what would the be when plugged in?


would it be 8


Not really, try again, we are diving the part (9) by the whole (72)


You do need a calculator to do that!


oh um I don't have one with me right now


Okay, that is totally fine, the number would be 0.125


because 9 would be the num and the 72 would be the dom


okay, now we multiply now, so what is 0.125 times 100?


Close, it would be 12.5% because 100 mine move is 2 decimal places


oh


ok


Great, is there any other confusing ones?


um


not really Liam


bye


Welcome! Have a good rest of your day!


Hi! How can I help you?:)


algebraic expressions and order of operations. I need help to understand those a little more please


I can definitely help with that! Do you have any specific problems you need help with or would you like me to give you practice problems?


nope


sorry


some practice pls


Okay! One moment, I'll quick write some down in the white board


Try working on this to first practice just order of operations!


GEMS is what my teacher said to do also


Yep! That works too!


i domt know what 8 and 4 multiplied is


*dont


Do you know 8x3?


hold on i have an idea, what if  we add 16 and 16


That works perfectly too!!


Actually, I am going to stop you before you get too far. With "M" in GEMS it means multiply/divide, right? While you were super close with starting with 8x4, you actually go left to right with this, so you will actually want to start with 24/8. Does that make sense?


yea


can i type the stuff here in the chat


yes!


ok 24 and 8 split is 3


Perfect!


What do you think you should do next?


3 and 4 multiplied


or//


12 is perfect!!


What's next?


get the sum of 12 and 6?


So just like multiply/divide, you want to go left to right.


So you'll actually want to start with 7-12


Perfect! and now +6


Don't forget the 5 is negative!


There you go! That's the answer to the equation!


Would you like to try another order of operations problem, or try some algebraic equations?


oohhh yay


yes


hold on can i be back in like 3 mins? i need to get a drink really quick


Okay!


ok


exponents first


Ready? Where do you think you should start with this next equation?


Yep!


i dont know what 4 cubed is


Perfect that's 4 cubed!


What should we do next?


2 and 64


Exactly!


Yay! Yes!


128 and 4  divided'


Remember start left to right.


3 128


Yay! yes!!


and 384/4


Try again, do you think 4 can go 384 only 9 times?


OHHH I GOT IT


YAYY you got it!!


Great job!!


Do you want to try some algebraic equations now?


can i come u/p with a ooo really quick


i just need  to solve one more ooo problem


Okay!


What should we do first?


exponential number


Great!


If 2x1=2, then what do you think 1x1 is?


There you go 1^2 = 1


Now what should we do?


divide


Yep! 4/1 = ?


Not quite, how many times can 1 go into 4?


4, and btw i will have underlind or circled a number when i have an answer oki


ok!


Now what?


Perfcet!


Do you feel better doing ooo now?


yes


i think i am comfortable with it now thanksm to you


Good!


You did a great job!


should we start AE {algebraic expressions}


Sure!


ok


Try the problem I have on the whiteboard! What do you think we should do first?


3 and b


What do you want to do with 3 and b?


Okay what next?


add 3bs answer yo 40


What if we don't know what b equals, or have you not gone over that in class?


i choose


Lets try a different problem, one minute


Not quite


Try plugging p=5 into the equation


Yes!


Would you like to try another problems that's similar?


no thanks i think i understand everything now


Yay! Great job today!


thank you


bye


Hello


How are you?


Omgg you speak 3 languages, how cool!


I am good how are you?


You saw my profile?


I am good.


How can I help you?


Nooo it’s says that you speak English, mandarin and cantonese


I have some questions that I’m going to put up, one sec


I see.


Sum of all interior angles in triangles is?


Yes


hold it there


You should add 2 on both sides


of equal sign


Excellent


Thanks Mark !!! :)


Let's do #33.


Ok, I need help with this one


Let's see


Do you know the Z method?


Tell me if you can explain it?


It shows what angles inside are equal and parallel


Inside what though can you show me?


It’s an isosceles triangle for both


The question does not say that


Oh wait never mind. I thought did.


My thinking is can I say angle fcd = angle fad?


Yes!!


We have to apply the condition given in the question to the last two equations.


Wait, huh?


I am going to working on it on paper because drawing on the board slows me down.


Give me a minute


Ok , take your time Mark ☺


Hello?


Mark?


Are you still there ?


yes


We can prove angle DCB = angle EAB


because triangle ABE similar to triangle CBD


I am not sure can you explain


I feel like this question needs some verbal explanation


Yeah


These two are similar


Wait


Both angles are 45


They do not have to be right triangle


I did that because it is easier to draw


Ohh


They are not isosceles traingles


Do think about the right angle


I just do that for making it easy to draw


Can you remove the right angle sign?


Okay thanks Mark!!


You can see the red triangle is flipped


No


I meant fipped from the black triangle


I am going to flip the red triangle back to look like the black triangle


Now I can see it


Flip along the thick red line


turn counter clockwise 90 degrees


What this mean is that angle DAF = angle FCE


1that they are =


We have two pairs of matching angles.  That paroves triangle AFD similar to triangle CFE


Yeah


But I am not sure if verbal explanation is part of the answer.


So that's why I am trying to use geometry to prove it


Ahhh okay


Do you know I can add message to this chat after we close the session and you will be notified?


Really ?


I never knew that


Yoand vice versa


Huh


And vice versa


Let me work on it and I will attach the answer to the chat so you will see the answer.


And you can continue your study on other stuff.


Ok


It's a plan then.


I will let you know.  I will continue working on it.


Emily Mark


bye


Mark and triangle CBD are actually same size but flipped.


So We have angle AFD = angle CFE


angle DAF = angle FCE given by question


line AB = line BC


line DB = line BE


so line AD = line AB - line BD


line EC = line BC - line BE


so line AD = line EC


So we have AAS.  So triangle AFD = triangle CFE


hello!


hi i have a math problem


alright!


what is it?


it says the table shows the number of different types of birds that are swimming at a lake its 8 seagulls and 9 ducks and 7 geese and 1 swan and i dont know the ratio


what is the question that it asks you?


about ratio?


the ratio of swans total birds


okay! well, how many swans are there?


yes! so we know that is the first number


now for the total birds, we have to add up all the numbers!


so 8 + 9 + 7 + 1


yup! so that is the second number!


thanksss


of course!


is there anything else i can help you with?


yes i have a whole lesson


alright! any specific questions?


it says what is the ratio of cows to cheese and theres 5 cows and 2 chunks of cheese


well, the first number is cows and the second number of cheese!


so what would the first number be?


yup! what about the second?


so 5:2!


theres another one it says an artist used 6 tubes of red paint 2 tubes of yellow paint and 13 tubes of white paint and 9 tubes of blue paint for a mural


okay! what ratio does it want?


what is the ratio of blue paint to all the tubes used


which one is the first number, and which one is the second?


what do you mean


which one do you think will be the first number in the ratio?


out of all the numbers?


well, it tells you it wants the ratio of tubes of blue paint to all the tubes right?


well 9


yes, 9 would be the first number!!


what about the second?


idk


the second number mentioned is the total tubes of paint


so we need to add them all together to get the second part of the ratio


not quite! 6 + 2 + 13 + 9 isn't 21


we have to include the blue paint in the total


oh


no worries :)


can i use the board


sure!


d


yes, that is the second number! so what is the final ratio?


yess great work!


this other says the numbers in this math problem is 3,2,4,21 and they asked whats the ratio of 2 to 21


this one just gives you the numbers!


can you tell which one is the first number and which one is the second?


is it 2


yes, 2 is the first one!


21 is the second'


yup! so what is the ratio?


right!


so the next problems numbers are 6,7,13,4 and asked whats the ratio of 6 and 13


okay! do you want to try this one by yourself?


i did i got it wrong cause i put 6:13


hmm interesting, that seems like the right answer


can you put a screenshot of the question on the whiteboard?


it says it was 13:6


but the question put 6 before 13?


i know right but lets move on


alright


so this ones numbers are 15,7,11,4 and it says whats the ratio of 15 and 11 and i think its 15:11


i think you're right!


lets check


okay!


first number is 15


i was correct


nice!


t


do you want to do a couple more or do you think you got it?


i think i have it i will let yk


i have ratios with tape diagrams


alright, we can do some of those!


Elara has 5 trees planted an 2 harvested


what is the ratio it wants?


are you still there?


Graphing Systems of Equations


hi Ben!


Hi!


is there a specific problem you would like to work on today?


yes


I uploaded my math homework


awesome


I don't understand how to di this very well


no problem! shall we start with question 1


ok


can you tell me what you are struggling with when it comes to these types of problems?


grahing them


alright!


so tell me Ben, have you ever graphed a line before?


so this is similar! are you familiar with slope intercept form of a line?


y=m?


so starting with the first equation of the first question, y=-5x-8


can you start by telling me the slope and y interception of this line?


slope is -5 and y intercept is -8


awesome job!


do you know how to graph this line?


my teacher said she wants us to make a t-chart using three numbers one negative and two positive oand none number has to be zero


ah okay!


by t chart do you mean like this?


yes


ok!


what three numbers would you like to use?


or 2 i should say


zero, -1, and 2


would you like to solve the y value real quick?


feel free to write ur answers on the chart


is that right?


some of your answers are correct, lets double check them!


can i ask for a favor? can you delete the picture with questions 5 and 6 so we have more writing space?


ok so


for 2,


would you like to solve this again?


i did the math wrong


thats ok! this is why we should always double check our work


your answer for x=0 is correct, lets check your answer for x=-1


try solving this one again!


there we go!


yay good work!


would you like to plot those points on the graph now?


yes


we can graph now


alright


would you like to graph it?


I can't plot (2,-18) since negative 18 isnt on the graph


thats ok!


so we know the slope is -5.


have you learned rise over run before when graphing lines?


im not sure if i graphed correctly but i did learn rise over run


you graphed it right! good job!


so shall we use rise over run?


from (-1,-3)


i forgot how to rise over run


since the slope is negative


it would be down over run


does that make sense?


kinda


ok this part is kinda confusing but


down over run is also the same as up over left


does that make sense? its kinda tricky to explain


yes


perfect! so if we go left and then up, we arrive at point (-2, 2)


hello


Hey Alex!


what can i help with today?


i need to study for my upcoming pre calc test !


we’re starting trigonometry


ooo trig was tough


oof


but i think we can figure it out! im guessing youre figuring out sin(45)?


i also put up some of our class notes for reference


have you learned the unit circle yet?


yes she went over it


okay perfect, just wanted to check


since its an angle on the circle, we can just use that


okay


oh wait, this last note looks like you were learning a proof for the unit circle?


a proof?


uhh i’m not sure exactly


sorry, wrong word. but basically it looks like that note is explaining how the unit circle works


yeah most likely, during her lecture


i can upload the whole circle if youd like?


yes sure


can you see it?


yes Alex


so going to sin45? how do we start these things again?


so the way i learned it, cos values are your x coordinate and sin is y


so for this question youd go to 45 degrees on the circle, and select the y coordinate


yup thats it!


okayy but she’s definitely not going to give us a unit circle on the test for reference so what’s another way to figure this out?


thats fair! give me a second to give myself a mini refresher


no problemm


ok lets see if i can explain this


sin is the opposite over hypotenuse right?


yes


and we know the radius has a length of 1, and its a 45 degree, meaning its a right triangle


so for a right triangle with a length of 1, do you have a guess what the width would be?


umm


oops not width, the height


double the length?


why would it be double?


actually lets back up some.


okay


we know we have equal angles since the triangle will only 180 degrees total (45 +45 +90)


right


if the angles are equal, the lengths must also be equal, right?


yeah


now we can just say that our 2 equal lengths are 1, and use the pythagorean theory on them to solve for our hypotenuse


a^2 + b^2 = c^2?


exactly


just to check, which variable is the hypotenuse?


c


yup thats it!


so solving for c, what would the length of our hypotenuse be?


90 right?


good guess, thats the angle across from it


oh


if we use 1 for a and b on the pythagorean, what would c be?


almost! remember it equals c^2


youd do the opposite of square, youd use the square root


oh oops


square root 2


yep! kinda understand why?


because the hyp is sqrt2 times bigger than the 45 degree angles?


lol thats not quite the answer i was looking for but youre right!


lol 😭


okayy thank you for this. i’m going to work on more notes


okay, you almost have the answer. you sure?


yes i’m sure i’ll talk to my teacher also


okay good luck then!


thank you!


Hello!


hello!


I'm very confused on this problem


Gotcha! Gimme a min to read


Did you do this bit? Or is that part of the question?


that's part of the question


Oh! So it did a lot of the work for you. Nice!


Do you understand where that comes from?


no but some of it


What parts don't you understand?


so I understand x + 11 but the rest of it is just not easy to grasp


Gotcha! Let me run through it quick


This is just the formula for volume


With me so far?


yes d is for height right?


depth


is yes in volume its  whl


which is guess is kinda the same


oh okk


i love different formulas that mean the same thing :(


but I don't get this part


Does these formulas make sense?


ok I see yes


you isolated the d


by subtracting w and l


Right!


yes I originally thought the first way you wrote is how its supposed to be and got confused on how they wrote it


I actually wrote all these variables wrong


hilarious


I get the top 2


but the third one


did they solve it


So we do one more thing with the blue equation


DO you see how I took the result we got for l in black


And then plugged it in the the blue side?


yes!


(thge arrow)


So that's how we get that!


ok I see!


They just use "x" instead of "d" in the formulas they gave


So we've learned that I'm bad at reading


But does it make sense how we found relations betweeen the variables


Then did some solving for l in terms of depth


And then solved for w in terms of depth


yes


So then we only have depth at the end of the day!


Cool!


Now the real problem


Can you solve the resulting equation for x?


Missing an x?


then we find solution?


Makes sense to me! Do you have experience solving equations like this?


yes!


Out of curiosity, how'd you know x-4 would divide evenly?


I have a graphing calculator so I found one factor of it


but I might be stuck on this one


That does work if you're allowed to have a calculator!


it gave me a decimal when doing quadratic equation


This isn't quadratic! The degree is 3


Oh that!


no synthetic division


yes


Then yeah, that might not work out well


it still gave me a decimal I thought it would be complex


I trust you on the arithmetic :)


Why do you think one solution would be complex?


because quadratic equation didn't work


but we could try 4 again


What do you mean "didn't work"?


it might be multiplicity


didn't work meaning decimal


That still works!


Decimals are numbers too :)


Don't divide again!


what did quadform give?


My calculator gave these two solution


whole number is a bit easier tho


That's true! But decimals still count as solutions


Not everything is a whole number all the time :(


Sometimes the real world is messy


Does it make sense how I got those answers from the quadratic formula?


yes but could we get whole numbers I think we could not using 4?


You cannot get whole numbers


Besides 4


To be clear also, you have to use 4


You can't pick a different number and have a zero remainder


so its complex because my teacher said that they come in pairs so 4 is the whole number and the other two are probably complex?


None of the solutions are complex


Let me draw some pictures to explain


Before the pictures, a quick fact:


If you have a polynomial of degree n, you must have n roots (real or complex)


So a quadratic (degree 2) has two roots always


This is a cubic, so it has 3 roots.


Does that make sense?


yes!


Here's a random cubic


It has 3 roots!


They're all real because I can draw them


THey may or may not be whole numbers


They might be decimals


But whole numbers and decimals are both real numbers


Make sense?


yes


Here's another cubic


It also has 3 roots


so are they the 2 possibilities?


Because it's a cubic, and it must have 3 roots


But I can only draw 1!


What happened to the other 2? They're imaginary


So like 3.5 + 2i


Imaginary means it has an "i" in it numerically, and it means I can't draw it graphically


yes that's what I meant not complex I get it mixed up


Does that make sense?


Cool! Then for completeness the last case is multiplicity


but would you say they are eimaginary because it didn't show up in the graphing calculator


Do -11.59 and 2.59 not show up in your calculator?


no not for 0


I'm not sure what you mean "for 0"


Can you explain?


so x intercept y would be 0


just like 4


if you input 4 in the equation it makes solution 0


That means 4 is a root!


and it sort of "Skips" it- I had 2, -32


yes


so I wasn't sure about deicmals


For context, here's a graph of the function kinda zoomed in


There's the root x=4


But there are two other roots!


Which is what we found using quadform on the result of dividing (x-4)


yea but my graphing calculator is from the school so I don't know how I'll be able to do that haha


but what's the answer?


To be clear, you don't need to have this graph :)


You just have to do quadform after dividing the x-4


You just seem hung up on the fact they're not whole numbers


true, but I did put in the answer we got, but it came up wrong and it shows the answer eventually and it said: 4.0 , 2.6


I just want to be clear that decimals are still real answers


If you round 2.589 to the nearest tenth as the problem says, what do you get?


2.6 but what about -11?


Ah, now the problem context becomes important!


Is -11 a possible depth?


no


So that means it's not a possible answer for the problem


Which is different from being an imaginary solution


Does that distinction make sense?


This is a bit pedantic, but important!


yes and I had another one! could you help me with this other problem


Sure!


To recap, I think you did all the hard math right


Sorry, think it's easier to clear the whole board :)


no its better actually


And just remember that decimals are real numbers too!


yes!


Oh I was scrolled down, I see now!


What are you thinking?


neither?


they're both opposite


its not even or odd


What do you mean by both opposite?


like its facing opposite direction


Let me do a quick explanation to be sure we're on the same page


5ish mins!


This is the def of an "even" function


yes


It's symmetric about the y-xis


its odd


Odd function are symmetric about the origin


Back to the function you have!


Is it symmetric about the y-axis?


if it was wouldn't it look like this


Yep! It's not even!


Is it symmetric about the origin?


Right! So what's the answer here?


odd?


That's what I got!


what about


For determining even/odd from graphs, keep the two symmetry definitions in mind!


numbers


What numbers?


its not letting me but its x^11-x^4


It's asking if it's even/odd?


yes


Can you use the algebraic definitions?


where f(x) = x^11 - x^4


so its 1 which means + and odd for 11 so its going down to up


I'm not sure what you mean. How does that help for even/odd?


I would start by finding f(-x). Does that make sense?


so there's a trick my math teacher taugt


so if the coefficient is negative it'll end in negative


and considering the exponent


if its odd or eve


That's true for graphing in general! But it's not sufficient for odd/even


it determines whether the arrows are together or seperate


What if I add some curves


That green function starts up and ends up, but it's not even!


It's not symmetric


The blue function is f(x) = x^2, which is even


Let me prove to you it's even, so you can see what I mean!


no I know what even and odd are but not in terms of numbers


like the example I gave


Do you see how I proved f(x) = x^2 is even in blue?


I computed f(-x), did some simplifying, and saw it was equal to f(x)!


can you do that with the problem I gave just for reference


That's the algebraic definition of an even function, when f(-x) = f(x)


I want you to do that one yourself :)


What's f(-x) for f(x) = x^11 - x^4?


Where'd that -1 come from?


Oh, it's an x!


yea


What happened to the exponents?


did you apply the exponents and still keep them?


You definitely need to keep the exponents. Otherwise, those expression aren't equal!


The goal is to remove the parenthesis to simplify the negative signs


The -x^11 you did correctly!


A negative sign to an odd power stays neegative


What about an even power?


it gets positive?


Yep! Is that what you wrote?


yes


Not quite! You combined it with the subtraction


so what would this mean for odd or even?


This is the same as what you said going back a step


Is it correct?


Let me make this simpler to focus on what I mean!


is it positiv x?


Right!


so you ignore the subtraction


So the subtraction stays!


This got kinda messy. Does it make sense where we are?


yes but how does this apply to odd and even or neither


Good question!


We did step 1: find f(-x)


Now let's check for evenness


The check is: f(-x) = f(x)


Or


-x^11-x^4 = x^11-x^4


Is that equality true?


no


Right! So the function isn't even


Does that make sense how we applied to algebraic definition?


yes


but then how do we know if its odd or neither


Good question again!


Let's move onto the algebraic definition of odd


Can you find it on the board?


That's the graphical definition!


Because you need a picture to figure it out


What's above that?


Aha!


Can you apply that definition like we did the one for even?


You can also see the f(x) = x^3 example I did


so we don't always put - inside of x?


And keep in mind, we already know f(-x) from before!


We do that to get f(-x)


Which is enough for even


But as you can see in the formula, odd also needs -f(x), which is different from f(-x)


Even though they look pretty similar


Does the difference make sense?


no I don't get -f(x)


or how to apply that one


Let's say g(x) = 4x^2 + 5x - 3


Then -g(x) = -(4x^2 + 5x - 3)


= -4x^2 - 5x + 3


Does the difference between f(-x) and -f(x) make more sense with that example?


For f(-x), we put the negative sign all the way on the inside


yes


For -f(x), it's allllll the way on the outside


Perfect!


Simplify those parentheses!


Nice! Now, the important question


Is that equal to f(-x)?


no


Right! So it's neither even nor odd


As a shorthand


That I think works after 1 min of thought


If you have all even powers, the function will be even


If you have all odd powers, the function will be odd


If you have a mixture, it will be neither


I thought about that for a full minute, so it might be true.


I think you can prove it with the same process you just did!


Although on a test, I would always do the full process and show my work :)


Anyway, that was a lot of info. Any questions?


no but I think I get it


Cool!


I do have to go know, but good luck and have a good night!


but I know its probably pretty late, thank you!!


you too!!


functions


hello


My main focus is that I want to strength reasoning with features of functions


sure


what do you know about functions so far


so far I know that for something to be a function its needs one input and one output


I understand where to identiy where a grapgh is negative and where its positive


that's a good start


to be more specific, you put a number into the function, and it gives you another number


so for example, the function f(x) = x^2, takes in some number, and squares it


so for practice what would f(3) be


yep


now let's graph it


In my class we are learning aabout how range can be negative infiity to psitive infity and things like Im confused on that


alright


so first do you what a range is


would it be how far right and left a line goes


actually that would be domain


range is the vertical one


mmm ok


so let me draw an example


if a function goes up infinitly


it goes up to positive infinity


and the opposite for if it goes down


so the negative infinity part is right


why does y equal 0 is it cux it stopped there


what what do you mean


oh i meant like the graph has a maximum of 0


you said that y-0, is that because thats how far up it goes


so the answer would be negative infinity to zero


mm ok I understand


here's another question


wait i'm confused on the answer


are you saying infinity to 1


infinity to 1


yes mb


yea then that's correct


but you want the smaller number first


so you would put 1 to infinity intead


but it's basically correct


mmm ok so like lets say for the domain it would be negative inifty to positive infinity


yea exactly


how can i know in like lets f(x)= x ^ 5   how do i know what set of numbers * natural, integers), rational, imaginary) can i plug in


wait what do you mean


like what types of numbers you can put into the function?


yes


well for normal functions you can plug in any number


even  imaginary and irrational numbers


Do Now: For each pair of functions
a. How do the graphs of the functions in each pair compare?
b. What conclusions can you draw about the identity given with each pair (are they
always equal)? Explain.
2
i. 𝑓(𝑥) = 𝑥 and 𝑔(𝑥) = x   lets say this one


alright


so notice how the functions are the same right


they both take in a value and give you that value


so you can probably guess what a is


Hi! How can I help?


Hi


1/5c-5/6=4/5c + 1/2


and you are asked to solve for c?


okay so what is the first step to solving this problem?


find the LCD


yes you can if that makes it easier for you!


so in this case what would it be?


now how would you begin to solve this?


you have to subtract 6/30c from each side?


yes!


now what is the next steo?


subtract 15/30 from -25/30


exactly!


and what is the next step?


divide


yup


does that make sense?


do you have any other problems do go over?


yes please


of course!


am i good to delete what is on the board currently?


yes


okay great! I will write it on the board


okay so what is the first step?


hello?


Hello!


How's it going?


salam how are u


Alaikum Ahmed!


I'm doing great :) How about you?


good


That's good :D How can I help you today


my problem is when they give me a rule like y=3x+3 i dont know how to represent it on the graph


Well I can definitely help with that!


Let me put a graph up first and I'll explain!


thanks


where are u from


Do you prefer chat or mic use?


let me guess


Texas


chat


Nope! Want to guess again?


California


Nope


Florida


No ahhahha


Illinois


Think more Mexico


im from Canada


Really?


I'm right above you!


USA


Exactly!


Hahahaha


hahhh


Alright, Sam I put the graph up.


lets lock in cause im cooked for the test


Let's actually do the same problem you provided: y=3x+3


Absolutely!!


ok


First, let's try subsituting x values


Actually, why don't you label the graph's x and y axis for me first?


thats easy


not the probllem


Very good!


Now, we can create a table for the input x value and output y value :)


kinda hard to write dont have touch screen


sure


Ohhh that's okay! You can just type it in chat and let me know what you think it is!


do 0,1,2,3,4, for x axis


nvm


Sorry! I should've asked you first what you wanted to subsitute :)


its fine no worries


I just used negative values first so we got a broader range on the graph


when x = negative 2 y=-3


when -1 y=0


growing =minus 3


What do you mean by growing=minus 3?


i mean


That's right!!!


typo


So it should look like this in the table ->


ya


Now, since we know the x and y coordinates, we can just subsitute these in!


thats not what my problem is


Oh, what's your problem?


actually nvm


my bad


All good! I think my wording was off: I meant to plot them on the graph :)


i know it though its easy just want to solidify


no actually my problem is


I see that! You're very capable it's just exactly as you said; solidifying it.


nvm im actually tweaking


Sam that's a-ok :)


can u please lable the y-axis


Absolutely


ill graph the points


what grade are u in


college


I am!


Good guess


Very good!!


But, for the input -2 make sure the output is -3!


Right now, it's still 3 wheras -3 is below the x-axis line


Hi! What did you need help with?


k let me look


K, so I marked the image with the information we know. Using what was provided, do you know what other angles you can find?


Angle e


Hmm there are multiple angles centered at point E. Right now, I would say focus on the two angles at point D


But yes, you will be needing to know the angles at E after


DEC and FEG


I drew a little diagram which I think could be helpful


Could you try and find the measure of angle ADC?


Angle ADC is 75, but yes, angles ADG and GDC are both 37.5!


do you know why?


should I explain?


Alternate equals are equal


hello i need help with this question


yea sure


can you see the equation


hmmm.... yea I see it


ok what is the area of the unshaded


can you find that?


correct


ok how about the whole square including the unshaded region


no, how do you find the area of a square?


you there?


yes


oh multiply that twice


yup,


what do you get?


nope, do you know the foil method


noper


nope


ok foil stands for firsts, outers, inners, and lasts


okay


to start multiple the firsts


come the place I am writing on the board


what happens if you multiply that


your gonna get 2x


no, x^2


oh ok


now multiply the inners


do you see me circling with my cursor


ummm lets see... yea


multiply them


6 times 6=36


6 times x?


outers


what if you multiply the outers


oh wait


look at the pink


6x right


coo


so whats the area of the shaded region


we are getting there first, I need you show you how to


okzy


okay


what happens if you multiply the blue


uhh


ok we have the complete area and the unshaded area. How do you get the shaded area


make sense


is square units cubic units or units


square


do you understand the concept?


yes


explain it to me


you there?


yeah im here im yeah


i submitted it and 90 percent


oh ok cool. anything else?


nope


thank you kind sir'


no problem, good luck


hey Chloe


im on a diff problem i need help


okay, you put the session as history but thats fine


kk


do u know how to solve it and nned conformation or need halp solving


idk how to solve it i never done a problem like this some of this stuff is new to me


okay, In a rational equation, the denominators cannot be equal to zero, as division by zero is undefined. To find the restrictions on x, set each denominator equal to zero and solve for x.


so 9x-8=0


i mean 9x-0


yup!


yes


now what


so for 7x - 2


yes!


oh sorry


8 - x= o is incorecy


k


so then what is it


8 -  x = 0


8 = x


x = 8


so jus 8?


0, 8, 2/7 would be ur answers!


i thought the 8 becomes -8


nope


so then why is 7x-2 pos


becuase it turns to 7x = 2


ok


get it?


ye


perfect


how manuy more u got


5 not counting this on


okay


need help or ocnfirmation


i need help


or is all of tghis stuuf new


new


alr


is that aleks?


yes


oh yess i have that too


yeah its sometimes difficult lol


so with this one


yesss


can i find the lcd or no?


hmm


you would start with isolating


ok can u show on the whiteboard


ok


wait i will be right back for a sec, u can still write it out and stuff ill see if it makes sense when i come back


okay


back


alright!


lmk if you got questions


ok u kinda write it in like a difficult way


oh so sorry this is js how i learnt it


we combine it?


mhm


the 9 and 7?


well yes, but first u isolate


then u cpombine


after combinig


yoy solve for k


then u fiond your answer


that should become


bc ur distributing


yes if you were to distribute


but


so then why is it written like that


u have to clear the denominator


thats why


so then what happens to the 2 infront of it


u multiply bopth side by (k - 6))


yes thats whty its a bit confusing


out of respect im going to request a new coach no worries


u divide both sides by to


oh okay thats fine, hope tyhis helped


hello


Hi! I need help with turning absolute value into piecewise functions, I don't understand why the greater than/less than sign faces the way it does


Can I write a question on the board and can you go through it step by step to help me understand it


okay


sure


Alright, I wrote it down


so absolute values change behavior where the inside equals 0, and these are our break points


x−7=0⇒x=7
x+4=0⇒x=−4


wait can you write the work on the board instead of the chat to make it easier to understand


Thank you!


how do we know that its both less than signs?


where? mark on the whiteboard with a different color


because the interval is from -4 to 7


so does this mean that in all cases it will turn out to be less than signs


[-4,7] is written as -4≤x≤7


no


for the last interval we have x>7


wait im confused, how do we know that these are less than or greater than signs


okay, so this is just math notation and how that is used to interpret the intervals


so we split the number line


suppose we split the number line into 2, one for numbers less than 3, and numbers bigger than 3


so it is written x<3, and x>3 respectively


wait, is it if x was in between those two numbers it would be greater than -4 and less than 7?


yes


but wait please keep going because I don't understand the other notation


okay now lets say we take all the numbers between 2 and 5, not including 2 and 5, that in math notation written as 2<x<5, that means x is all the numbers in between 2 and 5


when we used ≤, for example 2≤x≤5, that means x is all the numbers in between 2 and 5 including 2 and 5


Ohh!! Okay, I think I really needed a lesson on math notation, not piecewise functions!! I think I get it now thank you so much for your time and help.


that's all?


Yes! I had already completed the question I just had no idea how to do the signs


oh okay


do you get the idea now?


Yes thank you! Have a nice day


you too


Hey! How can I help you?


need help with math homework


okay, show me the questions


Simplify the given expression. 3x^2-14x-5/x^2-25


put it on the board


are you able to do it?


sorry got disconnected


okay


okay, so what do you think we should do first?


are you there?


yes on here


We can tee hart the second one.


T chart.


please type, do not talk


We can teach chart the second problem.


we can t-chart the second problem


first simplify the denominator


how do you do that?


don't know what to do


what can x^2-25 be simplified to?


-5 x -5


do a t-chart


do it on the board and show me


can you see what I wrote?


yes


ok did I do the t-chart right


do you understand what I wrote?


do it using my method


What's 3 times 5.


Hello How are you?


Hello


Im good


How can I help?


Could we use voice chat?


yes pls wait


Can you hear me


Yeah, I can hear you


OK, is the volume OK?


Yeah.


OK


I haven't done geometry in a long time, but


when I saw that it was Alex, I figured I would try it.


Mhm


I have an exam tomorrow, so.


Yeah, yeah


I thought tomorrow was a holiday, but OK.


Oh


So what, what can I help you with?


Um, I need help with, hold on, let me upload it.


I see


a student


What, what kind of, it's all right.


Well, not right now, no, I, I later.


Sorry, I had to talk to my wife


Uh, I'm gonna make this picture a little bigger.


All right


and then I will make a copy of it.


if I can remember how.


I can't find


OK, I have a copy. I'll take a look at it here.


maybe


Let me try this again


All right, so now I can magnify it.


Oops, OK


All right. The figures, two figures are congruent.


if


they can be made coincide


with justtua


OK, so where should we start?


Oh


we could start with


congruent triangles.


OK


Let me see what that is


I'm trying


if that would be fine


Um.


Oh right


let me read this again. I


I'm not sure I agree with this.


OK, well, I, I see what they're saying. OK, so


I, I read the part and read. Now, what questions do you have?


Um, I need help in like understanding the concept.


Um


here's what I think now


A mathematician might not agree with me, but I think they would


The the the real ideas that


if, if we have these two triangles here, A, B, C, and well, I guess they call them, yeah, ABC and


DEF


and, and you notice that the order ABC


if we go from, you see my cursor?


Um, no, I can't really


see.


00 yeah, yeah, right, I see where I'm pointing on the wrong screen. Let me try that again. Maybe I can do that this way.


Yeah.


OK, see my cursor now. OK, so ABC


and then they call the other one DEF and you see the order is important because


they, they're following sort of the same pattern.


OK.


Now


the general ideas of


I, I, I'm not sure they've drawn these exactly the scale, but if two triangles are congruent, you could take one and put it right on top of the other, and they would be identical. We wouldn't notice any difference.


So that means that for congruence, the the corresponding angles have to be equal and also the sides.


See, it says corresponding sides


so


there's another property called similarity. I don't know if you've studied that. Two triangles can be similar if they have the same angles, but they're not the same size, like if you magnify one of them


but to be congruent, they have to


all the the the angles have to be the same and the lengths of the sides.


Oh


It says, and then they, they write it, the symbol.


My eyes aren't so good, but I think they have like an equal sign with a squiggle on top of it.


He's doing let me put my curse, uh, yeah, it's kind of tiny, but I think right around in here where my cursor is


there's a symbol, like that's not, I think, I think it's just a little bit blurred but


if you look at that, that's not an equal sign, that's sort of a


equals what the upper part is sort of curved. Do you see that?


yeah


So, so that means that's what they use for congruent. I think most people do use that symbol, OK?


Wait, could we solve the activity number one.


Yeah, let me find it first. Let me see where it is.


there


Uh


I think, is it above or below or?


That's above that's OK.


Refer to the


day.


time.


OK, so I'm looking at uh activity one, but now.


what are they asking you to do here? It says,


two figures that that the figures are congruent, OK?


The corners of the first one have been a signed letters.


according to the numbers.


Oh, OK


So


the idea is to imagine


the way I would do it. I mean, you can, you could do it from either left to right or right to left, but I would consider, you see the one with the numbers on it?


How, how could you set that up so that it, it's exactly on top of the one with the letters and then what letters match what numbers.


Um


wait


D and


um


Yes, that's right, and


then what's next


A and 4


BN 1


OK, wait, let me think. He is going to, OK, and 4, OK, go ahead.


BN1 CN2.


2. Yes, yes, that's right. Is there another way to think about, I would think about it is I think


if you look at this, the longer side, let me try my cursor here. The longest side of this one is length 18


See my curse name


I


the side of the other one is 32.


Mm


So that means that either D goes with 3 or D goes with 2, but because of the


because of the shape, it turns out the goes with 3, but I would, that's how I would look at it, but what you did was fine, so


I, I, to me


I mean they don't exactly say this, but


the idea is that if you can take one figure and put it exactly on top of the other, and they match in they're congruent.


Wait, what about like


actually


never mind


Um


should we just like so


questions and then if I don't understand it,


Yeah, yeah, that's fine. Um, let me just see where are the questions here?


the example.


and


Yeah.


Oh, do you have to upload something? Oh, I see, I see, I see they're separate here, OK. Yes, so, so what I'm gonna do is


I'm gonna copy that. What I do is I copy these to another screen so I can make them bigger and actually read them, so I will copy


the first group of


questions here


and so we'll do that


and we'll do this


and I'm gonna make it bigger


OK, so the one I have


right, it's, it's, I'm gonna make it even bigger. It's uh, I'm not sure it's in focus, but I will do my best here. Let's see.


OK, now, it starts with hens, oh, I guess the hens.


I guess that's a continuation from right above.


Uh, you see what I mean? Hence means they're like therefore, so.


it must um


be relating to the previous one. Let me just see here.


Yeah, you see, if you read


on the previous page, the page above it.


let me magnify that.


OK, so at the bottom of the previous page, it says


we write to indicate that they are congruent


OK, and I think that now if we go to the next page, I think that that hint


means this sort of continuation.


you know.


Wait, so should we solve the example?


Yeah, yeah, yeah, just a minute, just let me read this so I'm sure I understand this. There's a correspondence.


OK


All right, well, do you understand what they're talking about above like angle A equals angle D and angle B for, for the exam for the example.


Yeah.


OK, OK, so


right, we'll look at the example


OK.


Um, I'm gonna magnify it a little


more here


The problem is when I magnify it, it, it's a little blurry, OK.


So when


headaches


I


like myself


to see if I know


I'm uh


I'm sorry, go ahead. What did you say?


explain the example in my like own words to see if I like.


Yeah, yeah, that'd be a good idea, yes.


OK, so first, um, triangle F.


uh, triangle D, yeah.


right


which can go to triangle, uh,


EEF


QRS


OK, wait a minute, wait a minute,


let me.


the


OK, wait, I'm trying to find the example. I'm having a problem here.


But what, what was it, what are the triangles called in this example?


um triangle DF and QRS


Yeah


Well, I'm trying to find what page is this on here. Maybe I'm on a different.


I load it here


OK.


Oops, oh, wait, wait.


wait, did I miss a


OK, so


oh, I see. OK, OK, I, OK, I thought that was a question that's an example. I see what you're doing. OK, go ahead.


you're saying


that


DEF


is


congruent to


you, and then how are you gonna name the other one now?


QR


Yeah, but you see, I think


first of all, are, are all the angles equal that the


Yeah.


they are OK, but


you see DEF when you go from D to F, you go from what what angle, 72 to 59.


Oh


I


you see my, did you see my cursor?


Yeah


So I'm going from D


E


oh wait a minute, let's let let's start with D to E, OK. I, yeah, I think you had it, so, OK, so tell me again what you were gonna say. I, I think I, I think I see what you're doing now. Tell me again.


and QRS.


OK.


But I, I lost the sound there. What's the name of the first triangle?


DEF


DEF. OK, so that's the same as


going from Q to R to S.


Yes, OK, that's good


and then


So they're congruent now


mhm


Now what does it say, triangle ABC.


is congruent to which triangle?


um MPN.


Yeah, OK. Yeah, that is a little out of focus, but yes, OK.


Also


1 may write


Now this is a little


oh I see, um, you, I think for this part, but you see there two, 268 degree angles.


and


in, in the, in, in the second pair


you see the second pair has another way to look at it is the second pair has two sides that are length 8.


What do you mean


Oh, OK, let, let's go back.


at, at the bottom there, you said that ABC was congruent to what?


MPN


MPN OK, but.


Yeah.


I think you could have also said PMN because


Yeah, cause of the


because that


I'm sorry, go ahead


because of the 68.


so you can still say that.


Right, and also it's a


it's not an equilateral what do they call it.


I sawilli's triangle, you see, so.


they're two different ways of writing it, OK. All right, so you've got that. OK, so now I'll scroll a bit, I'll move down a little bit.


OK, now


well


Yeah, this is a little out of focus here.


Um, maybe you can


I'm gonna try to read this. It's, tell me if I'm reading this right. There is only one way


the vertices of DEF


and QSR correspond, OK?


But oh yeah, it's just this is just reviewing what we already said, but there are two ways the vertices of ABC and MPN correspond, OK?


So basically that's the, there's the solution to the example.


Wait, can, can we solve Activity 3 cause I feel like that's hard.


I know.


Yeah, yeah, there you go


Yeah


they're kind of easy


yeah, you just have to bear with me because I have to get the page that that's on.


Yeah.


Let me see where


where is that


We're on on the screen, OK, wait a minute, is that that


you see these are so small, OK. Activity 3. All right, let me copy activity 3 to my other screen and then we'll work on that.


You see, we have this problem. First of all, my eyes aren't that good, but secondly, these pictures are not always exactly in focus and when I magnify them, sometimes it's hard to read the, but, but we'll get by, we'll do take care of this one.


anyway.


this OK


All right, so I've got, I think I've got activity 3 here. I'm gonna magnify it.


Let's try this


OK, so activity 3.


OK, so it says complete the oh yeah, this is a proof, right?


Yeah, Alex likes proofs, OK.


OK, so let me just read this quickly. ABC ABC.


prove anyone is a right angle


and a


certain is a size.


OK, so they, they give you the statements.


and


uh


OK, so what's the reason for for number A?


do you think, for first statement A.


Mm


wait


ABC is congruent to ABC, that's given, so.


Yeah, so are you right for A is just given, OK?


yeah


Now


me


go ahead for the


is that corresponding parts of congruent triangles are congruent.


Yeah, that's what I would say, yes, yes.


So I'll just write CPOCTC.


OK. I, I have, I mean, I haven't done this in a long time, but OK, but


now what about say?


1 and 2 form a linear pair. Isn't that definition of a linear pair?


Well


you see, I'm not so sure. I, I guess I


uh let me think about this.


Well, that would be all right with me. Um


I, I, I don't know if you have to say that like


each one is 90 degrees and they add up to 180 degrees, but I would say definition of a linear pair is OK.


And then uh DZ.


If angles in a linear pair are congruent, then they are right.


Yes, yes, that's good, yes.


Oh, and also


yes, that's fine. And, and also you might mention that in step B, we showed that or we


we proved there's some uh you know, stated that they're they are congruent, OK.


And then E is


CPOCTC again.


What is the cars? What, what does that mean?


corresponding parts of congruent triangles.


Yeah, a congruent, yes, OK, yes.


and then


ABD is isosceles that, uh, definition of isosceles triangle.


Yes, yes, good, good, very good.


And then it says given ABC is congruent to DF. DF is congruent to carry aum, Navy seas isosceles with vertex, it proves that KLM is isosceles.


OK


Um


the


there's some property, maybe you can tell me the name of it.


What?


Uh, I, I, I don't, it would, well, there's some property that says like


well, in algebra we would say


if A equals B,


and B equals C, then A equals C, but I, I don't know what they call that in geometry, but that's what we're using here. Do you see what I mean?


there's a name for that, but I haven't done this in a while. I, I could try to find the name in a book if you want.


I think I know this way.


Alright


OK. I, I'll tell you what, while you think about it, I'm gonna look in a book and see if I can, I'm not even sure where to look though.


Go ahead.


So I just wrote the proof first, ABC's Code to DF and, DEF is converted to KLM, that's given, and then I did ABCs congruent to KLM by the transitive property.


Yes, yes, that's a good name for a transitive, yes, that's what I was looking up. I'm just gonna look that up again to be sure. I know transitive property, yes, that's good.


and also


my book shows that transitive property works for equals like A equals b, but it also works for congruence, OK?


OK, so that's good


So now we're down to number 3 here.


Oh, I see. Now we have to do the proof with everything, right?


All right.


So we know that


UMN


is congruent


to


P


wait a minute, MN


and


is trying to go


to PM. OK


All right. So what are you gonna do for, for 3.


But


QMN is convert to PMN, that's given


Yeah


key lemon, uh, is angle QMN is converted to angle PMN.


So that's given


Well, it's slow down, slow down, I


Yes, OK, OK.


and then and MN bisects QMP and MN bisects QNP. That's the definition of angle by sector.


Wow, you're way ahead of me. Wait a minute, wait a minute.


um


OK.


I, I think you're right, but, uh, so, so run that by me again. You have


angle Q and and equals angle.


PMN


by congruence, is that right?


OK, and then by therefore


MN bisects


to


wait a minute, actually everything I did, I said was, oh, I see. OK, so that takes care of QMP and then


I guess you do the same thing at the bottom to get


the bisector for QNP. Is that right?


Yeah


You see, there, there are two things to prove, yeah.


OK, yeah, you seem to have it under control better than I do.


OK


Let me just


In fact, I was talking to a friend of mine recently who's an architect and


he said that


the he was in school


his method of proof was he would just write down it looks like that, and but the teacher didn't like that.


I'll upload some more questions.


from this book


It says student's image could not be uploaded. That's what it says.


Oh


I, I, it doesn't say why, but maybe you need to um


oh,


delete some of these, maybe they, oh wait, I see it now. I see something that's sort of hand up now it disappeared.


Sure


I see it now. I, whoops, now it disappeared.


which


I, I, that's very, I see it, OK. I'm going to um make it bigger.


Is this what we're looking at? It says congruent triangles.


and it, it's sort of


a little grayer than the other ones.


Yeah.


OK, I will copy that to my other screen.


Actually let me close this thing here first.


OK, now I'll copy this


And maybe before we do that, you could just


tell me again, I, I know I asked you about this, but I'm, I don't know if it


I looked up something about this, the, the, the program you're in, it's like some


um charter school that that


is sort of international, I mean, what's the name of it? Does it begin with a W or something like that?


Oh, there's like a lot of different branches.


Uh-huh, yeah, but what's, what, what's like the general name of it?


you know, what does it have a, like a name for that. I, I read about it on the internet.


like the name of the school or what?


Yeah, I, I mean, not your particular school, but


like they have all these schools all over the world, what's the, what's it called, do you know?


Well, the app, well, the app was like


the like platforms and apps. It says Sabbath.


it's, yeah, OK, I didn't get that, but OK. I'm trying to


I don't know what happened here. I can't. I'm trying to um


find my latest thing here.


OK, I've got it now. All right, so


I'm, I'm gonna magnify this and look at it.


We'll see if I can read it


Oh, OK. All right. So this is another proof, so it says, given


that


these triangles are congru and complete each of the following.


so as to make a true statement.


give a reason, a reason must not be the reflexive property.


OK, let me just


there's no, no, wait a minute, does that say reflexive yet? Let me look up reflexive to be sure I understand what that means.


Reflexive


The value is equal to itself. OK, so you're not allowed to use that


OK.


So the first line says


what does it say? AB is?


Um, A, B, and then like the reason I think it's AB is congruent to MN and that the reason is res corresponding parts of congruent triangles are congruent.


Yes, yes, OK. So let, let me just check this, so the symbol after AB there is congruent symboli. It's, it's sort of out of focus. I'll try to magnify.


Oops, maybe a little too much, but hang on.


OK, so that's all right. OK. So how about the


how about um


OK, so now, how about angle A? What are we gonna say about that?


In in number B


A would be angle M


M yeah, M as in Mary.


yeah.


OK. And what's the reason for that?


Yeah yeah


and CPOCTC, same thing, all of the.


Yes, OK, and I will see, it's the same thing, but what angle does C or is it congruent to?


P.


OK


All right, so


OK, now


what about D


D would be.


NMP


Wait a minute say that again.


Triangle MNP.


Well, I don't think it's MNP because you see,


MMP


and, yes, N as in Nancy, right? And what's the reason for that?


CPOC.


No, I don't


OK, but I, uh


I, I'm not so sure that's, have you had things like side angle side and theorems like that.


Maybe you haven't, there's, there's, there's theorems called like SAS, SSS.


I forget the other ones, but


you see what we have here is we have


two angles


and one side


OK, I


let me think about this


I, I, here's what I'm saying, in the, in the first three steps, you showed that one side is congruent in two angles.


Is that enough


to show that the DAC is um


congruent to uh


NMP. That's the question.


Um


I mean, it probably is, but


um, I'm not sure about your reason. That's what I'm


let me think here. We've got angle A and angle C.


OK


Well, I'm, I'm what I'm trying to ask is have you had any theorems yet like called side angle side or angle side angle or anything like that?


yeah, we've had that, but it's not included.


um


OK, let me think about the reasoning here


I


see


I'm a little one of uh


OK, so


do we have, OK, so you think corresponding


parts of congruent triangles


I don't


but it says all of them are supposed to be like that.


wait a minute, all of one


All of them are corresponding parts of congruent triangles.


Oh, OK, and where does it say that? Does it have a solution?


Let me look


Hello


Yeah, hello


Can you hear me


Yeah, I hear you. Can you hear me?


Wait


OK. OK.


So where does it say that that's what you're supposed to use? Is there a solution here that I'm missing or


I don't know, but on the like


answer key, it says it's CPOCTC, like all of them.


Oh, all right. Oh, so you have any, OK, it says that for all of them.


Yeah.


even D? OK. All right, it's all right with me if it says that. I didn't know yet, OK, I uh


I, I would have used different theorem, but OK, all right, so shall we move on to number 2?


OK


Yeah, so ABC is


an isosceles triangle.


Wait a minute,


wait a minute.


wait a minute, which one are we on now? #2?


Yeah


OK, and how, how do we know it's isosceles?


Um


Oh, I see. That's ask you to, OK, maybe, maybe you're right, like.


let me think here. Yes, yes, I think it is, but um


this is similar to one of the previous ones. What do we know about


angles's um


1 and 2


Oh, actually, I guess it doesn't matter because if


if


you


OK, and


if uh if AB


equals AC, then it's isosceles. OK, yes, that's good. You're right.


But that, OK, right, so what's your explanation for I just gave you. What's your explanation for why it's Ios.


because like AB is converting to AC.


Yes, OK. All right


Wait, we could just do it. These questions won't really come back, right?


OK, I didn't understand what you meant.


What about B


OK, let me just


um B would be


wait.


is AM the bisector of angle A. Um.


yes


obey


and why


because


um


angle like A is.


Isn't it cause of like CPOCTC and


uh


I think so, yeah, I think so because, because I know BAM corresponds to angle CAM.


yeah, so


OK.


OK, let me just hold on real quick.


OK, are you working on 2C?


Um, I don't really think that these questions will come back tomorrow, cause


we um


Oh, OK. All right. OK, well, if you would do, so you wanna skip these? I, I think I.


OK


yeah, I mean just find


it.


So where should we move to or are we done?


OK, I'll find some questions that might come back.


OK. When you say come back, do they use exactly the same questions on the test, or are they similar?


Oh, like the


or


yeah, basically like they changed the numbers and figures.


Yeah, it's OK, OK.


just not floating.


All right, I better go back and look at the other screen here. OK.


Wait, OK. Um, let me just upload them and


OK.


I think I have to take a picture of this.


OK, maybe also before you upload it, maybe you could delete this one. I, I'm, I'm worried that


Yeah


there may be too many pictures, uh, I mean for the computer, not for me.


yeah


Oh


OK, I think I see it, oh, I, OK, no, I guess that was the old one, not the new one.


How many should I delete all of them or?


I didn't hear you


Should I delete all of them?


Uh, well, just, just ones you think we're not gonna need again.


so that we haven't


Yeah, you know


OK, OK


Well


not really downloading the questions are.


um


and now.


I just keep trying for now and if not, we'll maybe, maybe um


No, it's like my


wait.


it's on my, OK, never mind. I need to take a picture.


right


OK


OK, so this one's given CPOCTC and definition of angle bisector.


But somehow my, my, sorry, my microphone got turned off.


Um, can you hear me


Yeah, I can hear you


Oops, wait, no, I don't hear you.


I, I see


Oh.


you know.


that.


00, OK, try it again. Let me see if I can hear you.


Well


Yeah, I hear you now


can you hear me


Yeah, for some reason


Oh, I know what happened when I rewrote it, when I refreshed that um


turns off my microphone and the speaker. OK, I hear you now. OK.


Sorry?


So what I was saying is I think this one is similar.


to the last one where you gave, you just described things, but now we have to do it as a proof.


OK, so


you wanna work on this one


Yeah


OK


Yes


OK. Um, first one was given. Second is super


yeah


PC and then definition of it.


Wait a minute, wait a minute. Tell me what you have for 3.


Definition of angle bisector.


OK, let me just think here. Okay.


Yeah, OK. All right


Now wait a minute, wait, wait, wait a minute


QMP


biceps


Oh, I see it. They, they list two things in a bisects. OK. All right, yes, OK.


OK. Well, that was quick


OK, let me


OK, I just looked something up on the internet. It says XYZ Education


is a global education management organization with headquarters in London.


So I guess your school was part of that


system, is that right


Yeah


I mean, I think it was like


founded in New York.


Yes, yes, I think so. OK.


OK.


the


what was his name? I don't know. We had like a thing about him.


OK


Wait, I'm just gonna upload one more and then.


Uh


so


OK. Tell me when you, it's uploaded because I'm looking for the bill from the plumber here.


All right.


So let me, let me magnify it and then I'll copy it here.


make it a little better.


make it a little bigger


right.


and it


OK, so this is number 11


Yeah


OK, now I'll magnify it a little bit here. Let's try this.


OK, you to the diagram below.


Mhm.


Wouldn't it be a no and BC and then O is just uh


degrees


OK, slow down your way ahead of me


where, OK, NO


is OK, NOBC, that's correct now angle


Oh yeah, I agree, yes, yes.


105, yes


OK


OK, are there, are there more, questions?


No, I think that was just like.


Well, that's good


Oh, thank you so much for this session, and I hope you have a really good day and


OK, you're welcome. I just, um


I just want to point out that, see, where I live,


uh, I mean, tomorrow's Martin Luther King Day, so we don't have school, but you're sure you do have school tomorrow?


yeah, I think my mom hasn't told me anything.


OK. OK. I was just checking. OK. All right. Well, I'll uh


I look forward to seeing you again. I'm a little rusty on my geometry, but I think you did fine.


Yeah. Thank you. Bye.


OK, bye-bye


a good day


hi how can i help


hello, i just need help with one question i can upload it


sure


do u want me to use my mic


to explain better


i find that helps w math a lot


sure you can


okay lets see the question


Hi, can you hear me


Just let me know


yes i can


OK, cool.


Uh, locate all extrema. OK, so, basically,


I'm trying to figure out how to do this. So, cause we just had a test on this recently, um.


OK, so basically, when the derivative equals 0


then it's a loc then it's a maxerin cause this is the slope of all the tangent lines that are on FFA. Does that make sense?


yes


OK, so it's literally just one


just put it here 12.


and yeah, those two points. So we know that those are going to be extrema, right?


So we know that right now, the slope


is positive, right? And then it goes to negative. So we know that this is


increasing, increasing, increasing, decreasing.


OK?


okay


OK. So at X equals -2, then if it's going up, up, up, up, up, and then down. It's gonna be a um local max. Does that make sense? Because once you start going down, you can't go up anymore.


yeah


Yeah. OK. And then


there is a, I think this is a minimum, yeah, cause you're going up, up, up, up, up, you're at zero, and then you start going down again.


So that would be the local men


or absolute cause, yeah, absolute local, I mean, it's on, it's a line, so we're assuming that the there's no absolutemen in the function cause like,


yeah.


is that all


OK


so would the x values just be that?


Yeah


Do you need help like of um


me explaining that.


or


yeah could you a little


Hold on


okay


Yeah, yeah, yeah, sorry, I actually explained it wrong because, oh shoot, cause the graph is really blurry. Sorry, I had a better look. So


when X, sorry, OK, now I can see it cause my thing is freezing. When we're in this, I'm gonna, how do I do have a highlighter? When we're in the top two quadrants.


it's positive


OK? Like, we're increasing.


When X is


above zero or mean Y is above zero for a derivative graph, we're increasing. However, when it's below zero, we're decreasing. So we know just by looking here, we're increasing, increasing, increasing, increasing. Local max for men, decreasing, decreasing, decreasing, increasing a little bit.


But I don't know if we touch zero, there's no way to know that. Decreasing, decreasing, decreasing, still decreasing even though it's less.


And then we start increasing right here because we go above 0.


oh okay


Yeah. So we're decreasing, decreasing, decreasing.


I mean, sorry, yeah, increasing, increasing, increasing, decreasing. If we're increasing, increasing, increasing, like, let's say let's do a sample graph right here, start decreasing, that's a local max. Now, if we're decreasing, decreasing, decreasing, decreasing, and then we start increasing, that's the local men.


ohokay


Yeah


I hope that makes sense. If you need any other explanations, I can give that to you.


yeah it does, so would my x values be like when it changes from neg to pos


Exactly


and pos to negative?


So if you are going from


positive to negative, so I'm like struggling to find the words. That's a local max because we're increasing, increasing, increasing, and then decreasing. However, if we're going from negative to positive. Yeah, negative to positives. That means we're decreasing, decrease and decreasing and increasing. This, yeah, this looks like a whatever, right? That looks like a match for a men. However, because we're still below, right? Even if we


um hit 0, maybe if there's like a tangent line, right? And that would mean the slope is zero, we're still decreasing, we're not increasing because like let's say that it would look like this, right, we're decreasing, decreasing, decreasing, tangent line, which would be derivative zero, and then keep decreasing. There's no increase in there.


So even though it looks like it could be a local max or men, a local maxerin is when we cross the X-axis fully.


ohh okay


so the min would be x=3?


okay and the max is x=-2?


Yes


So I, it's like very laggy, this website.


okay, i got it now thank you


OK


Is that all


yeah that was it


OK. Have a nice day


hi


Hello


any help


I have this math final and I rlly need to pass


we will do it together


let me know


But i can come back anytime and Sarah on her right


For later


what?


Like if I needed ne


He


Help I can come back later


yah


And like r ppl able to talk on here like call and stuff


I am on school right now , I can text but cant take call


share your problem screen


You need help with this problem?


Yes please


No worries, first let me ask you do you have any idea what any of these mean?


I know what the x intercept is and the y intercept is but I am not sure about the rest


No worries, then for those 2 fill them out first


Perfect!


Now for domain, this is a very simple concept, basically, what is the lowest x value this graph reaches and what is the highest x value this graph reaches


What do you see?


I'm a bit confused sorry


Ok, lets look at the left side first, at the very left, what x values does this line land on


Perfect, and now the right, we can see it continues on forever meaning it is heading towards what


infinity


positive infinity


perfect so its domain is [-1, infinity)


The bracket on the -1 means it includes -1 and the parentheses on the infinity means it does not include infinity because infinity is not a number.


Oh okay


Now use this same logic for the range, only now we are doing it with the y values


Go from the lowest (bottom) to the highest what it approches


Yes perfect, and it heads towards what y value


if it goes on forever


perfect


Great, your answer is perfect!


Now for the average rate of change, how would you find the rate of change of a straight line


I am not sure sorry


No worries then I will introduce you to the formula


This formula means that A(x) the average rate of change is equal to f(b)-f(a) all over b-a


And our point [8,15] is structured in the format [a,b]


Using this information, try pluging it into the formula


what would I put for f or does it just stay as an f for the formula


basically all the f(a) means is what is the y value at the given a value


same logic for f(b))


so basically for we know for our given range 8=a


meaning f(a) = f(8) = y value when x=8 = 12


Same logic for f(b))


Sorry for asking, but where did the 12 come from


No worries at all


Basically, 12 is just the y value when the x value is 8


so if we look at x =8


The red line I drew


the y value that intersects at is y=12


so f(a) really just means f(8) in this situation, which means the y value when x is 8


So for f(b)) that means what is the y value when x=15


yes perfect


now plug these numbers into the formula


for f(b)) and f(a) do I put 15 and 8


inside them


yes that would be a good extra step to show your work but we have already determined what both values equal so just plug those values in and solve for final answer


Like that?


Yes perfect now evaluate


Like that


yes that is perfect, thats all there is to it


Okay thank you for the help!


no worries, good luck on the rest of your work!


Thank you


Howdy !


Yellur


So what's going on in your math class?


Right now we are going over unit 6 in ap calc ab (like approximations and basic integral stuff)


So do you have some sample problems you wanna look at?


And i have a quiz tmr :D


I have the study guide and a few questions to like LOCK IN the final info loll


Sweet !


Okay i understand a-c but i can work through them for funsies, but im always messing up trapezoidal calculations and its properties :’(


I've not seen those acronyms in a b and c before - what are they?


Left end point, and ...


Left reinnmansum


Right and midpoint


More acronyms.


Don't like 'em.


Yeahh not the funnest


Funnest lol


Let me graph this real quick so we can work thru part d.


Be right back.


Alright also ap peeps don’t get a calculator sigh


bummer...


Ikr :\


So yeah, it looks like that.


You can plot this without desmos by plotting the intercept


Vertex at -b/2a


Oh wowww


And so forth.


I just like to get a picture.


So fancy


Chris


If we get Chris Math 101% doin that


It just works better than me trying to draw something by hand on this whiteboard.


It feels like I'm drawing with a crayon between my toes.


Oml that’s hilarious


Yep, square them and add them up.


Oh shoot mb those are the doubled answers


The ones i put in y


You gotta plug in 1, 3, 5, and 7


Its 1, -3, -15, -35


And double those you get the answer i wrote in y accidentally


The final answer is -104


And that's our answer and we're sticking to it.


You'll sometimes see this listed like this (see insert).


Yeah i never remembered the trapezoidal one


It's just taking the midpoint of each rectangle and using that.


This formula makes it more complicated in my opinion.


So mram times 1/2 times 8-0


Wait 8-0 over 4


delta x = 8 - 0 divided by 4 = 2


Okay so how would i remember yk if they ask me is trapezoidal over or underestimate for said graph,


Like uh concave up and increasing


Hold on a sec...


I'm not sure if it's over or underestimating.


We can integrate (cheat) and compare that to the -208


OH WAIT also for the trapezioudal calculation im supposed to also include like for example f(0)+2(f(blabla))+ at the end f(8)? And like the first and last number dont get doubled?


Oop using our recourses :D


Because think of the first rectangle.


The legs are f(x_0) and f(x_1) right?


Mhm


Ohh


And second triangle is f(x_2) and f(x_3)


Let me draw a picture.


Okay!


Just using a generic graph, not the real one.


You’re using right approx?


No, using the one in the middle.


Wouldn’t 6-8 be diff then?


Yes, like that.


Okay yup


The height of the 4th rectangle is f(7).


Area of the 1st one if x-value) times delta x


how would traperzoidal look?


Hold on a sec - I've totally screwed this up.


Like that


:’D


I was giving you the midpoint formula and speech, not trapezoid.


I was like huhHhhH


Hold on a sec - gotta quite down the dogs (barking at nothing).


HAHAH realll


Seriously - we get a deer in the backyard and they go bezerk.


That is so cool!


There aren’t much deer in our backyards thankfully


we've got TONS in Vermont...


I bet :’D


Colorado is just a chill guy


So for the trapezoidal method, we take the average of the two "posts" at each end of the rectangle.


Not the function value at the midpoint of the rectangle.


Mhm


So f(x_midpoint) and other "posts" get counted twice.


Once as a "left post" of one rectangle and once as a "right post" of the adjacent rectangle.


Oh but since the first and last dont get repeated then they get multipled by one onl


Yes !


Gotchaaa


It's hard to explain in dialog box but easy to understand once you get it.


It clicked now


Do you want to go thru the algebra part of it?


Yeah sure!


Here we go.


Yes, that's it !


Yeah? :’D


Yep, we finally got there after some turns.


Sorry for starting out with the wrong formula.


It’s negative cus the graph is reflected right


It's because I mixed up the midpoint method and the trapezoidal method and now my head has exploded.


Uh oh :o


That’s not good! I still got tons of problems


Do you have any easier problems?


lol yes


Just for extra practice


Post 'em !


it’s one is literally the easiest one there


Yup, so far so good.


We slow down this time.


i need to pract=ice explaining!


for FRQ’s


Say that when you multiply 800 gallons per hour times 5 hours you get 4,000 gallons.


That represents how much oil was pumped during that time.


Ahhh


Wait i thought for area ou have to multiply each rectangle and add them


We already find the areas and wrote them in each rectangle.


But why is it getting divided by 12?


Oh, I thought they wanted average rate.


Oops.


Haha youre totally just testing how locked in i am


Exactly.


Chris got this one locked in


Right on.


NEXT !


On to the next ADVENTURE


Ah yes your fav


OH SHOOT


THEYRE NOT EQUAL


Subintervals not equal.


Mb


They are tricky buggers !!!


Yep.


And there's your bacon !


Yummers


Bacon for dinner?


That's my way of saying "there's the answer !"


Ah nice nice’


Are we done yet?


Nah


ah!


Mb doin mental math


Are you sure about b?


I hope so?


But let's say the curve is under the x axis (negative)


What if its positive tho?


Then you'll get a less small negative number.


Oh wow


Yes, different answer if it's positive.


That's my point..


I never thought of that


Seems PA boy is of some use.


What thats crazy


Literally sobbing rn


Okay uh lets go to integrals


Yes !


The fun partt


I got 2 more screenshots and then i think im done


Yep - pull that 20 outside the integrand.


See do yk how to write that in the fat Riemann sum form?


Im always confused when i need to do it


what's a fat jax?


that :’D


Like say i got the integral with just -20


How would i rewrite that into this form?


So you're doing Riemann sums when n goes to infinitity.


You start with the formula f(x)


But what would the formula be?


Just y=x?


No y=num


It would be y = -20


So let's get back to part a.


You're integrating the function y = -20 from 3 to 7


So area under curve = -20 x 4 = 80


Yeah


One down !


Wait how do i rewrite it tho


:’D


Part b?


No part a


Like into the other form


YK what ill save it for the other screenshot


They are not asking you to do that though...


They will later :\


They are just asking you to use geometry, not Riemann sums.


Yep, rectangle for part a.


Triangle for part b


circle for part c


Transposed circle for part d


Semi circle and rectangle for part d


yay!


Houston !


okay final screenshot


and no reimann sums either.


:D


Say what


So you're okay with delta x ?


It being 4/n ?


Mhm! Im working a bit lower


Okay, we got the same answer.


Yay!


So you're FAT JAX is another way of doing it.


It’s how I remember the order


You're just starting at the left point a and incrementing by delta x as you go right.


F(a+jAx)


Brilliant !


Miami!


Then you do all these clever substitutions so get rid of the i term.


Then take the limit as n goes to infinity.


Yeah, yuk is right.


That looks miserable to memorize


Im done!


Sweet !


Now for the last part!


You are one SHARP COOKIE and will do fine on your test.


Just slow it down a bit !


The reverse (also this is where imma get quizzed the most on :’D)


AH sorry


That’s!


What problem are we working on?


see part c was my question


So you've got a and b?


Yup i can do them rq


So how to do c is the question?


mhm


I say -6


Not solve it but rewrite it?


You can bring that 1/n term inside the summation sign but I don't know if that helps.


I'm stumped.


Want me to ask GROK?


Ask what?


Grok - it's the AI bot on X


Haha suree


Can do amazing stuff.


That’s crazy


Be right back.


Gotta check that out one day


It also got -6.


Let me ask it now for the rewrite.


Chris


Okay but why?


Is -2 just its own function?


Am getting there...


Whoops


So when I math tutor, I always keep a tab open for Grok and for Claude.


Smarttt!


More like lazy but I'll take it.


I need to tutor bruh, free money


Nah lazy is genuis


They invent some crazy stuff


That'Lincoln High !


Def gotta pick that up! Some basic algebra or something


You'll be fine.


Okay, so best of luck on your test !!!


Quiz* thanks!!


Take care...


you too


Hi! How may I help you?


Good morning, I need help with a problem but I only have 15 minutes.


I’ll put it on the board.


That would be great, Thank you.


What specific part do you need help with?


The solving part.


Okay, what do you think we need to do first?


I want to know how do I factor the 8+2a-a^2


Okay, what do you think we can factor out from that?


Hint: It might help if you put it in standard form.


I don’t know.


I haven’t been using standard form to solve it.


You can put the ones with highest degree first.


Now, what do you think we can factor from here?


Ok, you can factor out the negative, because it makes it more difficult to solve.


Yes, great job!


What do you think the next step is?


To factor the bottom.


And do KCF.


Yes, try that.


Yup, so according to keep change flip, what must we do now?


Yes. Try to factor the bottom.


Yes, you would get (a-4)(a+2)


Now, we can cancel out few things here.


How they’re the opposite of each other.


No, we can actually cancel out (a+4) and (a+2)


To make it simpler, I'll try to put it in a different form.


Ill put it in the bottom


As you can see, if you factor out the negative, you can cancel it out.


Wait but why did we change the signs?


Because we factored out the negative, so now it became opposite.


you can do this in the beginning of the equation, or later on.


Now it reveals that we can cancel out everything on the first part, leaving us with -1.


Now try evaluating the expression I circled.


I don’t get it.


Ok, so do you get why the signs went opposite?


To cancel it out.


All of that canceled out equals 1, so


Yes exactly


What I boxed would be the end solution.


Okay thank you.


Bye.


Your welcome! Great job!


Hello How are you?


hey thanks for joinin me!


You are welcome. How can I help?


OK I will copy to other screen Pls wait


ok no worries!!


OK I will rerad it now


OK


Question: Do you think you are supposed to just use trmnsofrmations and then ge the ordered parirs later?


getr*


get*


yeahh so basically they want me to start off with a table for the parent functoin and then use those points to get the transformed form of the new graph (like take those values and do all the transformations to them)


function*


So where should we start?


lets set up a table for the parent function


which would be f(x)=log2(x)


OK what do we think is the parent function?


OK I agree


would u like to put the tanle on the whiteboard?


table*


sure thing!


OK go ahead  I will help as needed


ok but can u take the log of 0 ?


ohh true true lolll


or of a nge number?


neg*


hmm yeah let me use diff ones


maybe 1/2  1/4 and 1/8


OK good


can u label first column "x"?


yeah my bad!


I sort of disagree


I think the left col is x


and the right col is y   or f(x)  ot y = f(x)


hmm how so?


or*


well we start with an x and then we take its log to base 2


so I think the first col would usually be x


ohh ok ok


and the 2nd col f(x) = logbase2(x)


can u change that?


so you want me to rearrange the column names or the values


no


jus the column nmes


the first col will bex   and the 2nd f(x) = log2(x)


wow you moved those quickly


ok good


LOL


now can u fill in the 2nd column?


ok go ahead more labeling


Good


are you using a stylus to write?


no my keyboard, which is hard


you do very well


OK now can u fill in 2nd col


1 2 and 4 might be eeasiest to start


ok


thank u thank u!


-2 is fine go ahead


kk


excellent


some confetti


i love it!


OK so now do we do the ranformations step by step OR do we go to the "final function?


yeah step by step, what do u think


well I don;t know How do u do Robert in ur course?


it*


yeahh so we usually do it step by step by differentiating the horizontal transformations and the vertical transformations, then we take the values from the table and just do the ramifications


OK pls show me and I will help if needed


ok so now i start with the horizontal


ok good


I get confused by Oakville


yeahh since 1/3 means 3x


do we take the 1/3 first and then shifth left by 2 ?


OK


the stretch first


what u have is good


now how do u use that?


ok


Maybe you want to make a table


yeahh


and maybe you want soem different x values


I  mean x = 1/4 gives 1/12


finding log2(2 + 1/12) is not IMO easy


wait


I am confused


why do you pull out the 3


same lol


maybe that is OK


but I am not sure


bc the stretch of 1/3x is actually 3x


well yes in the *grpah* there will be a strecth


and then i just distributed it


BUT I *think* we need to sue the new f(x) as is


hmm


let us think


x = 0


yeahh


is a good vlaue to use for the new function


maybe also x = 6


ok


and x = -3


why not start with those 3


see what you think


ohh


see with logs transformations r more confusing, but i think i see what ur getting at


x = 0 will give log2(2) = 1


wait


i is jsut the log


but you need to mult by -1


ands then add 6


add 5 *


so what will be in 2nd column?


hmm


well the log part is 1


so don;t we have 1(1) + 5?


Im nea -(1) + 5


-1 + 5 = 4


everyhting to the left of the +1 gives -1


I mean to the left of the +5


I need a typign course!!!


right


hahaahaha!


so for x = 0  I htink we get 4


ok


Be sure you see that. I sometimes go to fast


too*


now please try x = -3


I will be quiet LOL


ok!!!!


I have to help my wife with the TV


I will return in 3 or 4 minutes


ok ok thats fine!!!!!


Pls work oon the table


take your time man, ill be here


I am back


About twice a month my wife decides the TV is borken


Modenr elkectronics is better than that


HAHA I can relate with my mother


ok table looks good so far


hows this


OK I can check your numbers but I suggest you look for x vlaues that give "nice" logs


like try x = 6


ok


btw the vlues you have so far are fine


u sure


Yes


my calculator made a tbel for me


and u will see why 6 is good


ohhh ok ok


you get log2(4)  !!!


good


do u see why 6 was a good choice?


yeah i do


yes log2(40 is easy


I mean log2(4)


right


OK do you think that is enough points


wait wait im understanding this now!


i think this should be enough


OK one comment


I was concerned that the y vlaues were not always decresing


but then I saw that -5 is out of order


that is OK


I was just fooled


yeah want me to fix it


no


just be aware of that


now what would u do next in ur course? Graph these points?


yeah let me graph it now one sec


OK


wait let me put this in order my desmos is glitching


ok


BTW do u know how to use sliders in Geoffrey?


i am not a wiz at desmos


just as an aside


you could use sliders for the 1/3  the 2 and the 5  and vary their vlaues


the graph looks good


I sued my latest new claucltor


but your grpah is great


thank uuuu


especially the way it shows the points you used


yeah yeah


let me draw the asymtpote


I am not sure it really has o ne


yeah at y = 5


is that the red line?


yeahhh


but can a gprah cross an asymptote?


no


the scale is off since i spaced it out


i think the log has no horiz asy


at x = 90 the grpah changes sing I think


sign*


try extending x axis to about 110 units


wait wait


ok


my bad i messed up


its vertical asympotoes here


you learn that way


the transformed one has one at -6


OK


but ques says horiz


yeah its wrong idk why they didnt catch that


well are these questions for a textbook?


yeah


I think there is vert asy at x = -6


and ur grpah agrees


yeah and the parent function had it at x = 0


I think that makes sense


becuase when x = -6 we have log(0) whic is not sllowed


yeahhh


for x < -6  we have log of neg number  !!!


and BTW the parent function has asymptote at x = 0


Now if we shift left 2 and then strecth by 3 we are at -6  !!!!


I have 7 more minutes beofre I must get ready for be


bed*


let me write all this down befoer you go


OK


DONE


thank you thank you David for all you have done


now get your rest that you deserve!


You are welcome This was fun


you just made me 10x time smarter


haha it was


Well you jsut *discovered* how smart you are !!!


take care now, talk to you again hopefully!


Yes hope to "see" you again


BYE BYE


Sarah


Hey can you help me


Hi Maya! I'm David, nice to meet you :)


Of course I can help! What's the problem?


Nice to meat you too! i recognize your name lol


nvm\


:D


Oh were you able to solve the problem? Or


oh noo i was just saying i like your name


is it Korean


Oh that part lol


sorryyy


No, it's an French name :) But my Turkish friends have told me it means food if I remember correctly in one of the languages though?


Yup there right lol


You're good :) whenever you're ready, upload or write the problem!


i have 49 assignments btw


Ooh that's a lot...I won't be able to help with all, but is there a common topic among them, or one you're especially struggling with?


yes:(


Okay, what's the problem about?


Or like an example problem


If you're still struggling when you get back don't hesitate to reach out!


hi there


Welcome to your 1st Maya's session!


hi


I need help with interior angles of polygons


ok


how do I find the sum of the interior angles of a heptagon


how do you determine what that sum should be?


I put some info on the board


are you asking how to know what that sum should be?


yes


how many sides does a heptagon have?


idk


you need to know that to answer this. heptagon has 7 sides


so in the formula, n=7


what is n-2?


ok thank you


yw


is that the only math you need help with?


no i need help with more problems too


ok. let's finish this one, first


please finish it on the whiteboard


correct


the next one is: the sum of the interior angles of a convex polygon 1080 degrees. classify the polygonby the number of sides


solve for n, then name the polygon


I put the equation to be solved on the board


does that equation make sense to you?


yes just give me a second


so it has 8 sides


right?


yes


what shape is that?


octogon


spelling is octagon


right


find the measure of each interior angle of a decagon


deca means 10 right


ok


how do i do that


same formula we've been using for the other questions


ok i got it


correct


how do i get the measure of each individual angle


do i just divide it by 10


since there are 10 angles


ok thanks


so 144 degrees per angle


if it is a regular decagon where all angles are equal


yep it is


an interior angle of a polygon 150 degrees. classify the polygon by the number of sides and find the sum of the measures of its interior angles


its a regular polygon btw


this one's a little harder. can I clear the board?


yeah


we're going to write the sum of the interior angles in 2 different ways, using n as the number of sides.


what's one way to do that?


i dont know


we've used 2 different ways already


what's the sum of the interior angles of a polygon with n sides?


oh (n-2) 180


(formula containing n)


right


polygon with n sides has how many interior angles?


polygon with n sides has how many vertices?


unknown?


no


n


im confused


triangle has 3 sides, 3 vertices, 3 interior angles, right?


rectangle has 4 of each


oh


pentagon has 5 of each


so, polygon with n sides has how many interior angles?


n angles, each one 150 degrees


what's the total of all those angles?


use a different formula


n angles, each one 150 degrees. just use tht


what different formula?


*that


like when you divided total by 10 to get individual interior angle


adding 150 n times is the same as 150n, right?


im so cconfused


measure of an interior angle times the number of angles gives you the total


two different formulas for the total of the interior angles, and they have to equal each other


solve the equation on the board to find n


are you still here?


yeah hold on a sec


it would help me if you did your work on the board where I can see it


sorry i have to go


ok


thank you


yw


Ready


hi


What's the first question?


I just need to solve the chart


fill in the blanksw


The combined number of students who use Vans and Trucks is 40


Without additional information (such as a specific ratio or a value for one of the other categories), the individual values for Vans and Trucks cannot be determined separately.


oh... thats all there is for this problem 😭


anything else for today?


no, thank you


bye


Hi, I'm Alex


What do you need help with


sovling linear equations please


alright


how to solve them?


or graphing


both


do you know what slope intercept form and standard form are


no


what do you know about linear equations


or are you completely new to it


new


basically a linear equation is the equation of a line, where each variable(x and y) have a power of 1


the equation models the relation between x and y


in our example, the equation y=2x+4 is like a rule


like a machine actually


x is the input, or what we give to the equation


then we put it through the rule


so if x is 2, then we do 2 times 2 plus 4


and this gets us our result y


how is it so far


i understand a bit


is there anything i should clarify


nope


alright


so basically our equation is like a rule to take an input x and get a result y


you know how graphs work right


yes


do you know how to graph equations


alright, so in our example equation, what do you think are the points for our line


or I would need a line to see if I'm wrong


ok


so you know how a point is graphed right


theres an x coordinate and a y coordinate


so in our equation


we have our x and y


however, the values for x and y are in the table


try to find the points for our equation again


using the table


2, 8 but yeah the others are right


so for our equation y=2x+4, the 2 and 4 dont represent coordinates


2 is the m and 4 is the b?


yeah thats right


good job


the b moves the graph around


up down left right


the m makes the line more or less steep


do you know what the y and x intercepts are


no


alright


ive got to go right now, Horizon High or youtube


hi


Hi there!


What do you need help for today?


can u pls help me with my homework


yes Liam!


I don't really understand it and it due tomarrow


you can feel free to send it in chat or on the whiteboard!


and I only have a few min to work on it


like 30


ok ty


let me just get it ready


i see!


it's okay we'll work through as many as possible


ye


umm its kinda a long problom


I will try to write it down


thats not a problem, you cant send it or upload a picture!


at grocery store A, 5 cans of baked beans cost $3.45. At grocery store B, 7 Cans cost 5.15. at store C, 4 cans cost 2.46. at store D, 6 cans cost 4.00. How much money would you save if you bought 20 cans from store C than if you bought 20 cans from store A.


sorry it took a long time


I had too write what was on my paper


no worries! lets work through this together I'll try and use the whiteboard!


ok


ty


of course!


does this make sense?


ask me if you have any questions!


umm hold on


let me see


Basically firsly we divided the price of the cans with the amount of cans, that gives u the price per can.


oh


then we took the price per can for both store C and A and multipled it with 20 to see how much it costs for 20 cans at each store


and that gave us 12.3 dollars for store C to buy 20 cans


and 13.8 dollars at sore A to buy 20 cans


so then we just check the difference which its 1.5 dollars here, so you save $1.5 dollars


oh ok


that kinda makes sense


but can u pls explain the first part I not really understand it


what part is confusing I can explain!


okay so look at the board


k


so for store A it costs 3.45 to buy 5 cans right?


ye


but for store C it gives us the price for 4 cans and not 5


so we have to first find out how much it costs for one single can at both stores


does that makes sense up to here?


so in order to do that


we take the price for 5 cans at store A which is 3.45 and divide it by 5


that gives us the price for a single can at that store


oh


and we take the price for 4 cans at store C which is 2.46 and divide that by 4


so that would be this part


giving us the price of a single can at store C


thats the division


ok lemme explain


ok


The 0.69 is the cost for only one can


yeah and thne the same for store C


oh ok


so when you do the thing on your paper this is how


that makes sense


ty


thats basically how you do it!


can we work on the next one now


of course! you can take a pictue or write it down and yes we can move onto the next


let me know when ur ready


I only have like 5, 6 , 7 min left


thats fine lets try and do it quickly!


Emily drove from New York to Chicago. she drove 284 miles at a constant speed of 58 mph. how long did it take Emily to complete the trip


is that all the information they gave u?


ye


okay so for this there is a formula to use


lets look at the board the formula ill write it


ok


so to find out how long we have to take how far she travelled and divide it with how fast.


now im gonna plug in the numbers from ur question


when u divide 284 with 58 u get a longer number but we can shorten it to just 4.89


so that means that it took her 4 hours and then we have the decimals


we take the decimals and multiply it with 60


which gives us 54 minutes


so the answer is 4 hours and 54 minutes!


ty


ofc!


I have to go now can we work on this later


as long as u remember the formula its easy!


Liam bye


and yes have a good evening!


byee


Hi


how can i help you


i need to solve a math question


and i dont understand


ok do you wanna type it or just take a picture of it and load it onto the whiteboard


i'll try to take a pic


ok


i'll just type it actually


ok im gonna solve it on paper first then walk you through it


does it tell you the measurement of 1?


or only that measurement 2 is 2/3


because its gonna have x in it if not


it doesnt say the measurement of 1


so measurement one we will say is 1


1 is x


were gonna call it x


and measurement 2


is 2/3 of x


so measurement 2 would be


2/3 * x


which would be 2x/3


thats the only way you can do it without having measurement 1, you would just call it x


oh


ok


have you ever learned it like that in class?


or is this your first time doing a problem like this


we're learning similar but with numbers


not like


unknown


if that makes sense


my teacher said what the answer was in class but i forgot what she said


ohhh


yeah i dont think ur teacher is gonna give you problems like this one


ones with numbers you should practice more or ask her what she meant about this problem and if similar ones would be on tests


for linear equations and stuff


do you know if there's other ways to solve it besides disbrutive or smth property


like


2(13x+2) or equations with more numbers


yeah there are many other ways to do it but im not sure if they would be easier for you unless the way you do it already doesnt work well for you


oh ok


i would do it the way your teacher taught you in class because many teachers dont like you doing it another way other than what they taught


but if you want i can show you


yeah can you show me


ok so first we can do the elimination method


do you ever get questions like this


2x + 3y = 16
4x - 3y = 8


like linear ones like this


only works for these


we're not really working on those


but i'd like to learn still


ok


this style


is more what you get right


yeah


for that type of question


There are other ways, but i really feel like distributive is the simplest and easiest way to get the answer


so if you can do that method really good you should be fine


i can practice it with you if you want if you think you need more practice with it


its fine


ok do you want to practice anything?


or is that all your questions


i have one more


ill write it out


ok so first


we distribute the 3 and the 5 on both sides


so we get


after distributing to remove the ()


next


we want all x's on one side so we do


then we get rid of the -30


so we do +30


then divide by 4 to get x = 20


then


the perimeter of a pentagon was the equation 5(x+10)


did you understand each step i can repeat anything you want or didnt understand that well


its okay i understand it


ok good


and you understand why its 5(x+10) for the perimeter of a pentagon equation and not 3(3x-10) right


yes


ok good is that all?


thank you so much


np have a good night


Hi, how are you


good


I got my mic on. You may not be able to, but I've got it on.


ok


that's the problem


OK


I find it useful to write out the first few terms of a series to help me understand what's going on.


So let's, let's try to do that. Let's plug in i equals 1, do it. Let's get the first few terms uh


and so forth and see what happens.


Right.


So we'll get


for the first term, we should get 0, right? So let's go down below and


so we get 0


+ 1


and the next one will be uh


4, right


And the next one will be


uh 9, right.


all the way up to the last one, which will be 19 squad, which is


let me see what that is


19 square


is there a faster way?


OK. So how does that help us with that at all. Um,


instead of manually adding


are you supposed to do it with a formula, presumably?


yes


OK.


So, let me look at this for a moment. I got 0


+ 1 + 4.


+ 9 plus 16. So it looks like we've got squares


The squares of the numbers