now


Awesome!


Any guess for 5(e) ?


no


5(e) tells us that the limit from the left is greater than the limit from the right. I'll draw two open (white) dots at x=-3.


y=-2 will be our limit from the left, so I'll extend the curve to the left of (x,y) = (-3,-2).


And y=-5 is our limit from the right, so I'll extend the curve toward the right. Finally, -2 > -5.


so thats how the graph should look like?


Yes, it's one way to answer the question.


I just noticed that the graph must satisfy "all" the conditions at the same time. Let me adjust.


We only satisfied the conditions one at a time.


Can you give me about 3 minutes to fix it?


yes


I think it's complete. I'm checking it...


Does it seem to meet all the conditions?


Looks like it works. What do you think?


I think it does


That was not easy!


That completes the problem, and it's all the time I have. Any quick question before I go?


no that's all


thank you


You're welcome. Enjoy the rest of your day.


you too


Hello!


hii


did you need help with any more problems?


yess  can you help me solve this


sure!


determine the length of the missing leg and hypotenuse of each the special right triangles


I'll draw the picture now


okay then!


so okay do you know what are the special right triangles?


they have a 90 degree right


not exactly


all right traingles have 90 degree angles


but these are the special right traingles


i put the image up for you


okay


it basically describes the ration of the sides of triangles with these angles


ratio*


for example


in the 45-45-90 triangle


which means the other 2 angles are 45 degrees each


if the 2 legs are length x


the hypotenuse is length x√2


ok


so lets try to aply this


so can you tell me which type of special right triangle do you have


looking at the chart?


just focus on the angles


30-60-90 triangle?


no nice try!


idk man


look at the angles in you triangle that you drew


okay


also what do the angles in a triangle add p to?


correct!


so is the other one 45


yeah exactly lol


because 280-90-45


my bad


yup perfect


so looking at the angles


we have a 45-45-90 triangle


hold up my computer is about to die I'ma get my charger


since we have 2 angles that are 45 degrees


okay then


so since our triangle is a 45-45-90 triangle, it follows the pattern shown in the image


with sides of ratio: x, x, x√2


right?


I'm back


okey then take a look at what i just said and let me know if you understand?


okay


but mines only has one side


which is 5 quare root 2


thats okay, remember this is just a ratio


so lets look at it


k


okay lets say that 5√2 is our "x"


ok


what would be the next leg of the triangle


following the ration


ratio*


x


which is?


no remember we said that our "x" we will set to 5√2


since this is one of our sidelengths


that as given to us


just think of it liek this


the ratio just shows that if we had one side


what would the other sides be in relation to that one side


so if x was 3


the other side is 3


the hypotenuse is 3√3


right


oh


no you are right


the other leg is 3


and the hypotenuse is oops


3√2 i mean


oh okay


but yes you are correct!


follow with me so far?


wait how did you get the 3 tho


its just the side i started with


the idea is that


you can plug in any sidelength value for x


and this rule can tell you what the other side lengths would be


so IF x was 3


the opposite side would also be 3


and the hypotenuse would be 3√2


since its x√2


if x was 3


its like a pattern


so then for my problem it would 5 for the other two sides?


close!


so first look at where your side 5√2 is


is it a leg or the hypotenuse?


leg right


yes


because Infront of the right angle is the hypotenuse


so then would it be an "x" or an "x√2"


since its a leg


not the hypotenuse


an x


perfect!


okay so look below the triangles


i set up the ratios next to eachother


so if x = 5√2


the other side would be...


5squareroot 3?


mb


yes!


the same value


since they are both "x"


wait is it 5 quareroot 2 time 5 quareroot 2?


lets look at that!


okay so then, couldnt we also break 5√2 down into 5 times √2?


wait what happened to the 5 Infront of the 2?


so when we say 5 root 2


that just means 5 times root 2


so i just seperated the 5 away


so you can see its 5 TIMES root 2'


but isnt there two 5s?


no not exactly


yeah look you put it here


can you show me where?


ooohhh


okay so let me explain that


please


we know that x = 5√2 right


ok


so to find the hypotenuse of this


we dont need more than one x right?


since this is just 1x TIMES √2


and we have that 1x = 5√2


so we need to find (5√2)(√2)


which is what we are doing right now


understand?


It makes makea bit


alr lets continue then


okay so we have that (5)(√2) = 5√2 right?


so when we are multiplying these together its the same as 5 times root 2 times root 2!


right!


so what does it mean when we multiply something by itself>


squaring right?


so √2 times √2 is equal to (√2) squared!


well the square here can cancel ou the sqaure root, since they are just opposites!


right?


yes


okay so then we are left with just 2 there


then we still have to multiply by 5


so whats 2 times 5


yup!


so that means that x√2 is equal to 10


so our hypotenuse is equal to 10!


and out lef is 5 root2


perfect!


just remember this can be much easier when the leg is an easy number like


jsut plain 2


then if x = 2


what would x√2 be?


okay y


hello?


would it be 2


the other side length would be 2


since its also x


but what would x√2 be


this would be the hypotenuse


no nice try tho


it would just be 2√2


think about it


ohh


if our leg was 2


and we need to get that times √2


its just 2√2!


so this works for easier ones


so you try


oh okayy


what if our leg is 4?


whats the other leg?


and whats the hypotenuse?


yes thats the hypotenuse!


what would the other leg be then?


since its also x


4 root2


no remember x is just 4 right


since thats the 1st leg


so x is 4


so the 2nd leg would also be x


which is 4


so both the legs are equal


and the hypotenuse is x times √2


got it?


ohh okayy okayy


alr i have to go now, but you can apply this same idea for the other type of triangle too


its just


find whatever side you have


plug it into the diagram


find out what x is


and then use that to find the other sides


best of luck!


wait


Hello


Hello! I am Mark!


My name is Liam


Although it says i am Alex


Okay nice to meet you Liam!


Elara is my mom


Okay!


what do you need help with Liam?


So can I send a picture


yes you can upload a photo


It is here


nice!


What question are you stuck on?


or do you need a review?


In 6 do we have to solve the exponent on 9 or do we leave it there


And solve the p


I think you have to solve the exponent!


other than that, you are good!


I asked this because pemdas


Parentheses


Exponents


yes, but you cant add X and Y


So


so you have to multiply


You do this


but exponents come before multiplication


so you are right!


But aren’t we supposed to solve the parentheses first the rule pemdas says we have to follow that


Mark?


yes?


What I said


but the parenthesis is unsolvable further


Pemdas


it is in its most 'solved' state


No


You can multiply the 9^2 by X and y


we don't know the values of x and y


that is why we express it as x + y


That becomes 9^2x and 9^2y


Mark


yes you are right!


you can solve it that way too!


how can you simplify this further though?


But then we solve the e


81x and 81y


yes that is right!


good job!


And the sign is add


yes that is the final answer!


I’ve done this


I’m in fourth almost sixth


I do this a lot


In extra work


nice practice helps you get so much better


From my mom


I like this site


should we move on to the next question?


Yes


okay!


Can you undo the other work


what do you need help with?


yeah sure


The next one is 12-8x


Good?


that is correct!


good job!


Does the exponent on ab count for both of the variables


Hello, I am, are you there?


I


I mean Mark


This mic kind of bums me out


Mark?


Hello?


Are you there


Hello!


hello


may you help me with this problem?


I will try.


ok


This is what it looks like


The question asks, ' Point Z is on EF such as that ratio of EZ to ZF is 2:3 on the coordinate grid shown. What are the coordinates of point Z?


From what i've been taught, I'm supposed to add the two ratios, a/a+b


Where is point F


and E is at (2,-2)


I am not sure what you mean about adding the ratios.


so I add the two ratios, and the dividend is the first ratio


so 2/5 is the fraction


ohhh


I think that might be it.


Yeah that looks right


OK, actually it is late here, so I need to go.


Oh no worries


Thank you for the explanation tho!


You are welcome.


Have a good evening.


Thank you you too


im stuck on this equation ill write it out


ok


now whay


what*


i was working on this with a past coach but they had to go and i was still confused


past this part


uhh


is this the original problem


or is this the version they simplified


yepp


i hve to simplify complex fractions


circled in the red is the problem


so basically you can start by multiplying everything by xy


im gonna write it on the board


waiy


the other parts are what the other coach did right


kk


did together


ok


is it like


a fucntion


or is it just that


idek im learning this befor school starts


did they give u anything else tho


cause if its not a function I think this is the most simplified verson


Nope


i just know i simplify


i dont get this


u mean my work


nvm Sarah


yeah i dont


ok lemme write it out


i dont under this


"xy"


why isn't it yx on the bottom


its the same thing cause xy is just x multiplied by y


this is confusing


basically I just multiplied both the numerator and the denominator by xy


oh ok i think i get it


ok


is there anything else u need help with


and it quals y+x/y-x?


yea


because


if u just divide all the individual fractions


kk


that's the answer u get


can u heplp me with another equation


yea sure


do you want to erase everything on the board


do u still need it


here


is it root 50


mhm


2(25) is better


10 times 5 = 50


o


cause 25 is a perfect square


so the u can take the root of 25 and move it outside the square root


how do yk if anumber is a perfect square


if a number is a perfect square it means its the result of a number multiplied by itself


5 square root 2


you can't take 25 out because you have to take the root out of it


the root of it


ive never solved this so i wouldnt know lol


so whats next


then 5 root 2 is your answer


because u can't take 2 out


oh i had that


i thoughtu said it was wrong


I thought u wrote 25 root 2


sorry


i did have that


and then i wrote = 5 root 2


yea sorry


I didnt see that


18 + 8


both square root


ok


so you do the same thing with this problem


you take the square out


8 turns into 4?


yea so


oh  u write it as


18 suare 8


its 2(4)


you can take the root of 4 outside the equation


do you get how to do that


can u show me it im a visual learner


ok yea


i cant see past that my screen small


oh


which part


all of it?


the side like with the square root (2)(2)


its basically just 2 to the second power in parenthesis multiplied by two


which is just equal to 8


so 18 square root 2?


no


is 2 outside the square root and 2 inside


2 root r


and then for the other one


u might have to scroll down a bit


I tried to make it bigger


answer is 5 square root 2


yea


my screen is so zoomed in


for some reason


oh


yea mine too


could you still read it


i need help w this


ok


and then you can take the square root out


like this?


uhh


not quite


here lemme write it


the exponent two kinda cancels with the square root


so you can take the two out


k


wait


is that a multiplication sign


anser is 36


sorry wait


I thought that was a addition sign


is it multiplication


multiplication


mhm


oh sorry I did it wrong then


since its multiplication


you just multiply the two numbers inside the square roots


do you still need help


I have to go for a bit


i have another one


but i can request a new session since u have to go


thanks in advance! :)


Hello! How can I help you today?


Hi! I am working on a confusing assignment about applications of quadratic formula and was to get some help answering the questions and getting a good overall understanding of  the topic. I can put the first question on the board if you would like.


Okay.


Alright, I will put the question up then, just one second please.


Okay, can you see it at the top?


Yes


ok, do you mind if I move it to left a little so I can see the whole picture?


No, go ahead.


okay thanks!


Okay, are you able to see the whole thing still?


Yes.


doke doke


Do you have any idea what to do for the next steps or would you like me to show you?


Well maybe we could subtract 56 from both sides for the first step


Very good guess, but since T represents the time and h(t) is the height. We first have to plug in the 0 to replace h(t). Do you understand why?


Not really, sorry


Okay, for the problem, it requests for the time before the ball reaches the ground. Since h(t) is the height, t is the time, we would need to plug in “0” as to represent the ball on the ground and figure out the “t” value to find how many seconds it takes for it to reach “0” or the ground level. Does this clarify the question for you?


oh yeah, thank you


so to solve it we first plug in 0 for t but then wouldn't we get 0?


Yes, there are more steps. We would have to plug “0” to h(t) since it represents the height.


so we plug in 0 for h and t?


No. You can look at the whiteboard if you want. I wrote down the steps.


oh okay now I get it


so then we subtract 56 from both sides?


No. Since we don’t know the value of T. We have to use application, or different methods to solve this.


None of them are common terms so we can’t subtract 56 due to the “t” value. Do you understand?


yeah


Very good. Do you know the next step?


no


Okay. We have to plug out the T so that the value of “0” would equal to t(-16t+56). The value T and (-16t+56) will separate into different factors. Do you understand?


I will write this on the board as well.


ok


Do you see it?


yes


Do you have any questions? Or do you want to move to the next steps?


we can move on


Okay


We have found one of the answer, which is 0. Now, we continue with rest of the equation.


You can solve the equation I have written out, and I will be here to guide you if you need any help :)


ok what do I plu gin for t to solve it though


You would have to subtract 56 from 0.


i got t = 3.5


Very good. That’s your answer!


okay, thank you!


Okay. Have a good day!


you too!


hey, how are you?


good and you


doing great. What would you like help with?


my math homework that I need to do I have two math homework assighmints


ok


can you send some images?


sure but I am on computer


thats fine.whatever is best for you


hold up sorry need to get on the camera


that's fine


that good


could you zoom into it?


what is that textbook called? maybe i have a copy?


its alright but still blurry


Saxon math student edition lesson 8 page 42,43


do you?


give me a second trying to find it


I'm listening to music to focus


thats ok i do that too


I'll give you a second


apreciate that


is there a number on it like under the name?


maybe like 5/6 or something like course 2?


yes it's course one


Found it!


yes!!!


Let's begin!


ok


question 1


in written practise?


yes


it is lesson 8 page 42,43


ok, how do you think you should start?


reading what to do


a useful tip is to find what the question is asking you to do and breaking it down


could you do that and explain it to me?


Don't mind the loudness.


done?


that's ok I can read your voice chat the noise won't bother me


it says in a auditorium 25 rows  18 chairs in a row and asks how many chairs in the auditorium


yes thats right


but how would you calculate it?


I'm reading it but it doesn't give clues if its add subtract divide or multiply


hmmmm I see


in this case you should try to imagine the situation to decide


if there is 25 rows  and 18 chairs in a row I believe to add hmm if I'm wrong its alright


very close! but not quite right


think: if there is one row with 18 chairs and that is one row. Then there are 25 rows meaning there are 18 chairs 25 times what would it be?


multiply?


Great job!


cause you said times in your sentence


yeah i guess but could you still imagine the situation and come to that answer?


yes


thats excellent


so I know 18 x 25


I multiplied and 450


thats correct good job!


yay


question 2


just a quick question - how many question were you aiming to get through right now?


*questions


maybe to sixteen if its ok to you or if you have to leave soon


Let's do it


ok


Ok Question 2? How should we start?


it says sixth graders collected 765 cans of food for a food pantry last year and this year collected 1750 and it says fewer so I would think 1750-765


that's absolutely correct!


So what is the final answer?


and I calculated 985


correct!


onto question 3


oh first try


yeah you're really smart!


thank you


ofc


it says a basket ball is made-up of five players  suppose there 140 players signed up for a tournament  and it says per so maybe multiply


ohh close try again


um add


if the total 140 and one team is 5 how many teams can u make?


is it add


how many groups of 5 can you take out?


its not add


oh you said take out so subtract


no


it's actually divide because you are making groups of a total


I make mistakes the last thinking is divide


that's perfectly fine


so what would the answer be?


so divide 140 by 5


yes correct


wait does 14 fit in 5


no not perfectly


hmm I got zero I know its wrong


so how many times can 5 go into 14?


oh 3


wait a minute you sure?


cause 15 is the closest number to 14


but its more than 14


yeah


oh ok


so what woudl it be?


can you look the board and see


oh I see


yep so what would the answer be then?


divide multiply, bring down and reapeat


yes


and then how many 5s go into 40?


that would be 50 its less tan 10


oh I I counted wrong its 8


thats right! so what is the final answer now?


hold on hat about the two from the 14?


oh remainder 28


remainder is 8


the remainder is actually 0, answer is 28 but thats right


whole thing is 28


yes correct


question 4?


hey it turns out im quite short on time. I unfortunately have to go after we complete the next question. Is that alright?


well do question 4 tho


ok


it asks what the perimater of the triangle


yes do you know what the perimeter is?


no but it gives the millimeters


ok lets go over that first you are correct that the answer is in mm


so the perimeter is the sum of all the sides of a shape


can u calculate that?


so calculate 20mm 15mm 25mm


yes


hmm I learned to add


yes thats right


in mm


sum = add


so what I got is 60mm


thats right! Great job!


oh right you have to go


so bye and thank you


Ok, unfortunately I got to go now. You got this.


bye bye


Hiiiii


Hello!


How can I help you today?


I have a question about factoring polynomials


Of course!


how do we factor polynomials with higer degrees/exponets


Wait... there are a few different ways to do these


okk


basically, for things with a degree of 3 there are sum/difference of cubes we can look out for


Wait while I'm explaining this, did you have any specific questions in mind


would this apply for even higher degrees like the 5th power?


No, but the sum/difference of cubes is really useful knowledge to have (memorizing it saved me a lot in one unit of algebra two) that and the sum/diff of squares (which is more helpful)


okkkk


for higher powers, simplifying/factoring is really about finding the greatest common multiple


ohhhhhh ok


So 5x^5 + 10x^4 would factor out to 5x^4(x-2)


There's another cool case I'll show on the board


Alex


Sometimes, you can look at the ratios of the coefficients to simplify


This is called simplifying by grouping


yes i recall this


did what I show make sense?


I am stuck still on the power of 5 part. How does that part work. I get the rest


You can probably also use synthetic division for higher powers (but i'm out of practice with it, so I wouldn't be able to explain it


Wait... the power of five at the top?


Or just in general?


the power of 5, how did you get rid of it. with the 6? is that a 6 at the denominator?


oh, where I pointed in red?


yes


I am sorry i am just stuck on that part


that is supposed to say gcm: x^4


It's okay!


ohhhh


did that make more sense?


Yes


Yay! Is there anything else you'd like me to explain?


Can i show a sample problem?


Of course!


ok


x^5 + 11x^3 -80x


Does this make sense?


You can basically factor the x^4 the same as x^2, you just need to make the xs x^2s


Oh okk got itt


that makes more sense knowing that


Yay!


okkkkk


Thank youu


Do you have anything else you want to go over?


for now no


this is all


Okay!


Goodbye then!


byee


hi


Hello


Hi


Um


I need to make on an assignment, um, just real quick, um, can you please unmute it a bit easier for me to understand things when I'm talking to someone and it's a bit hard to like be beyond what I'm having to do and then like switch tabs to go ahead and like look at what you're typing.


ok sure


lemme know if my mics works


Thank you.


OK


Hello, can you hear me


Hello?


I, I don't hear you.


Oh what


Don't hear me?


Oh yeah, now I do


OK.


So what do you need help with?


OK. Um


I need help with this. My the other tutor that was before you, she helped me out for a good like half hour and she had to go do something.


I need help working through this stuff.


Mm


All right. So are you


What they mean number the club.


are you stuck on this question or?


Um, no, it's mainly so that if I get stuck, you can give me like a helping hand and so you can like give help me understand things a bit better.


Oh, OK.


If you cannot do that, that's fine. I'll.


just try and work on this by myself.


I have a bit of a better understanding about this stuff because of the past tutor, um, named a number that is an integer but not a whole number integers or none that go from 0 and both times.


One give an example of an irrational number that was that.


irrational numbers or numbers that cannot be expressed as a fraction and go on infinitely.


OK, um


um, hey, question


Yes


Do you know how to type in the pie symbol


OK, I'm gonna try to do that.


Moy place.


OK, so it did not wanna do it, so I guess


I'm gonna use to 18 PI given an example of a rational number.


rational number.


or the numbers that


that can be presented as a fraction.


decibel like decimal. OK, so I can just do one that


33, 30, 33, 33.


That's irrational


All will not or all real numbers, rational


real numbers are a mix of rational and irrational numbers.


or not


Then after I answer these last, these last two questions. I got, I need, I'm gonna need help on a quiz


Um, this ain't even actual work. This is your's practice.


E A E T.


E A E T


OK, yeah, I can help you. Um,


000, all natural numbers, whole numbers


OK, um


actual number


natural numbers are numbers that are common, so common numbers.


poll numbers are 0 and up with the decibels, so that is a yes.


but now


i cant hear you for some reason


Hello can you hear now


And.


For all fractions irrational numbers.


That's a no


because irrational numbers cannot be expressed as a fraction.


OK


Yeah.


I


OK, so the thing is clear.


What was that noise


It was just my chair


To submit, begin.


It's only 10 points. You cannot be that bad.


Tell me two questions.


What are the following is a rational number.


Rational number


s or numbers that can be represented as a fraction


numbers that


and repeat was repeating decibels and terminating decibels.


that can be represented as a fraction.


so


that


negative


I want


Hi, Ben uh sorry to interrupt, but I can't see your screen.


You can't see my, oh God.


let's just go ahead and do


microscope


OK


OK. My bad. I, I completely forgot. So rational numbers are numbers that can be represented as a fraction, fractional numbers.


are repeating das and terminating decibels.


So that's a fraction.


So it square root of 16 is next.


The root of 6.


is for


so 17.59.


use a fraction


I'm not seeing any other things that can be represented as a fraction. That's a um er that's a irrational number.


It's natural.


your rational


Did I miss.


5. I forgot to write about irrational.


I find that real quick.


Yeah, go ahead


I, I completely forgot about the irrational numbers.


With no, why?


OK.


no, no, I, I did not. I did not, um, let me just


distinguish them.


with, with the


OK, now that should make things a lot clearer.


OK, irrational numbers or numbers that cannot be expressed as a fraction and go on infinitely


rational on the numbers that can be represented fraction.


So let's do that represented as a fraction


Let's do 21, 21.


Nope, that is a


that is a um what's called


that's entered yours I get to 21 is an integer high is irrational, that's irrational, and the square root of 16.


is a


whole at natural number.


So those are the only two ear rash waters.


Oh, wait, wait. Can you go back?


Yeah


There's still more because


remember integers and whole numbers, they also count as rational numbers, because they could be expressed


as a fraction


Integers or decibels, numbers that go from 0 to both sides.


Those are the only two that can be expressed as a fraction.


Yes, but think about um 21. We could say Ben could be considered a fraction, so 21 is also a rational number


It


OK, one second. rational numbers that are numbers that can be represented as a fraction.


One sec, let me go to the actual definition. OK, rational numbers and numbers that can be represented as a fraction, including


fractions integers and terminating decibels.


You know, from the teacher, from what the teacher said, the rational numbers can only be written as fractions. So from the teacher's standpoint, these are correct.


All right, if you say so.


Well


I be your teacher


56/7 classified 56/7 and as many possible ways.


equals 8.


56/7 equals 8, so that is natural.


natural, whole integers or decibel numbers that go from 0 and both positive that's an integer.


No, that's an integer. Now, rational numbers


OK, um


uh, submit and let's see what did we get?


What the fudge


OK, we get one more attempt.


cause knock don't lie, a 62 is not what I am going for that the decreased my math grade.


All right, let's do it again.


OK, one second, um, today,


if the,


if the stupid page will load.


One sec


The, the page is loading slow


OK, so today,


exit


OK


check now


take um the access code


was


I'm gonna go ahead and put in the answers that I know is that was correct. Oh, they are already in. Let me just share the new screen.


OK. Can you see my screen?


Yes.


So you said 21 was rational.


Yes. And there's one more that's also rational. I want to see if you figure it out.


square root of 16, it is 4 is rational.


Hm.


That's correct


because both of those are irrational because they go on forever.


Yes


Now there is one more, now there is one more on this.


And I am thinking rational numbers can be represented as a fraction that is represented as a fraction. It is stupid of me that I missed that. Let's see. Did I get them correct? Survey says,


can, can, can you load? Thank you. Survey says yapper.


Oh, great job


that that was called as I, I felt there was sarcasm in that.


No, there is no sarcasm. It's just usually when I react, I'm very


very, very plain.


OK


Well, I'm pretty sure there's one more thing I gotta do for math.


because there's another 10 point thing in my to do list for today.


All right, let's do it together


Um, it


let, if it, if it wants to load,


irrational numbers, order of operations.


I'm sick after it loads, I'll share my screen.


It's slowing, slowly but surely.


It's loading.


Let me just pull out the demo scientific calculator.


Steel load


slowly but surely


achieve that.


share a screen


Can you see my


Yes.


OK, it's floating still loading


Choose the best answer, and I can reach if I don't get anything good.


10 questions.


OK. Consider the following sets. All the statements in Part A and S.


A through D true.


OK


is P a subset of T.


So


let's think here, yeah.


I P a subset of team?


We just go to, of course.


for heat. Oh God, my computer's up


OK, so subsets example.


B is


So subsets.


P is a sub


he is a subset of T, the states are true because I live in numbers are on multiple of 2. The statement is true because all numbers on multiples of 6.


see the statement is because some numbers are not multiple of 62 or 4, the statement is false because not all is multiples of two such as


I know, that doesn't make sense because both of these are multibusettes.


this is the statement is false because


some numbers are not multiples of 6, such as 2 and 4.


2 and 4 are not multiples of 6.


That looks correct


But see, yep


Now is tea a subset of S.


OK, OK 69 126 1218, 24.


The statement is true because multiples of 6 can be written as 22 and our naturalist and natural of numbers, so they are also multiples. The statement is false because some multiples of sex, such as 18 or 24 or not multibos of 3. The statement is false because


multiples such as 3, such as 3 over or not multiples or six of 6, the statement is true because allables of sex can be written as 2, 32N which are where wherein is a natural number.


I, I'm thinking it's this.


Yeah, that looks correct to me


Nice work. OK


The sum of any two elements in S where the element of for, OK, but some of any two elements in us will always be an element in of sad ***.


What does that mean?


Um, so, basically what that means,


is that if you add any two numbers in the sets, so let's say 3 or 9.


OK.


It's always, it's always gonna be an element in S that's gonna equal the sum of 39.


So is this?


The statement is false because the sum of two multi multiples of three is a multiple of 6. The statement is true because the alum multiples of 3 is a multiple liver is a multiple of 33 and plus 3N equals 3M + n, the statement is false because some of er, yeah, I'm


this because the sumbies only started multiples of 3 is the multiple of 3


The statement is false


because the thermal multiples of 3. I, I'm thinking that it's this


Um, it might be another option.


uh, my next choice was this.


like let just first, let's carefully read the statement is false because 2, the sum of 2 multiples of three is a multiple of 6, 3N + and the statement is true because uh


of 3 is a multiple of 3, no, it's, it's a


It's a


Mm.


oh


Oh


if not my next choice would be.


Yes


So I was correct on it being me, the first time


The the set of elements common to PS and OK, the set of elements common to PNS is a subset of settee.


OK, so, OK, what, what are they asking?


Uh, can you repeat your question


Um, what are they asking? I don't quite understand the question at hand.


OK


Let me first read the question to myself again.


OK, take your time


OK, so


basically what it's saying is that in both sets P and S


Numbers that are similar to each other, so we could see that both P and S have number 6.


How um


how do those numbers relate to SETT?


It's basically what now


I mean, all three of them have 6 in them.


Mhm


So


so it's gonna be


So the statement of the gens.


so it is true because all of them have 6 in them, so technically PNS is a subset of T because all of them have 6. Am I correct?


Um, you're half correct because it's, it's not saying all elements in PNS are subset of T. It's only the elements that are common in PNFs that are subsets of tea.


Yeah


s


PNS have, both have 6 in them, and he has 6 in it, so it's, so PNS are subsets of tea.


Yes


So it's got, so the statement is true, so it's a 50/50 chance.


Hm


So the statement is true because all elements in P and all elements are as oh.


but it is gonna be this. The treatment is true because never at all, multiples of both 2 and 3 can be written as 2 times 3 times and or or 6 and they are multiples of 6 checked answer and survey says.


OK, which, which numbers and A


uh which numbers and are elements of both subsets B and C, so 3


OK, so


999 and


the numbers are in all three sets


Rs 9.


survey says, great job.


What, which numbers in AR elements of both B and C.


routine


and I am thinking it is 10.


and survey says that's incorrect.


Oh, I believe there's more.


let, let's, oh, numbers.


use commas


So tin, comma.


OK, let's just figure out, so we have 10.


OK, let's see here. All of these have 10. All of these have 2.


Yeah, all of these have 10 and 20.


Um, only one of these have very only 2 of these have 25 and only one of the, oh wait, A or subsets of that.


Yeah, honestly, I'm thinking it's only 10 and 20. Am I correct?


Yes


OK.


and


loading, loading, loading, pop, loading pop, loading loading, loading, hop, loading.


And if the dang bang wants to know that would be nice.


Mm


Now a loaded on your part?


Uh, no.


It's still loading for me as well.


OK, be right back. I'm gonna use the bathroom by the time I get back, it should be loaded.


And after then after I'm finished the stupid ma, I'mma Liam, 20 minute break and then


we try to work


I


two different


Never mind, I guess I did not have to use the bathroom.


OK, I'm, I'm back. OK, good, it loaded.


Relax


OK, tell me


tell me which set set or set a number belongs to a natural numbers, toll numbers, integers, dang, this pro this question is easy.


OK, so let's already go with natural numbers.


poll numbers.


enter your.


integers.


and they count as rational number


um


and let's check if that's correct, if it's not, well, let's add real numbers.


You there


Yes


OK. Just making sure I almost just lost my pen.


Tell me which sets up the number belongs to the actual numbers, phone numbers, integers, block.


Pi.


He expressed


OK, so,


uh she is 23.


/ 7


Pi slash even.


OK, so it looks like it counts as irrational.


because it goes on and on as a decibel.


OK, um


let's see here. It's not natural, it's not whole. It's not an interior.


a rational number


um


it's a real number


Mhm


and it seems like it's irrational.


Oh wait


But it's not irrational.


Can't be both rational and irrational. It could be just either one.


Yeah, you're, you're right. That's why I said, oh, wait, it cannot be earrational.


Hm


and I mean to click back.


OK, tell me what set the stat number belong to?


So let's already go with natural rational integer real


hole


It potentially those


OK, so,


so it's


whole.


integer


It's yours


phone numbers that can be represented as a fraction


in.


OK. It would count as a real number.


Um


Mhm


but question, would it count as a rational.


Uh, yes, cause there is a way to express zero as a fraction.


OK, now let's just get the square root of 12 real quick. We read of 12


That is irrational.


OK. Wait, wait, actually, yeah, I know, that's just stirred up irrational.


What did make irrational because nothing goes well goes with irrational.


Um, sometimes there is something I could go with irrational. There's um


real numbers


OK, let's do, OK, I'm gonna just try with a rational cause I get 3 guesses.


Hm


OK, real numbers. I rational and real numbers and surveys fantastic.


OK, and tell me the 14, so.


It is an integer rational.


and real


I


because it's not always put your number that can be expressed as a fraction.


OK, it's not a rational


It's a real number and rational number.


Oh wait, there's more


Yeah, um, well, let's see here. Hon natural number is 0 and up phone number is 0 and up with no decibel integers.


integers go up and down with no da go from the go starts from zero and goes into the positives and negatives without a decibel rationals can be represented as a fraction.


irrational numbers or numbers that cannot be expressed as a fraction, and you cannot have both rational and irrational.


and it's a real number because it's a mix of rational and irrational.


So


what, what would be, what, what would it be?


Um, it would also count as an integer.


Integer


Mhm


integer, a non-decimal number that goes from 00 my God, I forgot to fill an integer


A I'm a bit dumb.


OK, so negative 9. So it would be rational and to be real.


Yeah, cause it was basically the same thing as last question, just a different negative number.


And let's see what I got. 100. OK, so


I know I'm, I'm done.


Thank you so much, good sir. Wait, let me just check something.


Take your time


OK


Yup


Well, thank you so much.


All right, no problem, Ben. Have a great day.


hi!


How are you doing today


hi can you do 4 of them so I could understand and you see me doing to res of the four


hmm let me see


here


ok so for the first equation x <= 3


that is going to be a straight vertical line because there is no slope


can you draw it


and the line is going to go through 3 on the axis the entire time


no matter what point/coordinate you choose on the line


the x-value will always be less than or equal to 3


sure


do you understand


yes


ok what about the other line


it is a solid line because it says less than or EQUAL to not just less than


ok


the other one


has a slope of 4


and slope is rise over run (rise/run) or y/x


so a slope of 4 means you go 4 up 1 to the right from the y-intercept which is -9 in this equation


understand?


sorry can you show me the second line


its a dashed line instead of a solid line since it is not less than or EQUAL to... its just less than


ok can you shade where the two lines intersect


just redraw the line i drew at first again


in a different color so I could understand


and you'll see where it interesects


no cause it asking us to shade the part where the both lines intersect


heloo


in pink is where the two lines intersect


no the pink line is the first equation


they intersect where the two equations lines overlap


ok but where is it where the two lines intersect


can you show me where


you can't see it on the screen?


where the pink and orange intersect


can you show me in a different color


ya


do you understand this?


yes


great!


here


hello


ohh


you know how to do this now


I don't know


but you said you understood the other problem?


its the same concept as the first equation of the problem


hwere


good but remember sinces its just greater than and not greater than or EQUAL to.. its dashed line not a solid line


ok


also shade the greater than


is the other line right


can you shade in the part they intersect


shade each of the lines


the first one is greater than -7


so do you shade up or down?


above or below the -7


below


is -5 greater than -7 or less than -7


then above


ya because -5 is greater than -7 right because its closer the positive numbers which are larger than negative numbers


and the other line when have to shade blow


since that is a vertical line


you either shade left or right


right


its a less than or equal to sign


so shade which way?


left


great!


can you highlight in red where they intersect


don't you see where the black and pink intersect


thats where the two equations intersect


thats why you did it in different colors


can you pls just highlight because its easier for me


but i dont think your understanding


I do


then you would be able to see where they intersect


hi, how are you?


What would like help with?


Hi, I was in an upcheive with someone name Maria I think and we randomly got disconnected a few seconds ago and I was hoping to reconnect with her, do you know ow I can do that, just because she knows what I am working on. If not I am totally okay with working with you.


I'm not too sure. I guess if she knows that you're trying to connect back she would probably look out for your requests.


I'm happy to help, but it's totally up to you.


yeah, would you mind if i end this session and try t reconnect with her, it is nothing personal?


Of course, I would do the same tbh


Thank you, I am sorry!!!


Have a nice day, hope you find her.


Thanks you too


dont be sorry!


hi


I will put the problem on the board


Hi Ethan :)
Sounds good!


To clarify, they want you to solve the equation for x=2?


simply and then evaluate each  exponential expression


that what on the thing


Okay, sounds like we'll need to start with simplifying
Any ideas how to start?


I feel like this one first


Do you know the PENDAS order of operations?


no


That's okay! :)
I'll explain


ok


It acts as a guide for what order you should solve an equation in
(I got one of the letters mixed up, it's PEMDAS, oops)

P -parenthesis
E-exponents
M-Multiply
D-Division
A-Addition
S-Subtraction

First letter is where you start, then you want to move down


so the first thing is x^2


right


not exactly, Ethan is already simplified completely


correct!


this


Do you know how to raise an exponent by another exponent?


Yup, amazing!


Can that be simplified any further?


I think so


As far as I was taught, it can't, but no worries!


oh ok


then it fine


Any ideas for the next step?


Yup! Can that be simplified at all?


yea


Actually, since they have different exponents, it can't actually be simplified


oh


you can only subtract terms with the same exponent


Right now, we'll want to keep it as is, and move on to the (x^2 X x) part! :)


ok


Any ideas for how to simplify that part?


no but probably like 3 x 1


What power is x raised to?


the one on the right


yes, now, do you know the rule when multiplying two terms?


no not really cause I forgot thing


That's okay! :)

When multiplying two of the same variable, you'll want to add the exponents


oh now I get it


great!


like that


yup! The equation we're working with is (x^2 * x), any ideas how to work that out?


not really


What powers are the two x's raised to?


Does it help if I write it like this?


yes


Remember, when the variable is the same, you want to add the exponents


Do you think you can simplify it?


add it


yes, can you do that?


Yes!


I wrote down our equation so far, can it be simplified further?


yea


How?


oh wait because you can't yet because there no way yet to simply that ]


Yup!
I'd write that onto your paper for the simplifying portion

Once you do that, we just need to do the x=2 part


there I put it on my paper


good! Any idea how to do the x=2 portion?


x=2 mmh probably by multiple something with it


What the question is asking you to do is put a 2 where-ever an x is, then solve


no, sorry


Hold on, my pen is being glitchy


ok


So I put a 2 in at every spot there is an x


now I get it


that's what the equation means by x=2, you literally want to replace every x with a 2 :)


Do you know how to solve with exponents?


like that


no, sorry. If you can't do that with the x's, you can't do it with the 2's

No worries, though, you're learning!


what


what's 2^2?


yup


okay, so an exponent is when you mutiply a number by the same number


oh ok


Is that making sense to you?


yes


Yup! :)


correct!


yup!


do you know what to do from here?


I think add them up


subtractiom


I think you might've made a mistake with your math, but no worries!

What's 16+8?


Correct, but since the 4, the smaller number, is in front, the number would actually be -20


And that's the answer to the question, -20


You can write that on your paper :)


Any additional questions>


yea and thank you and no more question


You're welcome! Good luck with school!


thanks


final year


of school


Wow, I bet that's exciting!


yup


hii


Hi. How are you?


Good


How are you


Good.


That's good


I see that you are interested in topics from 7th grade math.


Yeah, because I'm going to 7th grade and I need to catch up


on my way because


I didn't pay attention in 6 and 7th grade classes.


and I need to catch up a lot. I need help.


Um, square roots


um, the, the equations where


um


where you


the ones with the shakes.


and um the the uh


the um


the grids and yeah.


Okay. No problem.


Um, and


on my variables


and


uh yeah.


All right.


We can cover each topic step by step.


OK


Let's start with square roots first.


What are you having trouble with?


Um


uh, I have trouble


with, um, everything.


Um.


well, I understand some parts of square root.


when you, when the number


you have to like uh what


I think it's multiple wise or something.


I


You are very close.


OK.


Hm.


Eastwood, can you hear me?


Yes


Good. Hi. So, so we are talking about square roots right now.


yeah.


All right, so


now what do you know exact, um, can you now tell me, what do you know now about square roots.


square, I think square roots is like the taste of like, you know, like the, the, the little symbol and the numbers underneath the like symbol.


and I think you have to like find where what


the number and the square root symbol.


is like what you have to find what


what like


what like an example


like 2 times 2 is 4, but the square root is 4, so.


um, the answer to


square root


is


4 times 4, I think, I mean 2 times 2, that's what I said.


Well, you're, well, you're right on.


right on spotting it, you're real correct. It is a symbol that has a number underneath it's so a square root is a value. Now when the when you multiply by the original number, you get get numbers. So let's say you have


Mm


3 x 3 = 9


x 3 equals 9.


Mhm


So


and the square root is like a reverse, yeah, of, of this operation, those square root of 9 is 3. So that's an example


OK


So,


3^2 = 9


so here you have 3 squared equals 9.


and the square root.


of 9


square root of 9 is 3


is 3


Oh, so you don't have to like when you like answering like this answer to like a square root. You don't have to like put the whole entire


3 times 3


equals


number.


that


it multiplies to


Exactly, exactly, you're right. So now, all you have to do is find a number and then you find uh and then you multiply it by the same number and you get and you get the product, and the reverse of the product is that original number. You know, you know what, you know


what it is?


Yeah


All right then. So let's say I have


uh 5 times 5.


5 x 5


You know what's 5, what's 5 times 5?


Correct? Correct. And as I said, the square root of this is the reverse. So what's the square root of 25?


OK


square root of 25


Correct? You're absolutely right. You got it.


OK, it seems like I'm not bad at this at all. It's probably.


some


Yeah, OK


Um


but


It's OK. It's OK.


um


OK.


uh, every, everybody now struggles with something at times, but that's OK.


we also need help with my division because


7th grade, I was


dividing 32 with bigger numbers and it wasn't, I know most of my uh timetables, I don't really know.


I know, I don't really know my sevens, my


nor my 8 and I almost know my tools.


mm, not really so.


I need to catch up on most of my timetable because


So,


yeah, I had a whole bunch of things distracting me for from sledding and


so you're struggling, you say you're struggling with sevens and eights.


yeah, most of them, yeah


I see. Well, that's OK. We can cover that too.


Um


so do you have your timetable with you?


I don't have any timetables


with me


All right then.


Do you have a grid next to you now that you can, you know, draw.


Um, the joint is the drying thing on here.


So, one of the easiest way that to multiply is.


So now let's say you have as an example, you have 7 times 2.


And


I know, that's 14.


no, that's right. That's right. And


and then let's go to the next number 7 x 3.


Um.


You can know when you go the next number, you always add 7 to it. Let's say 7 x 2 is 14 and 14 + 7.


is 21. That's so 7 times 2.


7 x 2 = 14


Also like you just add on the number to like the answer you got from there.


Oh


7 x 3 = 21


That's right. So, 7 x 3 is 21, and if you go on to 7 x 4.


the what, what do you think the answer can be?


um


wait, I need time to eat. Let me see.


That's OK. That's OK.


I'm a rehab


The basement grow is that you always have to add 7 each time.


That's correct. You got it. Time's tour is 28.


OK


And the same goes with 8s. So you have 8 times 1 is 8.


What do you think it's 8 x 2?


times 2.


uh


is it 16


That's right, 16. And if you go to the next number, 8 times 3, you have to add 16.


+ 8. What do you think 16+ say this?


Right


Close


16 + 8


Correct. You got it.


Mhm.


Or um


another easy way to have this, so let's say you have


a grid


I don't know if you can see.


Yeah


I


you


that if you have a piece of paper with you from the button you draw up.


a square


customizing


I can see it


All right then. So, let's say you have uh


you have 7 tiles uh horizontally.


Oh


let you have 7 tiles horizontally to 34567, and you have 3


3 tiles on the vertically. 123.


OK.


Another intimately say is that if you just multiply 3 tiles horizontally.


Here is


3, and here is 7. All you have to do is just count how many tiles are in that square.


Um


uh


Yeah


Like all of them


like this in the square


Do you remember what 7 times 3 is?


Uh.


it's 28, right


Not quite. Count how many in the tiles are in the square.


Oh, OK


Correct, you got it


You're doing a really good job.


OK


All right then.


And the same goes for AIDS.


OK.


You know, if you're really struggling with it always, you can always draw a square like that on a grid


and so let's say 8 times 3, just 8 tiles horizontally and 3 tiles vertically and see how many uh tiles are in the square like that.


Oh, I'm listening, you


know how I know it, they do like those um letters plus a letter and I get like the answer.


That's what I'm pretty sure I don't know what I'm doing for 7th grade, but I don't want to be prepared.


and stuff


So


Mhm.


so now those are, are you struggling with variables?


Yeah, variables


I see. So


um,


I think what you're studying right now is basic algebra. You go into basic algebra


Um


let's start with the the most easy example.


So let's say you have X + X.


x + x


And let's say


and let's say that in front of those exes you have


we have an invisible one.


1x + 1x


It's almost the same as 1 x + 1 X.


Mm


What what do you think 1 X plus 1 x is.


What's that


2 X.


You got it.


to it.


Right, how, wait.


so like


like our exes like that, um, like, are they like


do most letters represent a number like how like is


X always one


So, if you have a coefficient. So a variable is also called a coefficient.


Um.


and in there's only a letter, just imagine that there's always a one in front of it.


That is called the coefficient, and the letter is the variable. So 1,


is the


coefficient


1 is the coefficient


and x is the variable


and X is the variable.


And let's, so I'll give you another example.


Let's say you have 2 eggs.


2x + 3x


3 X


Um


5, you got it.


equals 5 X


Wait, wait, I'm confused cause


can you like explain how like


the


like, how do you like know how, like what letter represents one on because


I said didn't catch on to that part.


Well, to be honest, it doesn't really matter what kind of leather you choose. You can choose any letter. The moon's most important thing is that to what kind of numbers are you solving? The letter doesn't really matter.


OK.


It could be


you could choose 3A or 3Z or


3Y. it doesn't really matter.


All right, and have you grassed consent or do you need help additional help on this topic.


Then


Do you need more help


um


he like, like, like give me like some more examples so I know like if I really caught on


like if I really understand


All right then.


Here are some examples. Let's say have


5z + 3z


Right.


AD


Correct, you got it. How about this one?


9y + 6y


You got it. Correct.


OK


Good job


All right then


Now, Liam, is there anything else you needed help on?


Um


uh no


So, yeah, so you got everything you needed?


Yeah


No


So you, you stood how square roots work, um, yeah, how timetables on certain numbers work and the coefficients.


All right then. Well, have a good day.


You too


Bye-bye.


Bye


hi


Hi Alex!  My name is Jessica.  How are you doing today?


im good how are you?


I'm doing good!  Thank you for asking!


How can I help you today?


Thats good! im glad to hear that! today im working on multiplying radicals.. im pretty decent at it but i was hoping yo could check my problems as i work?


Like double check your answers?


yes ma'am


How many problems do you have?


And have you completed them yet?  Just trying to assess if I will have enough time to help out


not all of them are done, but im getting through them quickly.. the part im struggling on is finding ut when and how to simplify after i have solved


I can probably help out with 3 of them depending on how complicated the problems are and how quickly you can get through it.  I have about 30 minutes before I have to go


okay thats fine!


Great!  Let's take a look at the first one


for this one i got 50


Ok, do you have any work to show as well?


no


Ok


Do you mean 50 or (50)^1/2?


Ok.  Then yes, it;s coorect :)


okay ty, no need to simpify that correct?


Actually, yes


There is a square that can be multipled by another number to make 50


Can you guess what it is?


5 and 10?


What numbers can you multiply to make 10?


2 and 5


Yes, let me write this on the board


How should we simplify our answer?


multiply it?


Yes, so what is our simplified answer based on what we talked aboit?


about*


5 and 10 unless its 1 and 5


im not sure


So when you multiply numbers with the same radical, you can place all of the numbers being multiplied under the radical


Like how I wrote it just now


What is the square root of 5 multiplied by itself?


Yes!  So how can we simplify our answer then?


i dont know


That's ok


Is the way I rewrote the equation easier, or not really?


5 and 2?


the square root of 5 times the square root of 5 times the square root of 2


Since the square root of 5 multiplied by itself is 5


our final simplified answer would be 5 times the square root of 2


Like I wrote on the board


Does that make sense?


yes


Good :)


I'm going to reset the whiteboard if we are finished with this problem.  Is that ok?


Ok, go ahead and post the next one :)


Your answer is correct, but it still needs to be simplified


Based on how we solved the previous problem, what do you think we should do first?


to simplify it?


tbh idk im confused still


No worries :)


thank you for being paitent


Of course :)


So one of the first things I like to do when simplifying radicals is determining if the number inside the radical can be broken down into smaller numbers multiplied by each other


How can we break down 48 into smaller numbers multiplied together?


wouldnt i just say the numbers i already multiplied by or would i change the numbers?


You could as a first step.  So we are breaking down 48 into 8 times 6


Could we break these numbers down further?


4 and 3


So 4 times 3?


i dont think we can break those down any further


What numbers can you multiply together to get 8?


Other than 1 and 8 of course


4 and 2


How about 6?


3 and 2


Let's rewrite this


Can 4 be broken down further?


2 and 2


YEs!


You are getting the hang of this


Now what should we do?


multiply


Yup, what is our simplified answer based on what we have here?


2 √3?


So we have 4 numbers 2's


4 √3?


Or 4 square root of 2's


Yes! :D


- 4v3


to be more specific


yes yes!


Does this all make more sense now?


yes it does thank you sooo much ^^


You're welcome! :)


Have a wonderful night ma'am thank u!


Hi hi


Hii! How are you doing?


I'm good. How are you?


Great.


wonderful


example.com


lets do some practice problems for inverse trig


Okay!


did you make this?


no


found it


oh okay!


I think questiin no. 7 is wrong.


correct


pi/3 >1


therefore outside the domain


yes. right


undefined the answer key says


calculator says invalid input


how it will be undefined


because its outside the domain, we don't know what having an opposite that is larger than the hypothenuse looks like


there is no triangle like that


yes, there won't be such triangle


can give little hint for question no.12?


yea


oh okay. no don't solve it


I wasn't, that was the hint


Okay. I thought it was csc - pie/2 like subtracting.


lol


do I write answers over here?


you don't have to, the second page has the answers


you can compare


example.org


this one can you cast it


it involves graphs


ok, gimme a min pls


I got them all right.


yes


first page is good to do


yeah


this is a great worksheet to do if you can scroll down


that was fine lets do the graphs starting with the first page


ok


Is that correct?


Is that the first or second triangle?


first


can you scroll up


x is not the hypothenuse


you swapped the x and 9


right, sorry


what u think now?


correct


thats better


yup!


good catch


I keep swapping them.


you also reflect the triangle over the y-axis


not a big deal but you forget to move the side values with the reflection


yes, I keep getting confuse in it. have to check value multiple times.


is that correct?


yes but you can solve that further


what is the angle


you can do degrees or decimal


can we solve x in degrees without calculator?


not really


its not simple calculation


you could multiply radians 180/pi


yeah, that would convert radians to degrees


but not simple


oh okay. i was just curious.


double check you domain and range


this is for sin not arcsin


your range was right my bad


the domain was wrong


whats the entire domain for sin and cos


yes


good job


thank you!


what does it mean by principal values


they are the values in the range of the function that are used to define the inverse


its basically the values we have been using


I think they wanted flipped range and domain from sin function


those are all range values that are used to define inverse


right


can you graph it


i think that graph you are doin is for middle graph


good


are they asking same thing in arc sin and principal values?


they are asking for the abbreviated range


in the principal values


what does "abbreviated" mean?


so remember we consider inverse as the flipped x and y


so first range for arcsin is R


first graph is
x=siny


second is y=arcsinx


can you see the difference


it says y=sinx


if it sin y, it should be in y axis?


with the full range (-inf, inf)


the only way to get that full range


arcsin has abbreviated range to satisfy one to one


does abbreviated range mean, having two ranges?


'abbreviated' means shortened form


oh so, abbreviatetd range would be [-90,90]


in degrees yes


for principal values


yeah, only it would be one-one function.


and otherwise, domain and range will be flipped for arcsin


right


is this correct now?


yea, that makes more sense


did i do it right?


yes


good job


now we can discuss transformation


nvm continue we can do transformations later


go back


nvm Chloe is right


here are the transformations for inverse


do i scroll down for it?


please


sure


what do i have to do now?


try the graphs


this is about transformations


dilation, phase shifts and vertical shifts


try a few values


for x


think about our standard trig functions


what does a coefficient to sin do


it changes its range


yes


do you know what type of transformation it is?


it strected along y-axis


its called dilation


ohh, interesting.


okay, got it!


wait


dilated and vertical downward shift


you said it affects range


you changed the domain


remember, domain is input


range is output


yes, right.


so it doesn't change the x-values


but changes the y-values


its a vertical dilation


check the board


yes i'm looking at it


does that makes sense


can we say like, when a>0 it will expand and a<0 it will shrink?


its like our 'a' from parabolas


yes


but it doesn't stretch it horizontally


yes. i was thinking it like that.


yes, it will be vertical


but you are expanding it horizontally


can you give me 10 min please?


yea


i;ll brb


Hi! I'm back.


welcome back


sorry for the dealy, I had run errand


all good


no problem


yes,


lets take a moment to discuss transformations for inverse trig function


yeah


ok


so for standard trig functions


A is what


dilation


correct, its the amplitude which dilates it vertically


same for a parabola and a line


it dilates vertically when it's sin graph and horizontally when its arc sin


is that right?


not quite


lets look at an example


this is what you are talking about


a dilation in sin causes a period change in arcsin


ohh i wasn't thinking like that


right


does that make sense


I didn't understand dilatin in arc sin comes from period of sin


period is the horizontal dilation


of sin


determines how quickly it cycles


if k is large


sorry, let me take a step back


what is confusing exactly? like what it looks like from a graph? what does it mean realistically?


i don't really what confusing me.


haha


thats fine


dilation in arc sin come from period/angle of of sin. is that right?


the reason i expressed it this way was because i was showing what you were explaining


^^yes


is the period is small, sin wave gets smushed horizontally


What i meant to say is that


thats cos but your amplitude is correct


nvm you fixed it


yes


keep going


that is not true


but our domain would change now?


due to 2


the range would change


not the domain


since its outside the arcsin


if you want to change domain of arcsin, manipulate the inside


think of 'h' vertex form of parabola


y=f(x)


domain is [-1,1] , it will become [-2,2] right?


not for 2arcsinx


it still takes [-1,1]


for domain


range becomes [-pi,pi]


because A directly affects output


in order of operations, its after arcsin operation


y is our input, and x is output


sure


is it like sure right?


if it helps, can you cast desmos


yes


lets get some answers


do standard arcsin, then 2arcsin and (1/2)arcsin


dont forget regular arcsin


do you see how its just vertical dilation


does stretch it horizontally at all


doesnt***


yes, It's stretching along y-axis only


this happens because the coefficient is outside of the arcsin operation


its like ax^2


'a' changes direction and dilates


yes, it's exactly like ax^2


now try arcsin(2x) and arcsin(x/2)


remember this arcsin is a reflection of sin


over y=x


it swaps x and y


yes, I remember that


which means it swaps anything that affects x in sin, affects y in arcsin


so an amplitude change in sin becomes period change in arcsin


and period change in sin becomes amplitude in arcsin


all this is to help us solve the graphing questions in the second worksheet i sent


the one we were looking at earlier


if you want to experiment and change arcsin to arccos or others feel free


yes, gimme a min


of course


This is a very basic question. but i wanna ask


is this correct?


yes


that is exactly right


is this right?


its the reciprocal


of a and k


x and y switch values


why are they reciprocating?


remember inverse is opposite order of operations from function


multiplication becomes division in inverse


yes, that's right. i forgot about that.


understood!


do you see the corrections i did ot your graph?


yes, i can see that


they are both wrong. sorry, the graphs have to be stretched and shrunk


respectively


there, thats what it should look like


I;m having diferent values of for x for each of them\


look back at desmos


the red graph stretched it to pi


yes, right


the blue graph was flattened to pi/4


but neither were stretched horizontally


amplitude doesn't affect period


sorry


i mean amplitude doesnt change the bounds of x


its still [-1,1]


not [-2,2] or [-.5,.5]


it's only y, the domain


yes


this x and y stuff is getting confusing


lets use either input/output or domain/range


compare desmos to your graphs


do you see how your graphs have the same vertical dilation


but different horizontal dilation


you were doing arcsin(x/a) manipulation


yes, I have same domain but diferent ranges


not (1/k)arcsinx


wrong, you changed domain but kept range


remember domain is always input (x-axis) and range is always output (y-axis)


for sin


for everything


they will swap for arc sin


right the values for each will change for inverse but how we define domain and range doesnt change


ohh, then you're right. i changed the domain but kep range


but again, when in doubt plug and chug


try a t-chart


with each function and look at the values you get


this will tell you the behavior or affect of each coefficient


either that or graphing it


arcsin is correct


doublecheck, your domain is right, but your range needs to change


you flipped your manipulations


2 is bigger than 1/2


so teal graph should be 'taller' than red graph


yes that is better


how do i know how much it changes vertically?


look at your output values


did you see the table I did


below the graphs


yes, you chose those values for x which make those respective function -1,0,1


no, I chose x as -1,0,1


those are the bounds and intercept of arcsin


yes, right. sorry


alright. its late. I got to go to bed


yes, okay. can we continue from here tomorrow?


i will have to do this earlier in the day tomorrow.


maybe morning.


say 11AM PDT or 8AM for you


okay, works for me


awesome. have a great night


message you tomorrow!


*finger guns*


I check out those books. i noticed it had inverse trig topic.


would you like to do some of that tomorrow too?


yes the Class 12 part 2


we can work on that tomorrow


okay.


have a great night.


sorry part 1


Oh, you got emojis


yes lol


Im on my desktop keyboard with no emojis


it has shortcut for it


where?


on whindows, it's ctrl .


no, win .


got it


ohhh


alright, final goodbye


ready


Hii! are you ready?


Hi, how are you today. What would you like help with?


Hi, I'm good and you?


Doing good


I just had a few questions I needed some help with in pre calc.


sure lets do this


Okay, this is part A of question 1. Solve the systems. 5y = 4x + 6 and 4x+5y=14


Ok, I see. What do you think is the first step?


I'm not sure


that's perfectly fine. Could you tell me the methods on how to solve questions like these


I'm also not sure about that. I've never done one like this.


thats fine. lets brush up on this then


questions like these are called system of equations


Right


and the two methods we use are called substitution and elimination


elimination works by eliminating one of the letters to create a sungle variable equation


*single


Do we have to get the same answer for both of those equations?


no you don't and that's the fun part


you get rid of the variable by either subtracting or adding


Got it


lets say you have 2x + 5y = 10 and 2x-5y = -10


can you see the whiteboard?


Yes


ok good


now you can sort of make a substarction table


*subtraction


do you tink we should add the sides or subtract them?


Subtract


ok lets try it


so 2x - 2x gives us 0


now what would happen with the 5y?


Also 0. So it's adding?


very close but what is in front of the 5y in the bottom?


A negative


yep and then the negatives make a positive making the total?


I mean 1


you very close before take a step back and rethink it a little


yes


great job


so what would that side be?


perfect


now since we subtracted the left side we must also..?


Subtract the right


yes good job what woudl that be?


*would


Would it change to plus again?


yes correct


prefect


now wht woudl y be?


*what would


what do you think we should do now?


Figure out what x is?


yes, how woudl you do that?


Sorry I am having some internet problems. Give me a minute


all good, no worries


Hi, are you still here?


Hi I'm back. I had to power off my computer


all good. now back to the question since we know y = 2 what do you think x is?


close how did you get 8?


8 + 2 = 10


close but to get x you have to substitute y back into one of the two equations


Ohh


Like that?


yessss


Great job


So x = 0?


yes correct


now do you want to try to apply what we just learnt into your question?


Yes


ok lets do it


5y=4x+6 and 4x+5y=14


how would you start this off?


By subtracting again?


close but there is a step you have to do before you subtract


Get rid of the 6?


close but the first step is to move things around in order to get things in a line


Ohh so 5y needs to be swapped with 6?


you see how the y's and x's ad numbers in the equation i wrote are in one line?


yes exactly


Or 4x can go to the side with 5y


yes you can do that what would the equation be now?


5y + 4x = 6. But how would we get it to be like that?


super close but you are missing one small thing you have to do when you take things to the other side


Subtract


yes so what woudl the sign be?


good job now what woudl you do now?


I don't know


thats ok


you see how the letters are still not lined up like teh old question?


Yes


So we need to switch 5y and 4x


But how


since you are just switching on th same side you can just chnage their position


what should i write now?


5y + 4x


yes correct


Then we add them?


what do you think we should do?


If we subtracted, they'd just be 0. So should we add?


thats exactly correct way to go!


so when we add them what would happen?


10y + 8y


Or would the top 4x be negative?


yourse getting closer


10y + 0?


thats eaxctly right


now whats the next step?


Add 14 and 6?


yes!


so now y =?


yes now what is x?


wait a minute take a step back


We have to go back and put 2 in for y


yes


you can pick either of the two equations


It would equal 1?


yes you did it!


That was actually not to hard.


exactly all it takes is practice


excellent work


now our time is unfortunately up.


Oh okay. Thank you


have fun and good job today!


hello


hi


what can I help you with?


my name is Ethan and I'll be your tutor


I'm currently working on this packet that is for school which hasn't started yet so i'm working on it to get a head start and understand how to solve the equations before the school year! :)


thats great!


so how would i solve that?


would i subtract the 1 and 7 by 2?


I would start by subtracting 3 from all parts of the inequality because you want to get the variable (x in this case) alone


which is 1 and 7 right by 3?


yes


kk


divide all by 2


yes that's right!


answer is -1<x<2


correct!


good job


i'm gonna go rest and practice some more tmrw, thanks for ur help! have a great night/morning :)


Hello! How may I help?


Hello, can you connect me to coach Ms. Davis?


Hi I’m sorry I’m a newish tutor and I don’t know if I can manually do that


I am chatting with her


That’s great, is she saying anything about how I can transfer or connect you?


She gave us few questions to answer.


*I was chatting with her


Okay Id be happy to help with the questions


We already answered the questions. Can you please check to see if it correct?


Yes! Just tell me the question and what you thought the answer was


What did you think the answer was to number 1?


Or I can help you setup an equation to start it.


1. 11


2. 60


The first one is correct!


3. 3/6 or 1/2


4. 14


One second! Checking number 2


Do you mind checking number two or telling me your thoughts?


I got a different answer. Let’s walk through it, so we know that the pencils are 3 for 1.80, and how many did we buy?


Hold on


Alright!


3.60 and 6.4


Yes correct! And added together that would be….


Correct! Number three is also correct well done. Let me check 4


Yup four is correct!


Well done.


I am about to start 8th grade. Ju


Good luck! I am currently going into Sophomore year of highschool :)


Just want to be prepared.


Yup I completely understand! You’ve done super well on these questions, and I’d be glad to help you with others if you need.


Can you please give me few more questions?


Yes I’ll write four done.


Feel Free to do this one while I write the others


👍 ok


The result is 3


For the first one


So sorry I forgot to include it


Ok, that is fine.


Let me know once you’re done with these questions!


Oh, I don't see the questions. Did you send it here?


They’re on the white board! Maybe you need to scroll down?


2. If 4x-34=y, what is y when x=9
3. Jessica went to a store. She saw apples costed $4.00. She had a coupon for 75% off. If she bought one apple, and used the coupon, how much did she pay?


4. David rolled a 12 sided die, what is the probability that he rolled an odd number?


I sent them in chat just in case you can’t see it still.


I saw them in the whiteboard. I just didn't check there.


All good!


I am a little confused about Question 1. Could you help me through it?


Yes! So first we want to make an equation to help us. Think of th standard max+b=y


What could our y be?


MX+b=y**


Y is also known as a result if that helps.


So x = 2 and b = 32 right?


Yes!!


No wait switch x and M


M is the thing we multiply by so that would be 2


since we multiplied


Oh so like 2x + 32 = y


Yes perfect


We still need y though to solve, what do you think that is?


Hmm, I don't really know. I think younnn


Well I wrote that the result would be three, so maybe 3? Do you agree?


Yes


Ok perfect now we have the whole equation, 2x+32=3


How do you think we should start to solve it?


Also, think of x as the number the question was asking for.:)


Minus 32 from 3 I think


Yes minus 32, what does that give us


3-32 would give us a negative number.


Since 32 is way larger than 3


2x = -29


Now what do we do next? This next step requires the use of a calculator though, since we get a decimal


Oh ok


Let me know once you get x!


I think x is -14.5


Correct!!!! Well done.


Need help starting question two?


I got the answer. I say 2


Yes correct.


Well done once again:)


Need any help with question 3?


I think I got #3 as well.


Okay what do you think


Not exactly. Mind walking me through your steps?


Sure, First I turned 75% percent into a decimal which is 0.075


Ah I see, well to convert a percent to a decimal we divide 100


So 75/100 is...


Oh wait it's .75


Yes perfect


What do we do next?


I subtracted it from 4


Nope! We need to multiply to find how much the percentage takes out of 4.


Good try though, knowing this instantly will just come with time, its a rule. For example if we want 50% of 2, we do .5 times 2


Oh yeah, so then it would be 3


Yes perfect, what next?


Then we subtract


Yes exactly, and what would the final answer be?


Perfect, she pays one dollar!


Good job, hope you learned something about finding percentages through this question:)


Yes indeed.


Need any help for number 4?


Nope, I think the answer is 6


So close, its probability so the answer is usually a fraction, in this case it is a fraction


Oh yeah so it's 1/2


Perfect!! Need me to write any new question?


That will be enough for me. However, if I need more help in Math can I still contact you again tomorrow?


I am not sure if you can directly get me, but if you go in chat history you might be able to reopen this chat, and I will be available from 12pm-4pm


How do I do that?


How to go to chat history?


Not too sure Im sorry, but do you see any tab that says session history?


It does say that there is an ongoing session and it allows me to return to this chat


Let me ask my superior if theres a way to reconnect with coaches or people you tutor.


But, I only think that's open because this is currently ongoing. When this chat is closed it might not show that.


Ok, sure.


Okay so there is no way to get specific coaching but if you get online from 12pm-4pm I will be there, and also it says that you are able to "favorite me" as a coach. It says that after the session there should be a heart under my name in "session history" Or you are able to mark me in the feedback form as favorite. If you do this I get a priority alert when you request help next time.


Can you please give me homework questions so I will have it ready for tomorrow


Yes how many would you like?


Okay give me some time to think of them and write them down, do you want me to make any of them specifically about something?


Like percentages, probability, or the first question we worked on that asked to find the nuber


numbr**


number** oh my goodness


Lol, also yes I would like percentages and probabilities on some of them.


Sure! I'll write them now.


Ok.


1. A number is divided by 5, then 87 is added to it. The result is 45. What is the number?                                2. A grocery store sells tomatoes for $5.00 each. A shopper bought 4 tomatoes. At check-out, the shopper used a 65% off coupon she had. What did the shopper pay for the tomatoes she bought, after using the coupon?                                 3. If y=4x-13, what is y when x=2?             4. Sarah rolled a 6 sided standard die, what is the probability she rolled a 3 or a 4?          5. A number is multiplied by 9, then 3 is subtracted. The result is 17. What is the number?            6. BONUS HARD QUESTION: A shopper is buying pencils and markers for back to school. Pencils are sold at 4 for $2.30 and markers are sold at 2 for $2.10. The shopper buys 8 pencils and 10 markers. After picking all these items up, the shopper uses a 50% off coupon at checkout. What is the final price of the pencils and markers in total?


I will seperate them im sorry


One moment


It's okay.


Alright! It's just on my screen it looked like they were below eachother my bad.


That's fine


Good luck on them! Do you need anything else?


I am available for another 19 minutes today if so.


Maybe i'll solve my homework questions now since we have some time remaining.


Okay, let's try to get as many done as possible, anything left I will check tommorow if we manage to get into the same session.


Ok, sure.


Yup! Let me know once you think you finish the first one.


Ok


I think the answer is -210


Nope not quite there, mind showing your steps?


Oh my gosh I am so sorry you're right!


Oh, ok


I accidentally got -220 thats on me trying to quickly do it in my head


Super sorry


Oh, that's ok.


Yup but good job on this question, really improved from the other one we did that was similar:)


Yes, it felt much easier now.


I am glad.


For #2 my answer is 7


Yes correct!


For number 3 I got -5


Yes!


Well done.


Ok, #4 my answer is 2/6 or 1/3


Yes well done! Usually on a test they ask to give the simplest form so 1/3 :)


Ok ill remember that.


You can leave number 5 as a fraction if you want


Ok


Yup


I need a little help on #5


Okay well let's setup the equation.


A number is multiplied by 9, then 3 is subtracted. The result is 17. What is the number?


What do you think "m" is


the thing we multiplied by


9x - 3 = 17


Yes perfect


Good equation


What would the first step be?


To add 3 to -3


Yes and add 3 to 17


Yeah


So whats our new equation after


9x = 20


Yes perfect, next step?


Division I'm pretty sure


Yes exactly, and this is where I said we can leave it as a fraction since without a calculator it is pretty hard to go 20 divided by 9


Oh so it would be a repeating decimal


Yeah perfect, but we can also just let it be 20/9


Well done!


I can stay for the bonus question don't worry, until you're done:)


Ok


6. BONUS HARD QUESTION: A shopper is buying pencils and markers for back to school. Pencils are sold at 4 for $2.30 and markers are sold at 2 for $2.10. The shopper buys 8 pencils and 10 markers. After picking all these items up, the shopper uses a 50% off coupon at checkout. What is the final price of the pencils and markers in total?


It combines two topics so that's why its a little on the harder side.


Yeah I see that


Need any help?


By 4 and 2 it means time or how much he's getting


So it would mean he would get 4 pencils for the price of 2.30 dollars


Oh ok I understand


It's kinda a bundle deal


I think the answer is 7.6..


Try to round to two decimal places


since when calculating money that's the standard for cents


Oh so 7.60


Or 8


My answers a little different. It is close to 7.60 though


Walk me through your work


I calculated the total price for pencils = 4.60 and Markers = 10.60. They both bring a total of 15.20


Then I divided it by 2


Your marker price is a little off.


Mind doing the calculation again?


Ok one second


Yup!


Ah, it's actually 10.50


Yes exactly


I got 7.55


And also for your second step, dividing by two, that is correct and will get you the correct answer but we want to stay persistant. Divide the percent 100 and then multiply the 15.10 by the decimal


Yes your answer is correct


Ah ok


Just imagine if the question said 75% off


Yeah then I would have to do it the other way makes sense.


We cant just divide by a whole number you know? Just preparing you for harder percentage amounts.


yes exactly.


Go ahead and try 75% off


Ok let me try it


I got 11.3250


Almost. Hear me out, when multipling by .75 we find how much 75% is of 15.10


And you are correct in getting 11.3250


But if it is 75% OFF, we subtract what we got for the initial multiplication from 15.10


Remember back to when we did the other problem and you subtracted 3 from 4?


Ohh, yes I remeber


Yes perfect. But yes when we do even the .5 for 50% we get 7.55, 7.55 is 50% of 15.10 and now we find the 50% we actually pay for by doing 15.10-7.55=7.55


It's 3.7750


Yes perfect, and when calculating money we round to two decimals


So 3.8


Sorry I meant two decimals as in two places after the dot.


Oh so 3.78


Yes perfect!


Well done:)


Thank you so much for all your help. I'll work with you tomorrow if possible.


No problem at all, glad you got a better understanding of some concepts. See you tomorrow if possible (remember the favoriting thing). Have a amazing day!


Sure, you too!


Yes and good luck in 9th grade this year :) Bye bye.


Thank you, Bye 👋


Hi Alex I will be able to tutor you at 12pm up until 4pm, just let me know around what time you will be online and sending a request. If another coach grabs it, you can tell them you were waiting for me to accept if you want to do that.


I will join at 3:00 pm today


Okay!


Ah I wasnt able to click your session quick enough, so sorry. You can probably just tell them you were waiting for me if you want.


Yeah


Should I try again?


Hi


Hiiii


What can I help you with today?


I am preparing for AP pre-calc


simplify it?


and i need help with this


yes


ok


Simplifying with exponents


Did you multiply the -5 and 3/2?


okk


the key step is to figure out (4-9x)^(-1/2)


Ben i got lost at the part


why does it become rooted?


good question. let me go through the details


does this make sense? basically a^(-b) = 1/a^b


sorta


let me explain why this is true if you have time


we have to go back to basics


yes i have time


Okay


great


first, let's explain a^k


this is how exponents are defined


Right


it has it's own formula ?


yes


Ohh okkk


is that and imaginary number?


not imaginary. sorry, just a notation


Got it


we are almost there


my next question is what is a^0?


yes!


I will show why that's true


we use the formula


we are almost here


does this make sense?


-1/2 = 0-1/2


great


that's how I got 1/sqrt(4x-9)


OHH okay that makes a little more sense


next, we have make the denominator "rational"


so we multiply the denominator and numerator by sqrt(4x-9)


sine it asks for exponents


we need to convert 3*9 --> 3*3^2 = 3^3


ookk


any other problem?


yes one similar


it's shorter


sure


I will clear the board


okk


ok


does this make sense?


yess


cool


I think the hard part for you is when the exponent is negative


thank youuuuu


yes


you are very welcome.


okay yeah i think that's all


you are in good shape. bye


byee


Oh hello.


Hi again, Liam, assuming it's the same one.


hi again


Um


do you have something else you want to work on or?


Just needed to check one of my answers


OK, sure


ok


so the question is " Twice a number is 2. What is the number?"


twice a number is 2. What is the number? OK, so


uh, would the same method work, just kind of like breaking it down in a sense.


Yea I guess


OK, so you know, like the previous question, it was like


57, like it was equals the 57, it was like this.


yea


Yeah, so now if twice a number is 2. That means your 2 is on this side now.


So it's on this side of the equation.


because that's they're giving you the number.


So


twice the number, so


like for example, twice the amount of


apples you have


is 2 apples. How many apples do you have?


It would just be


Does that make sense


Just 2 times N equals the 2


because it's


double the number, twice is just double if you think about it.


The answer I got was 1


Whatever, how many apples you have right now?


Yeah, one is correct. Yeah, just divide by 2 on, oh God, if you just divide by 2 on both sides, you get N equals the 1.


Yeah


Uh, will that be all? or is, yeah, some other questions, concerns.


Cause if you're working on work ****, I could just stay here and help you with it.


just offering


yea I have a mathbook I am working on


Would you


like assistance with that? Like


would you want me to


yes, no, maybe so.


yea😅


Yeah, OK. Yeah, that's fine. I'm free.


Just wanna make sure that uh


you understand that


in a sense


All right. Um,


you keep working on that and just let me know if you have any questions. I just like put it in the chat and I'll do my best to assist you with it.


yea, ok


Sounds good.


Alright, great.


its a little funny cause I did one question with one of the coaches and he gave me a wrong answer😅


Oh, really? Well, that's not supposed to happen, um.


I hope that I'm not giving you the wrong answers for these.


yea I redid it though


All right, good job. Nice, nice.


he was a little mean about it too..


Well, that doesn't sound good. Um, if you do have any like concerns with the session, you could, I'm pretty sure you can like click a report button on the top, right?


If you have like something you wanna address cuz that does not sound like what


one of the coaches or tutors should be doing.


yea but it's a little weird cause I keep getting him too


Oh, yeah, yeah, um.


it's just like a, cause what happens is we just have like uh.


a low ping that shows up if someone needs help and it just whoever clicks on it.


uh


I guess luckily in this case for you, I was just like conveniently on. And then I saw it I was like, OK.


yeah, it's kind of like a luck thing. There's not really like a specific.


as long as like, you know, your tutor, the coach is like proficient as I see as expertise.


and knowledge on the area that you requested to, to work on, then they can see the request.


yea I met someone here and he was really helpful and sweet to me and my siblings


Well, that's always nice to hear


Um.


if you, I'm not sure if you could request the tutor or something, but I know you can favor one, and then I'm pretty sure then they get like a notice.


if you need help, if that's what you would like to do.


with uh that coach, then you could do that.


okay I have another question to do


Yeah, go for it.


oki


Uh, if you don't mind me asking, um, is this like summer practice or is this for like a specific exam, just so I can like help you prepare better if you, if it's like for some sort of exam and you get like resources or.


like as a reference


or just like summer work from school or something.


it's a math workbook my mom gave me to do


Ah, I see, I see.


its just that I am homeschooled


OK, sorry to bother. um. Oh, OK.


I see, I see


All right, well, let me know if you need help, and I'll just be right here.


Everything, uh, going well, Liam.


Do install it over there


yea


Srry I have to go my mom needs help...


Oh, OK. Yeah, no problem.


All right. Um, if you do need help, uh, just like make a request. I'll see if I could uh.


take the uh


oki


call quick enough. But uh, yeah


bye


Liam


Hello


Alex i need help with a math problem


give me a sec so i can write it down on the board real quick


Use the quadratic formula


oh okay


the photo on the right is the problem im trying to solve


the one on the left is the simplified verson i made


Those aren't the same equations


oh they arent?


my fault can you show me my mistake?


no they aren't


Show me your work


That's not correct


oh why tho?


i dont see it


Do you see what I wrote?


OHH okay i get it


i forgot to square the 2


got ittt thanks


that's only part of it.  You didn't get the middle term


I wrote the formula for squaring a binomial


alr thanks


imma try and solve it again


can i ask how you got 12x?


ohh okay i got it thanks


But they want you to solve it using structure


structire?


like the formula?


yes, I will show you what they want


okay thanks


Notice the (2x+3) ?


yeah?


We can simplify this by making a substitution


We will let p= 2x+3


Now we have a simpler quadratic equation that you can go ahead and factor.


oh...why is this lowkey so hard


can you factor that equation?


thank you so much thp


yeah


Right, but it's p, not x


oh okay


But remember, that p =2x +3, so now you can replace the p in your factoring with 2x +3


do you know what I mean?


ohh okay


yeah so like it would be (2x+3-6) and (2x+3+2)


exactly!


oh yayy


That's what they mean by using the structure to solve it.


ohh okay i get it


Do also remember how to square a binomial.  You will find it very useful to know in the future


uh..


not really


ohh okay got it


oh okay so like hwo would i find the one value of x that is a solution to the equation


It's (2x+5)(2x-3) =0, right?


yeah


So now you use the zero product property.  If two factors multiplied together =0, then set each one individually to 0 to find the zeros


If a*b =0, then either a must =0 or b must =0


Any questions about that?


yeah, so what numbers would be our b and a?


I am saying that if two factors multiplied together =0 then set each one =0 and solve for x


ohh okay so like you would move them separately?


you solve them separately


got it


So what do you get for x?


what are the zeros of the equation?


uhh hold up i messed up give me a se


sec


for the first one i got -2.5


Or -5/2


yeah that too


Looks good


thanks


for my eqation tho, it wants only one x


but in this case we have two


That


thats a bit odd. I guess you can use either one.  Usually these kind of questions ask for both


oh okay, so they would both work?


They are both roots of the equation.


got it thank you!! i think im all good now!!


Good.


Have a good rest of the day


you too!


bye


Hi that was my bad


I just went to gt some water


let's continue with the question


ok


so add 8 + 14?


yes!


then divide it by 2?


yes


and then multiply by the height


yes, 22/2 = 11


11 times 8?


what's the height here?


from base 1 to base 2?


yes, so 11 * 7


good!


is it 77 yd^3?


or 2


not quite. what is the unit for area?


next one


okay


so i add 14 + 5


yeah


and then times it by 8?


8 is the height here


thats 76


76 yd^2


wait a sec


14 + 5 = 19


2 divided 2


okay yes, 76 is right


i mean cm 2


i have one for volume of pyramid


ok here it is


keeps disappearing for some reason


okay, do you know the formula ofr the volume of a pyramid?


yes!


1/3 times (lwh)


would i do 8+7?


oh


length, width, height


I don't see the questions?


so multiply everything first


then divide


scroll up


I'm all the way up


I saw it before


but not anymore


i circled it


let me put it back


here


may have to scroll down a lil


I still don't see anything, but the question gives you the height and both sides of the rectangle at the base, right?


then you would multiply those 3 values and divide by 3


did u scroll down slowly?


yes


do u see where i have the 1/3 at?


But I think the reasoning is still right


let me try reloading


Okay I still don't see anything


wanna request in reading?


and i can screen share


or paste it easily