Yeah, that's it. You just forgot to make the 2x positive last time, that's all


Okay, I'll solve it with the corrected 2x


There you go. Well done


Thank you


Hope I see you again!


I hope so too. Have a great day!


You too! :)


Hello how is it going


What can I help you with today


i think i don't have a deep enough understanding of unit 2 of precalc


I'm unfamiliar to what unit 2 is. Could you be more specific?


Arithmetic and Geometric Sequences
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Modelling
2.6 Competing Models
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Log Expressions


Alright I should be able to help out with that


How can I help though?


coukd you give me some practice from each topic and ill do them and maybe you can see where I mess up


Sure


We can start off with 2.1 first


I'll put a question on the board one sec


ok give me a second to solve and ill put the work up


Alright


answer 25?


Let me double check


Incorrect


wait is it because the first term is 1 so i just use that?


instead of finding the zero term


Yes exactly


It's the first term to use, not the "0th" term


ohhhh okay i get it can i get another problem so i can try it out with that


Slightly harder, but same concept


okay give me a second


answer 49?


Yep


yay okay great we can move onto geometric then or try a harder problem if you want


Sure


Give me one moment


Done


k give me a sec


Alright


is this the answer?


Let me check


Yep!


great! can i get a harder one and then we can move on


Yep :)


great we can move onto the next topic


So exponential functions?


yes


Do you have any specific functions about them? There are a lot of different questions about exponential functions, so just want to make sure


it was liek the features of exponential functions, its properties and then later topics talk about like translations and manipulation


Oh okay


Alright then


Give me some time to generate some questions


np


I put it on the board


7 is the intial value, 1.3 base?


Yep exactly


Not sure if that's what is being tested


my teacher also asked about domain, range, concave up or down, asymptote, end behaviour


Oh great


Let me put some questions related to that then


kk


Two parts to the question if that's okay


thats fine give me a sec


Alright


Take your time


done, sry if its a bit hard to read i cant really draw well on a laptop


Domain is correct


Range is incorrect


Does the first limit statement say positive infinity?


It looks like a zero


first limit statement is as x appraoches negative infinity, y apporaches zero


Incorrect


The second limit statement is also incorrect


You drew the graph incorrectly


Your current graph is a negative but it's really positive


but isnt the y intercept negative


It is yes


But f(x) does not approach negative infinity as x approaches infinity


positive infinity


It actually does the opposite


I'll drew a rough sketch of the graph on the board


Looks something like that


OH wait okay so if the base is positive, its still going concave up, its just starting lower cause of the negative y-intercept


Exactly


so if the base is negative its concave down?


Yeah so if it was like -2^x


It would be concave down


so the range would be 0 to positive infinity?


Not quite


Agree with positive infinity but not 0


Because f(x) does get values lower than 0


It has a horizontal asymptote at y = -3


oh so negative infinity


No


Here's a good way to look at it


Can 2^x = 0?


no


Yup


So, that means f(x) cannot equal -3


So its asymptote is at y = 3


y = -3


Meaning the range is actually (-3, pos inf)


pos = positive


The asymptote means as x approaches negative infinity, f(x) gets closer and closer to -3 but never actually reaches it


And this is something you'll see in Calculus called a asymptotic limit


oh okay bc i thought its always that fx gets closer to zero but not fully but it actually differs based on the asmyptote, so if the asymptote was o then that logic woudl work but since this example if y=-3, its -3 to pos infinity


Yep exactly


So (-3, inf) :)


okay lets try another problem


And by finding the range, we answered the first limit statement


x --> -inf f(x) = -3


that makes sense now


Yep


And for the last limit statement, remember that it's concave up and NOT down


So it's actually approaching positive infinity


okay got it lets try with another problem


Alright


I'll give a similar question but I'd like you to attempt it and it will have all the parts you listed earlier


ok


Alright I know that's a lot


But you have the skills!


One sec I'll be back


ok i finished for when you come back


Alright I'm back let me check


You're correct for every part except the initial value


at x=0, y=3 right?


No at x = 0, y = 3


Because -(5^0) = -1


-1 + 4 = 3


OH OH okay i got you the initial value is the base raised to the 0 power


Exactly


Or just the y-int


whats 4 then, i thought that was the y=int


4 is the horizontal asymptote


oh okay i thought it was both


but yea that makes sense


Yep


lets try another one


Sure


One moment


Do you want to move onto a new topic or still this one?


i want to try one more of this topic so i can make sure i have it down and then we can move on


Sounds good


Done


Also I'm going to get rid of the concave question


It involves derivatives which is a calculus topic


ok


done


Let me check


One sec


Nailed it.


yay! okay we can move onto the next topic


Well the next two topics are exponential function manipulation and modeling


I feel like we kind of did that though


my teacher had different stuff ill show it on the board


Alright cool


this was manipulation


Oh!


I see


Yes, I can give questions related to this


okay great


But wait


What did the first top of the page say?


Rewrite...


I'll need to know that


can you see it on the image?


Yup give me one moment


Alright I think I have a general idea


let me put a question on the board


You can remove it now thanks


All of these questions are rewrite it to the form f(x) = ab^x btw


okay np i can solve it now


Great


done


Yep great


I'll put another on the board


Sorry just rewrote it


Not quite


And we shouldn't round ideally


It's better to have it precise


Because sqrt(7) does not exactly equal 3.5


so keep it as sqaure root 7


Yep


k i rewrote it


Incorrect still


Shall I show on the board?


yes


Could you erase your work please?


Done


y = (sqrt7)^2


*x


Since 1/2 * x = x/2 using exponential laws


Oh okay i got it i forgot about that


Yep no worries


can we do one more


Sure


done


Technically that is correct


But you could also say this:


y = 1/81 * 3^x


That one would probably be more accepted


Same answer, just in a more organized form


i was gonna say it like that but i thoguth because of exp rules, it should be in fraction form


kk i can do ti like that too


Yep


okay we can skip modeling bc thats with a calculator and i dont have mine on my right now


Alright sure


What is competing models?


ill put a image


Alright great


This might be hard for me to generate questions


I could potentially make tables?


Maybe not for the regression questions though


thats fine that works


Alright cool


I'll put the first question


Is it best interepreted by a linear, quadratic, or exponential function?


linear


Is that all the questions ask?


To determine the type of regression


(ii) Give a reason for your answer based on the
relationship between the change in the output
values of f and the change in the input values of f.


Alright I guess you can explain how its linear?


And possibly give an equation


as the inputs increase over equal length consecutive intervals, the outputs are constant


ill put th equation on the board


Yup your equation is correct


okay great can we do a quad and exp one


Sure


Done


quad


Yep


And I don't expect you to find the equation


ok i can give explanation


Alright


as the inputs increase over equal length consecutive intervals, the outputs are linear


Increasing by 10


Each time


yep


we can do an exp one then move on


Alright cool


An equation is good for this one


exp, as the input values increase over equal length consecutive intervals, the outputs are proportional, multiply by 2 each time


Exponential equation is correct


okay great we can move onto the next topic


Okay


i can show you example of composition of function is youw ant


if you want


That'd be good thanks


that and like this 26. If k(x) = 2(x − 3) − 5x, for what value(s)
of x is k(x) = f (h(f(3)))


the graph might be hard for here so if you want you can just do the equation one


Alright


One moment


Not sure how I can do this


can you do like the picture i sent


i can also just solve this problem on the board and you can check


Yeah that works thanks!


okay great ill solve right now


you can check those and then ill do 26 and 27


i fixed 23 i wrote the wrong numbers on accident


Cool I'll check


Correct :)


ok ill do the last two


done, but i have a question for 27


Yes


b/c its absolute value, is there two x value answers like for =5 and =-5 or just one answer


Two


okay so let me finish the second one


done


Correct!


Nice work


yay! okay we can do inverse functions now


Sure


Do you have any examples that go along with it?


yes ill put on the screen


Cool


do you want me to solve these and check?


Yes that would be great!


kk


All correct


okay great, last topic if logarithmic functions


Alright


One sec


Do you have a worksheet that goes along with the topic?


i put it up


Alright cool


I'll make some related questions


Thanks


np


First one is on the board


done


Yep correct


I'll put another on the board


Done


Yep


It seems like you've got the main concept


okay great i think thats it for now


thank you so much


Alright


Of course


Have a good day


Bye!


you too


Liam, how are you today?


Good morning


How can I help you


im working on financial algebra


i have a project


in it


OK, you can also screen share.


the problem with me. Do you know how to do it?


The problem says show your principal interest rates for the to table, principles should be the same for each account except for immunity divided by 20. You'll have to research interest rates for the savings account in CDs. So you take a um amount you wanna put into your single deposit and then you pick a bank and I picked American Express and the


rate is 3.5 and then you're gonna compound it monthly and then you can just do the table I like here I have right now.


Liam, if it is about project I'm not so I'm able to help you.


why


because the way that I understand it that you have to do some research on so forth here. That is something that takes a lot of time.


So if it is about calculation, it, I might be able to do it.


but as far as doing research is concerned, I'm not so sure


I'm able to do it


hi how can i help you


Hi I have a question about unit 4


on related rates


ok


Ok


so you have to think about what you are trying to find here, which is dtheta/dt


Yes


so differentiate the equation with resppect to t


I like to draw it before I get the setup


Because I want to really understand the process


I don’t know what I’m doing wrong


i would recommend not drawing it for this one


sometimes that can be helpful but it may confuse you here


How did they get 1


Oh ok


If I don’t draw it then how would I know which trig function to use?


Do you times t by 10?


makes sense


I wrote it down


good


do you want to try one by yourself and i can chekc your work


do you have one.


I also have one that’s confusing


let's do yours


Hi.  How are you?


hi


good hbu


Good.


Can I turn on my audio?


only thing I haveto do here is to find the vertical and horizontal asymptote


Ok


So Alice, I turned on my microphone if you want to turn on yours, you can.


Um,


let's


go ahead and factor the numerator in the denominator.


Um, can you do that for me?


Let's factor both numerator and denominator.


If you don't know how I'll help you.


ok


Do you want me to help you or do you wanna try it?


i will try


OK.


That's good on the numerator


That's good on the denominator, very good.


So we can see that you factored it properly and actually the X + 1's canceling means that we have a hole in the function at X equals -1.


yea


So there's a hole in the function.


Now, what the other one being, if we set 2 x minus 1 equal to 0.


We find out that


the horizon of the vertical asymptotepe is that X equals 1/2, if that makes sense to you.


Do you see that


yes


OK, uh, um, then, your other question is what about the horizontal asymptote.


You'll notice that in the original problem,


the degree of the numerator is the same as the degree of the denominator.


And therefore we can look at the coefficients of


the x-squared terms, the ratio, which is 1/2


and I believe we will have the horizontal asymptote as Y equals


1/2. I'm going to put this in my graphing calculator to verify.


but I believe that would be your horizontal asympto at Y equals 1/2.


Does that make sense


Let me go ahead and put it in my graphing calculator just to


be sure of what we're


so y=0


our answers are here


So give me a couple minutes to put this in here.


okay


Not Y equals 0. Y Y equals 1/2, right?


On the horizontal


oh yea i see that


So x squared


minus 3 X


minus 4 in the numerator.


and then the denominator is 2 x squared


X


minus 1


And I'm gonna


oh, I blew that


Give me a couple minutes to get this put in here.


ok


So the X equals


1/2 is definitely the vertical asymptote.


and I'm looking at the Y


values here


Let me go do


So it does look like Y equals 1/2 is your horizontal as of


the graph seems to verify that.


yes


you using desmos?


No, I was just using a Texas Instrument 80 TI 84 calculator.


just to verify what we did analytically.


ohhh


but I mean, when we factored it


we factored it and we saw that we have the hole at x equals -1


and we have the horizontal, I mean, vertical asympto at X equals 1/2.


And then just by looking at the degree of the numerator and degree of the denominator being equal, we know that


the coefficient of the


polynomial on the top is one on the x-squared term and the coefficient of the polynomial on the bottom is


yesss


on the x-squared term. And so 1/2


is your


Y equals 1/2 is your horizontal asymptote.


and X equals, I mean X equals 1/2 as your


Y equals


I'm sorry, Y equals 1/2 and X equals


Ah, no, X equals 1/2


Sorry.


X equals 1/2 on the vertical asymptode.


That should be your answer


for both of them


ok great


Anything else


thats it


Great


You have a great day now


your the best, thank you


You're welcome


hi


Hi Chris


I'm working on a problem, I just want to make sure I am doing it right


OK. Can you upload the question?


yes one second


so I have to find the radius and interval


so I started by using the ratio test


This is where I am at


Looks good so far. The next step is to try to simplify and find the limit.


Notice that (x-2025)^n cancels out top and bottom, correct?


I think I did something wrong because I don't have an n anywhere


I'll show you on the board.


We focus on the terms in n^2 and ignore the lower-order terms in "n" as n→∞.


Now we can find the limit.


OK so far?


yes


For the series to converge, the limit has to be < 1. This gives us the radius of convergence.


oh yea


ok I think I know what to do next


Awesome!


And the radius of convergence is *half* the interval of convergence.


The interval of convergence simplifies to: 2024<x<2026. We could also check the two values, x = 2024 and x=2026 to see if the series converges.


is the radius 1?


Yes.


ok


We can also show that we can include the end values in the interval: 2024≤x≤2026. I can explain if you wish.


No I think that makes sense


like [2024,2026]?


oki sounds good


thank you!


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


Hello, how can I assist you?


Hi can you please explain the angles and side congruence theorems


sure. give me one moment to refresh myself on the topic.


These guys?


yes


So, what is it that you don't understand?


they are confusing


ok, got it.


You're using these for proofs, correct?


The basic idea behind these is that each one is "proof" that the triangles are congruent.


You see if the current problem you have about triangles fits into one of these situations. If it does, then you have proof by that rule (e.g. SSS, SAS, etc.) that the triangles are congruent.


Does that help a little? This is like a checklist to see if the triangles really match up. "Do we know if all 3 sides are the same?" "Do we know if 2 sides are the same and the angle between?" if the answer is yes to any of those, then you have proof the triangles are congruent.


ok i get it


Great!


what about ssa? why that doesnt work


You're definitely reasoning the way you're supposed to be for this class. Excellent question. Give me one moment, I want to see if I can google a counter argument image on this.


So for SSA, you cannot know the extent of the adjacent angle, which means you can't know if the sides are the same. So, it's not enough information.


For AAA, as long as all 3 sides are increased or decreased equally then the angles will remain the same. So angles also are not enough to know for certain that the triangles are congruent.


what do you mean by 'extent of the adjacent angles'


Sorry, let me rephrase. In the image where I have the black arrow..


We know the length of the sides connected to each other, 6 and 11.


But we don't know the angle in between. Because this is the case, we don't know where the third side  starts.


so it's because the two sides aren't same?


It doesn't work because we don't have enough information. Not knowing the angle in between means that the 6 length line could be angled to end anywhere on that green curve...but we can't know for sure where. So we aren't 100% certain. So it's not proof.


The sides are the same though, that is true.


In this example, triangle DAB and DAC have 2 identical sides and 1 identical angle, but triangles that are not congruent.


Does that help to visualize why SSA cannot be certain proof that 2 triangles are congruent?


sorry i still don't understand but let's forget about it. can you give me some problems involving the theorems?


I'm terribly sorry these are ridiculous


Can we prove that these two triangles 100% identical?


we cant i thinmk


Very good. That's what we had just talked about with SSA.


How about these?


Does this pair of triangles align with any of these forms of proof?


we still cant we dont know if the angles are congruent


The single and double curves are to mean that the angles are identical. Single with single and double with double. Same applies to the dashes going through the sides.


So, one after the other, list what we know are identical between these triangles using As and Ss.


so it's asa?


Yes it is! Very good!


And, since we know it is ASA, we have PROOF that these triangles are congruent.


another problem please


The red show what is identical. How can we know if these triangles  are congruent?


With what theorem do these triangles align?


the first two are not. the second two is asa


Yes on the second one.


For the first, write out the Ss and As that we know. Then try to match it with a theorem.


though two sides and one angle match, but they aren't corresponding meaning they aren't on the same position if the two triangles are side by side


So, you have indeed identified a mismatch, however congruence isn't dependent on position. So, we could turn it again and the result would still be S(1 line) A(1 curve) S(2 lines) = SAS for BOTH triangles still. Therefore, since we know it is SAS, we know they are congruent. Even when turned.


This 3rd triangle is still congruent as it is still SAS.


oh that kinda makes sense


Pay attention to the lines and curves. Those will tell you what is the same, then pick a start point and list what we know as As and Ss. Then see if it aligns with a theorem that proves they are congruent.


Lines and curves, change to As and Ss, then match it up with your checklist. No match means we don't know.


sometimes i have to flip the triangle to match?


do problems involving these theorems are only finding what theorem is applied? or there are other types of problems with these theorems.


No flipping is needed. Just comparison.


And yes.


You will be doing "proofs" to imply things you know about shapes and how similar they are to one another. You will literally list off that the sides and angles match up according to SSS, SAS, AAS, etc.


The whole purpose is to 100% percent certainty with as little information as possible.


The theorems are proven examples of how little information you need about a shape to show it is identical to another shape.


So instead of doing all the extra math and working with cosines and tangents, you can just say they're identical because ASA.


And there are a bunch of theorems to prove what's true about 2 or more shapes. They become puzzles because the theorems are like short cuts.


thank you for your help


I would like to end the session


Absolutely. I appreciate your effort. Thank you.


I don't understand this partial fraction decomposition question cuz I got it wrong :(


What are we supposed to do with this expression?


I uploaded the instructions


OK.
Thank you.


yw! also can you use mic it would be much easier but if not that still works


Just a minute while I look something up, please


ok take your time!


OK, so we want  to express this as a polynomial plus a fraction with a simpler denominator.  Is that correct?


yes


wait can u open ur mic?


Can you hear me


Oh yeah, I can hear you. Can you hear me?


Hello


No, I didn't hear.


Oh, OK. I'm sorry.


Can you hear me now


It's OK if you want, you can.


No, but I can read what you said.


OK, that works


I've never used the mic before at my apartment.


Oh, OK, I understand.


You can get started now if you want.


OK


So


how do you start the problem?


Um, so what I did,


I mean, do you know how to start? Do you have a


so what I did was that I um I I got the answer wrong. What I did was I like simplified the denominator into x + 12.


and then I did A is equal to x + 1 and B is plus B is.


over x + 12.


uh


wait, just a second. I don't think this translated what you said right.


Maybe turn your microphone up.


They did not


I mean sound


and denominator is


X + 1


The denominator is (x+1)^2


squared, right?


what is said was I did that, so then I did A/x+1 + b/x+1)^2


OK


Now we want to find A and B


So, what is the next step


so you would multiply the denominator by the numerators


like that?


That looks right


ok from there I get confused


Just a minute


okay


And uh


If this has to be true for all x, we can put in values of x to get equations we can solve for A and B


pls show me how


But we want to use values of x that make it easy.


Hmm


im kind of confused, where did the -1 and 0 come from?


I chose x=-1 because it makes A drop out of the equation.


what about the 0?


But then if I choose say, x=0


I'm so sorry but I have to go now! I might come back but right now I need to go so sorry bye!


The form we tried, A/(x+1) + B/(x+1)^2  doesn't work in this case because both numerator and denominator have x^2 as their highest power.  In this case we have to use  A + B/(x+1) +C/(x+1)^2


Then we do the same thing as before, multiply by (x+1)^2 and we get


x^2 = A(x+1)^2 +B(x+1) +C


Then we can gather together all the terms in x^2, all the terms in x, and all the terms without any x.  And we can put everything on one side of the equation


0= (A-1)x^2 + (2A+B)x +C


wrong


0=(A-1)x^2 +(2A+B)x +(A+B+C)


If this is true for all x, then the coefficient of each power of x must equal 0


A=1, B=-2, C=1


If you put these values into the expression we started with and combine the fractions, you will get the original expression back.


Sorry I didn't have this at the tip of my fingers while we were in session.


Hi! What do you need help with?


hi i just wanted help on this


Hi! Okay, is there a small and big picture given?


Or is this all you have


Okay! So what they want you to do is measure five parts of each one


Do you want to start by selecting the 5 objects?


ohhh


I don't know which one to


Wait I am sorry


pick.


That's okay because they randomly picked the eyebrow for their example I think it's up to you


I feel like doing the star, the buttons, and ears would be easy


You can pick the other two!


Or if you don't like one of the ones I listed


yes


You can change that too


i think its fine!!


it doesnt have any eyebrows


but we can do the star


Yeah, idk if that was just a random thing they came up with?? That was confusing


but idk how should i measure like top or side


yes lol


I feel like it should be the same as long you measure it the same way for both


It shouldn't matter


wait like this


idk bc the big eyebrow was 4 inches and the same eyebrows were 8 bc they meausred the big image and then then the small image


*big


I think the example isn't good


I don't know how the big eyebrow can be smaller than the small eyebrow??


like that doesn't make sense


bc the small image the one i circled


is smaller than the big image


right! I get that, but that that would be that the star in the smaller image would be smaller than the star in the bigger image


right?


yes


Which is why the eyebrow doesn't make sense because the big eyebrow is smaller than the small eyebrow


isn't it 4/8?


Oh wait!


It's .8


That makes more sense


I was trying to figure out how the smaller image could have a bigger eyebrow


i still dont know how i should measure the star


ohhh


i see


You can measure the star any way you want as long as you do it the same way for both


If you measure from one tip to another


make sure you measure it from the same points on your smaller star


okkkk


Can you do that and let me know what you get?


3.1 inches


for the big image


and 0.5 for the small


I can't verify your answers because I can't measure it, but based on what we get for part b-e I can get a sense of if we did it right.


Great! Now we have to make a ratio


big star/small star


Let me know what you get


wait what


big star over small star and i divided


Yep!


That should be your answer for a


What do you want to measure for b?


Also what did you get when you divided


6.2 it the answer


Okay here is this issue because it uses things you have in person I can't check your answers


but if you did it right when you measure something else for part b and then divide that (big/small)


b we can measure the bottons


you should get the same answer


Does that make sense?


no


can you restate it


Okay!


So because both images are the same just different sizes


yes


Everything in the image should have the same ratio


If I took a triangle and doubled it in size


Everything inside that triangle will be 2 times bigger


Liam!!


So if you measured correctly everything should be 6.2 times bigger


yes i hope it doesnt change


bc the small star was closer to 0.5 than 0.6


If it's close we can always go back and fix that


So don't worry too much about it


Liam


should i measure the bottons now


Sure!


the shapes arent the same a little bc i had to draw it myslef


myself*


is that okay?


That's okay, I don't know if your answers will be perfectly the same but we can try and work with that


or should i measure smth else


okk


Try measuring it if we don't get the same answers we can go ahead and measure something else


the first botton is 2 and the second botton is 1/9


no i mean 1.8


the small botton is 0.6


and the other botton is 0.5


Okay, so that didn't give us the same answers


yea


Because 2/.6 is 3.33


Try something else that you didn't draw in?


That might be the issue


i drew the whole thing lol


how about the show


shoe


Sure!


how should i measure


I think that might be easier


Hmm?


the both too shoes or just one


One is fine!


i got 6.12 inches for the big feet


and the small on i got 1.2


That might be the closest we are going to get, so I would keep that.


okk


There is going to be some room for it being slightly bigger or smaller because you drew it yourself and I think your teacher would understand


Plus the second question asks if it is proportional, so you could just say that it isn't there


Because we didn't get the exact same answers


is it suppose to be the same answers??


I don't think it can be because you drew it yourself


There is going to be differences


So no, I don't think so


does that make sense?


yes it makes sense


Okay! What did you get for your ratio?


Yep!


Pick another object


this is def not proportional


idk which one to pick


Ummm maybe the eyes??


good one!!


0.6 for the right eye


2.6 for the big eye


Great! What do you want to measure next?


can you pick again


The nose maybe?


should i do it up or side ways


Sideways


big nose 2.4


small nose 0.7


Ok, what did you get for the ratio?


Great, which part are you on?


one more


Okay, do you want to pick the next one?


ears??


Sure!


sorry for taking to long


You're fine!


Don't apologize


i think i should pick a different one bc it doesnt look accurate


Ok do you have something else in mind?


no


idk which one topick


Uhh the arm might work?


yes wait can you make the line clear


lol


Oh?


The green wasn't working so I went over it with red


thank youu


of course!


4.2 for the large one


0.13 for the small arm


Maybe we should do something else instead? That's a huge difference


Liam


I got 32.3.07


samee


which one should i do


Umm maybe the shorts


yesss!


for the big one


and the small one 1.1


Okay that one makes sense!


I think we are good


yes thanks to you


What did you get for your ratio


i got 3.3.73


Okay Great!


And then for number 5 because our answers are not the same


Is it proportional or not?


no


because we dont get the same answers


Yep! That's right!


how should i right it into a sentence


The project is not proportional because the ratios for the different sections were not the same.


Liam


You're welcome!


Do you need help with anything else?


yes but are you sure your not tired of this


I can stay for fifteen more minutes so I guess it depends on what it would be


Cause it might be easier for you if you worked with someone who could stay the entire time if it would take longer


i was just going to ask if its good


wait let me show an image


wait is it hard to read


A little?


I can't see the first line clearly


But as far as I can see that makes sense!


Do you need help coming up with other professions?


yes im so sorry


Don't be!


I was thinking of architects?


They would have to create smaller models before they create an actual building


wait should i erase mines and make it smaller


the sentence


No, your sentence is fine!


I could make mine longer if you would like


can you make me the sentence


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


Does that make sense?


can you chnage the photographer to the smae way you worte


yes makes so much sense then mines


Umm I can try


thanks


A photographer uses similar figures in order to make certain images look bigger or smaller. Two figures that are the same size may appear larger due to its positioning in the photograph.


If you dont like that as much I think yours sounds perfectly fine


doesnt make sense can you make it claer


I unfortunately do have to go right now. I think you should just stick to your explanation for that one or request again and someone else would probably be able to help a bit better.


Sorry!


no ur good


Have a great day!


you too!!


Hope I could helpn


hello!


hi


Hi


is there a certain problem you need help with?


or maybe a concept?


hello?


ok hold on


Emma is trying to 160÷42.
Since 160÷40=4, she estimates the quotient is around 4.
Check Emma's estimate. How should she adjust her estimate?
Adjust Emma's estimate as needed and find the quotient.
168÷42=


Sorry, something has come up and i will need to transfer you to another person


ok


Hi, how may I help?


Hello


I just want help deepen my understanding with X and Y prealgebra problems


what type of problems are you having trouble with?


im not really having problems but i wanna keep practicing and maybe start learning linear equations


what are you working on in class?


so im in Algebra 101


okay sound like fun


kinda but i wanna push myself a little more


okay let me find something to work on


ok thank you


correct


is that the whole problem


yes


b


ohhhh ok


you forgot something


simplify?


negative


so it was the negative i was missing


ohh ok thanks


what i dont get it


find x


oh i thought the was a multipacation sign now i get it


i am confused


we can take it step by step


ok


we want to get x alone


is it x=6


is 0 but 9 doesnt go into 14


oops i accidently delelted your soory


i am confused again


we want to get v alone


do you understand how i got here?


no


why are you subtracting 10 then the answer is saying its addded by 10. I dont get it


negative + negative = negative


think of it you owe $104 and you just borrowed $10


now you owe $114


but how did you know to add -10?


10 is positive


we want to get v alone so we move 10 to the other side


oh ok


so then we divide 114 by 6???


correct


ok


ok thanks


start by getting 8n alone


did i get it correctz.


yes but how did you do it?


i did 31-7=24 and 24 divided by 8=3 so n=3


i dont know if its -5 or +5 tho


the negatives cancel out each other


oh ok thanks


how does 16=1?


I fixed it


idk how to even solve it


okay


what is the opposite of division?


multipication, but why will we need that


that is how you separate the fraction


what fraction??? i thought that was divioson


16 is dividing (n+5)


i dont get it


(n+5)/16 is a fraction


but im confused on why you put parenthasis after the 1


with 16 in the parenthases


1*16 that is what it means


( ) means multiplication


why did you put the n+5 over 1 and not 16?


I am trying to show how they are connected


how wgat is connecte?


(n+5)/16 being a fraction


ok then how do we solve it?


first step we want to get n+5 alone


so we would multiple


multiply n by 5????


no 16*1


why do you mulyiply that?


they would cancel out each other


how?


why are we dividing


to get n+5 alone


um ok?


i do not get this at all


to separate a fraction you have to multiple the bottom


so then how do we figure out n?????


how is it n-0 and not n+0???


it does not matter it is just 0


but its more confusing when you switch it from adittion to subtraction


we can countine working on the addition and subtraction


ok


do we add +9 to -9x and +9 to -103?


always start with the number that does not have a letter next to it


so i add 13 the???


correct


you owe $103 but you just got paid $13


how much do you owe now?


thats a low paycheck


lol


is it negative or positive


positive


how


its a negative divided by positive


i dont understand


negative * negative = postive


negative / negative = positive


negative * positive = negative


i sill dont understand


negative / postive = negative


its a negative 9x but the answer looks like +90


they are both negative


ohhhhh i covered with the equal sign


i get it now


you will understand when your teacher get to it


ok


Hey, my time is up, so I have to leave


Have a nice day


ok thanks you too


you are welcome


hey, Sam!


hi Emma


I was about to walk away from my computer when I saw your request pop up.


just checking my answers today :)


oh


I guess i was lucky


I stayed for you.


thank you :)


let's see those answers you want checked.


i got f= 5.5


wait


oh, that x means multiply


yeah


you're just distributing the 3


good, so far


you typed 5.5 before as the answer


yeah i totally forgot about the negative


thank you for the help :)


that's it?


yup :)


ok. yw.


hope you have a good rest of your dayy :)


you too


bye


byee


I don't know what I am doing for this assignment at all


Hi Maya. I'm sorry you are having trouble with this assignment.


Do you want to start with question #1 or #2?


one please


Okay- so what this question is saying is that you have two congruent triangles.


Do you understand what congruence means?


that they are equal to each other right


yes. Congruent triangles have equal angles and equal sides.


ok


So they want you to write that idea with "congruence" statements


if the Triangle is APV, what are the 3 sides named?


A P V


that is the name of the points, can you give me the name of the line segments?  EX: AP


BTW, can you see what I'm writing on the board?


AV is one right and PV


yes!


GS GL sl right


perfect


So those are the congruence statements for the sides.


Now you need 3 congruence statements for the angles.


yes


Can I erase part of the work so we can write the angles?


Nice - how there is more room.


What are the angles of the triangle APV?


what are considered angles is it just the letters like angle a angle p angle v


So angles can be named in different ways.  We can say angle PAV or just  call it angle A


If you use all three letters, the "point" of the angle should be in the middle.


oh ok so on the work it has three spaces are we putting PAV and  angle a in those spaces


So angle PAV is the same as angle A - its like your full name and a nickname.


oh ok that makes more sense but what should I put in the boxes above for angles is that one I should put


It might be easier just to use the one letter - make sure to use the "<" angle symbol though


I'm sry this is so confusing for me was I supposed to put <A in one of the spaces


That is the start, what is angle A the same as in the blue triangle?


same as G


Perfect, so you would write <A is congruent to <G. Do you see it on the whiteboard?


yes I can see it


can you write the next two statements?


angle s is congruent to angle p and angle l is congruent to angle v


and we are writing this where on the work on that line right


Great!


Yes.


Can you see the 6 lines I put the red box around?


those are what go in your table


so pink is angles and blue is the sides right


No.


The first three are sides, and the second three are angles.


The pink and blue were just to show you the two different triangles.


oh I see so I would for example would put <A for for the boxes that say angles


Yes! That is correct.


yay


Whoops, maybe I didn't quite understand, you need to put the whole thing - < A ≅ < G


The right side of that table is looking good.


do I do that for the angles too


ok I finished filling it out


It's a little small for me to read, but I think that is correct.  Does it make sense to you?


yeah that part makes sense so its showing the sides corresponding and the angles that correspond right


for each triangle


Exactly!


okay I feel better about that now for the congruence statement what do I do for that part on number 2


never mind


Can I erase what we have written so far?


wait a second let me write it down


Or better - lets's scroll down to a new part of the board


oh ok lets scroll down


Can you show question #2 again?


but what do I put for valid statement for number one though that the angles correspond or something


Let me look at the question again


Okay, I see


I think the teacher just wants you to show that you can write the same idea in a different way:


You could write triangle GSL is congruent to triangle APV


oh ok


so I would put < in front of GSl and stuff for that part


not < but an actual little drawn triangle


oh ok I thinking that ok


Yes, that should work.


oh ok it looks fine but isn't it just the same thing that is wrote flipped should we write it in a different order of arrangements of the letters or no


I think both things would be correct. If you decide to do it with different order of arrangements of the letters, just  make sure you change the order the same way for both triangles


oh ok ty


EX: Triangle SLG ~~ PVA


ok I guess we can move on to question two now


Can you see the two triangles on the whiteboard?


Maya?


yes sry I had to step away for a second


NP


So, I drew the triangles. Can you fill in the information on the angles and sides that is given in the problem?


ok


like this right


perfect!


for the angles parts do I just write it next to the letters like a is 56 or no


I think you can write it next to it or in the triangle, whichever is easier for you to read


I'm done I think


Im not sure where the 14 came from?


it said TS = 14


Yes! I had missed that. Good catch


have you ever seen how we can mark congruent sides on triangles?


yes with those lines right


Perfect!


So what side is congruent to side BS?


GD


GD right


yes! so since they are equal, we can write an equation


is that right


That is exactly right!


ok so 25= 4x-11


yes!


so how do we solve 25 = 4x -11 to get X?


subtract?


on both sides


idk


you are doing great! we are subtracting 11 already on the right side. To get rid of subtraction we use addition.


Add 11 to each side.


oh ok that makes more sense


you got this - keep going


I'm stuck now


just bring it down


oh ok


okay now we have multiplication on the right side, how do we get rid of that?


divide


yay I'm so glad I got that right


so X = 9 !!! We  are half done


ok yes


So now we have to look at the angles to find Y


ok


Which angle is equal to angle H?


T


Yep! Do we know the value of angle T?


no but we know the numbers for ts


which is 14


I agree, but we can't mix sides and angles :-(


We need to figure out something about angle T


We do know angle B and angle S


yeah b is 21 and s is 56 I don't know how to find t do we add b and s then subtract by 90 or something


geometry idk


you are right!


All the angles of a triangle add up to 180 degrees.


So now you know angle T is 103 degrees


yes


And you can write the next equation


you are getting this really well


I'm not sure what to write


its a lot of steps to keep track of.


Look at what you said angle T was equal to.


"Which angle is equal to angle H?
1:32 pm
T"


t


Yes! (We just had to do a lot of stuff since then :-)


yeah


So let's write an equation about angle T and angle H


is what I wrote fine or do I need to add more letters for it


Sorry - I dont' see it. Let me refresh my screen


I didn't see the equation, can you write it again?


ok


I wrote it next to the other equation


Something seems to be weird on my end.


Let me write and see if you can see it.


I put T with that squiggly sign and H is that wrong


Nope. That is correct.


Can you see what I wrote in pink?


If so, go ahead and fill in the numbers for angle T and angle H


no I cant see it


Hmmm


can you try to refresh your screen?\


I see it now


good


so for angles it would have just a regular equation sign


it should actually have the squiggles


it's actually and equal sign with a squiggle over it, but that is hard to show in typing


oh ok the squiggles  mean equal too right random but why do we put the squiggles instead of equal sign


The squiggly thing means "congruent" . If we want to be really correct, we would write"


measure of angle T = measure of angle H


oh ok ty


it's a bit of "math" language. I'm not sure how fussy your teacher is about it.


so what is the measure of angle T?


T is equal to 103


yes! and what is the measure of angle H?


perfect! Write that as an equation


Good. Keep going.


Make sure you have the right variable - y =14. But the rest is perfect!!


oops sry


ok


It's not a problem. I just wanted to make sure you wrote down the correct thing so you get credit for all your hard work.


ok that's fine ty


I just want to summarize what we did:


1) drew a picture to show what we knew about the triangles


2) Found congruent sides and angles


3) Used the congruent sides to write an equation for X and solve


4) Used the congruent angles to write and equation for y and solve


Did this make sense to you?  You did a fabulous job on each step.


ty when I was solving it it made sense how do I know for future which one was x because I could see the y for H but how to know which one to do first


if that makes sense


It doesn't really matter which one you did first.


oh ok


The x seemed to be a little easier, since we had all the information given to us.


For the y, we had to do an extra step to find the congruent angle.


yeah


In general, you want to write down everything you know first.


Then see if there is anything you can quickly see is equal


yeah definitely its always better for me to see it


Do you want to take a look at problem #3 and just talk through the strategy?


yes please


Ah - this is a proof, so what the teacher wants you to fill in is WHY you know each thing on the left side of the table


So the first question is, WHY/HOW do you know that S is the midpoint of RT?


becuase it is in the middle of the triangle


idk


You can't count on the drawing "looking" correct -  Read the information in the question. What is the first line?


I'm not sure i guess r is first


or p


Okay, I was showing you that it says "GIVEN:"  That means, these are the facts they are telling you are true.


They are what you know from the beginning.


ok


So the reason you know S is the midpoint is  "Given"


oh that's make sense I was overthinking it


I thought I had to solve something


Have faith in yourself. You are doing a really good job with the ideas in these geometry problems.


ok ty


is the second given as well


So now look at the Given statement again, and then try to fill in #2


yay I love the confetti lol


Now you may need to look at the formula sheet the teacher gave you.


Does it say anything about the definition of a midpoint?


no put it has the names of proof reason but not the definitions


okay - so how you write this has a bit to do with how your teacher has taught it.


oh ok


We know S is a midpoint.  By definition, a midpoint divides a line segment into two equal pieces.


yeah


When I was doing proofs, I would have written something like "Definition of midpoint" for #3


would it be something like SAS or SSS oidk


not yet. SAS and SSS are reasons for proving a whole triangle is congruent. We will need that in a second


I'm not sure how to find this one


I would write defintion of midpoint for now


so the definition of it would go on that line for now


you are actually going to write the words "definition of a midpoint" on the line #3


That means you are using the definition as the WHY you know the thing is true


oh ok I'll ask my teacher about that one probably make sure I can do that before I submit it


that is always a good idea


So look at #4 and tell me what it is saying


it is saying that's PS is equal to PS


or congruent


yes. So PS is congruent to itself


so definition of congruence right


We are trying to say WHY we know it is congruent.


wait I just looked and I think I just put the definition of for the answers of these


Hwy do we know something is equal to itself?


look and see if you have the "reflexive" property on your sheet


ok


reflexive property of equality


is on there


yay


That property means things are equal to themselves


So what do lines 2-4 tell us?


they tell us that PR = PT is given RS =ST is the definition of midpoint and PS and PS is reflexive


yep. So what does that mean in terms of the sides of the two smaller triangles?


so it means that they are either SSS or SSS right


You are even ahead of me! It means you know that the smaller triangles have 3 congruent sides.


oh ok


So triangles with three congruent sides...... are congruent, because of SSS.


ok that makes sense what SAS mean


SAS means Side - Angle - Side. That means triangles with two congruent sides and a congruent angle between the sides .... are congruent


oh ok ty


I think you have a good idea of what congruence means.  When you see these problems, just remember to write down what you know first, then go step by step.


ok I will definitely do that


Thank you for helping me


will I be able to see our work and chat when I end the session


I'm not sure. I can see our chat, but not our whiteboard.


You might want to try to take a picture or a screenshot of it before you go.


ok


I took screenshots I hope you have a good day thank you so much for your help I have a much better understanding now


Great. Have a good day


you too bye


Michael


HIIIIIII


Hi--I think I see what they are looking for


oh ooookiiii


Yes-- for #1


WAIT


that's right


I got that right?


yes, absolutely


I lowkey just guessed


well actually


i think i did that question before


in any case--you did it right


yayy


for #2, that funny square thing means it is a 90 degree angle


lol oki


#3 is a lot like #1


That's right angle C is congruent to angle D


#4 is a little different


Have you seen those marks before?


nope :)


They mean that the lines are parallel


Since it is a line, you want to say FE is parallel to HG


oh oki


#5 is a combination of #1 and #2


so #2 is just 90 degrees?


#2 is angle BCE is 90 degrees


sometimes for angle, you can use <


but put it first <BCE


you can also do that for #3


<CD?


or <CBD


in this case, you can just say <C or <BCD, the middle letter is where the angle is


oki


so it would be <BCD is congruent to <CDB


perfect


for #2 you need to put down that <BCE=90 degrees


ohki


ok, so number 5 has something from #1 and #2


ok


close, you can call the angle <TSR or <S and that is 90 degrees


and now the two line segments are FE and SR


and they are congruent


excellent


#6 there are two parallel lines marked


I read that first line as line s


and the second one as line t


yeah s,t and u


my bad


that's right--and the angle we are seeing is <C


yes


so <C is marked just like the one in #2, so it is also 90 degrees


thx :)


you are welcome--is there anthing else that I can help with


no thank you :)


have a good day :)


have a great rest of your day


Sarah


hey!


how can i help


hi!


i took a math test and lets just say it was bad, so i am retaking it but i need some help reviewing lol


okayy


do you know what you got wrong?


yes i have the test


okay


can you show it?


i could put the images


ofc


hold on one sec


okay that is page one


idk what i was thinking for two


uh oh!


mhmm


do you want to start with two?


yes


i think i switched the letters or smth


so look at the given


ABC=EDF


k


so that means A corresponds to E, B corresponds to D, C corresponds to F


ohhhhhhhhhhhhhhhh


that should always be the case


so b and d would be 85


but for c and f would i set that equation equal to 35?


or like the x


you would make c equal to f


so c=f


then you can substitute the values


so 2x+21=f


and f=35, so 2x+21=35


then subtract 21?


yes


subtract 21 on both sides, subtraction property of equality


so then x=7?


yerp


good job


and for the A and the E would i put in 7 for the x, to find the y?


yes!


ah haaa


yup


ayyyy i think i get this one now, but also i know how i messed up lol


lol, i think the only thing you messed up on was the angles and which ones they were congruent to


Geometry 201%%


also idk why i had the test at 7:15 am


no exuses but


woah


that is very early


okay, any other questions?


real


yes


hold on so when i am doing the top ones


when the letters have the line it means it is a messurement?


uh


can you elaborate


that means its a segment


but when there is not line


oh like the squiggly line on top of the equal sign?


no like the AC=EF


there is not line on top of the letters


well


im assuming that means the measurement?


but then you wouldnt use the 'is congruent to' symbol


which made it nonsensical


Hello! I could really use some help right now. I recently learned this topic, and while I somewhat understand it, I’m still a bit confused. I’ve had past coaches try to explain it, but their methods often feel long and not as straightforward as how my teacher solved the problem. Could you please rewrite two problems that are similar to the original for extra practice? I am currently on page 5, problem 10. Here’s the link to the PDF: https://example.com/document.pdf


sorry im not allowed to open links, are you able to take a screenshot and post it?


You can


its against the rules :(


It's not


oh wait


ok nvm sorry


alright let me see


Yep!


this problem correct?


Mhm


alright


so to explain the work on the problem


you want to focus on making the roots the same


so you can apply "like terms"


since you cant combine square root of 27 with square root of 12


so for this


we need to simplify our radical


so when we are simplifying radicals


we can do a nice trick where we split up what's inside the radical


for example


the square root of 9 is the same as the square root of 3 times the square root of 3


since 3 times 3 equals 9 right?


so try breaking up 27 into two factors and break up 12 into two factors


No I'm asking for


one with diff numbers


similar to 10


ok!!


let's just do 11 then


but yea we have 3 radicals right


there's two radicals we can simplify further


do u know which ones?


Holdon


yea no problem


if u want i can explain


I meant #12 my bad


its ok


but yea


we can see the radicals right


can you write them out for me


you can reference what i did for 11


omg i meant 13 why do i keep saying the wrong #


ok here 13


yea just identify the radicals


like how i did for 11


yes so creae a problem like #13 w diff #s


ohhh ok


sure


alright


there ya go


do u wanna try it first or wwalk through it


thanks workin on itrn


ok


is it right so far?


hmm be careful for the second part


yeah im thinking


try to see which one is a perfect square


30 sq 3?


yes ten times 9


but which one is the perfect square


square root of 9 or square root of 10


9 is


so its 3


30 sq root 3


wait here let me show u


one sec tho sorry :(


kk


ok so basically


you split up the square root of 90 into the square root of 10 times the square root of 9 right?


yes


what is the square root of 9?


is this riht


wait here let me finish explaining


the square root of 90 is equal to the square root of 10 times the square root of 9


but we identified that the square root of 9 is 3


so that means


it's just 3 times the square root of 10


so the square root of 90 can be simplified into


uhhh yea this is confusing


it's alright


basically


you're able to split up the square roots perfectly


but you mix up which one got multiplied to the -3 outside of the square root of 90


basically what we are doing is expanding the expression right?


-3 times the square root of 90


u might have to scroll down a bit to see my work


so then we break up the square root of 90


gtg


ok


Hi.


I need help solving a problem.


I started but I don’t know what else to do.


hello


Can you show me the problem?


Yes.


What have you done so far?


Just that in the green that how far I got.


That's correct so far


Now you need to figure out what goes at the red mark


not 9


yes, 81


why did you add 81 to one side but 9 to the other?


I thought I was supposed to put 9 there.


You always have to do the same thing to both sides - a fundamental law of algebra


Now you write the left side as the square of a binomial


Sorry I have to go.


It might take me 10 minutes I was called to do something sorry.


ok, bye


Thank you for your help.


Bye.


you are welcome


Oh


Hi, what can I help with?


are you able to


use my


Do you have a mic on your side?


Yes I do let me try to enable It one second


OK


Hello


All right, what is the problem you're working on?


This right here


and you


this is for homework, isn't an actual test.


I


and I have a few other ones that need to be done by 4 o'clock.


Sorry, what did you say?


Um, some other like


3 more


OK.


after this one.


Um, what are you stuck on for this


I like to


I'm confused on how to


go about it.


Yeah, like how to find, like which one.


which um transformation.


The dilation


and the dilation.


Let me look


because


reflect


a reflection


Mm


across the X, then the


y-axis


would make sense.


Yeah, I agree with that


Did you


Then


how does this like um program work? Are you able to check it multiple times or is it only once like


or do you just like turn it in at the end and then you see what you get wrong.


I, I'm not able to see why I get wrong.


Oh, you're not? OK


So you said you think it's um reflection across the X, right?


Yeah


And then what was the other one


Oh


I think it's ANC.


Let me see


but can we be


for whatless because


I don't wanna get wrong


Um, I'm trying to pull my grade up.


Yeah, OK.


I mean.


I just, it's hard to see the points on my end, so I can't see the exact like


numbers, but let me just double check cause


Uh.


Is that better?


oh yeah


Thank you.


Shouldn't just ask me


I'm just double checking the reflections really quick because I haven't done this in a while.


That's OK


Good.


Mhm.


OK, I think the reflection's correct, and I'm just trying to make sure that the rotation's right. 180 degrees, how would that move?


Oh, go into the negative.


So, what did you say going to the what?


into the negative


Yeah


So, let me just see, counter.


clock wise its


Yes.


So with the reflection across the X, it goes


would go up one, like


which one is it


applied to shape I to prove that shape I is similar to shape.


I, I, OK


Uh


the Roman numerals, shape 12.


OK


So shape one is the one we start with then, right?


Yes


And the reflect across the ax would just go down and then


across the why would go that way


and


then let's see


I


What was the, what was the bottom option?


Was it just a translation one, I think, right?


Yeah, just the translation.


Hm


I'm just not sure about the rotation because


I know it dilates


so


let me see. It might not be the reflection then because if you rotate 180 degrees.


counterclockwise


I feel that's like


just switching it


um


from like the 3 quadrant.


For that point.


to the 3rd


Sorry, what did you say


Sport chance points.


Yeah, so right now it's in the first quadrant, so it'd be


and it's all positive, so then it would all become negative, right?


Right


And then it says it's a dilation by scale factor 0.5, so then it becomes smaller.


But with the reflection, I don't see where you have to reflect that afterwards. Do you get what I'm saying? Like,


it would already be in that spot, I feel like.


The reason why I believe it's a reflection because


all reflects down.


across


Oh


the two


Oh wait, are these two separate like things that says, like, you can reflect it or you can do the


um rotation


This is


this


OK, then I think your answer is right then. I, I think I was just understanding the question wrong.


OK


now


OK, let's see


it's are, aren't too good room to shape it.


Hm


Look


similar but not congruent.


Like, not the same shape, basically.


Yeah


This one's similar.


All those are similar to Shape C, but


Yeah, cause


this one's also congruent.


yeah, that one's congruent cause it's the same size, right?


Um


Yes


maybe the green, is that yellow or green, that kind of looks


let me just double check, 12, OK, never mind, that's a little bit smaller.


Um,


What about the pink one


It kinda looks like the same size, right?


All right


So would that be, I think.


So similar shapes do they have?


eyes?


Also moves back for a unit.


OK, yeah, I see that


Um.


OK, let's see. So


actually I


this moves back


from right here to this point to that point.


it's free units back.


This is only 2 units back.


2.5 units


The orange one.


Oh, cause they're different um


like transformations


All right.


Yeah


Um


but this pink ones for units back.


Do you think that one's congruent then, right?


Yes


OK.


Mm


let's just check those.


Yeah, I think that looks right. I'm just a little iffy on the orange one, but you said


um if they're like similar, they could have like, they would have to have the same


uh transformations


not exactly the same, but if it's similar, a congruent, congruent, you need the exact same.


OK, so, orange wouldn't be.


congruent then, because it's, it's different


Yes, because this little triangle right here goes


Oh, I see, yeah.


yeah


yeah, I think that's


yeah, I think that looks right then


pink is the one that really looks concurrent.


Um


What shape is similar to Shape one.


So


OK


Um, I already forgot what shape one looked like.


shape one looks like this.


OK, so it's


right


Um, and then let's look at the second one first. You can just go down by each one.


Um, I don't think that one.


would be right


What was I asking if it's


huh?


Yeah


if it's similar, but if you're not


sure


if you're not sure about this, then I can just find another tutor.


Um, yeah, I'm just, I'm just a little confused on


like the similarity part cause I haven't, like I said, I haven't done that one in a while, but


you can try to request another one. I'm not sure how many people are online.


OK


So do you wanna stay in this one or do you wanna?


request a new


It's up to you if it, if it's too hard to.


for you then


I think we can try to work through it, but I just don't want you to get it wrong.


It will hurt your grade


Plus I only have 5 minutes left.


before 4 o'clock


Right?


And


yeah


the small one


the


it looks like the same exact shape, just a different size.


Um, which one? It's just a little bit like lagging on my end, so it's


B


D


or B


Now B


Oh, sorry


Yeah, I think that one looks pretty similar because it was like the same point


And then what about


It's just dilated.


yeah, let's look at um


11 more time just to make sure.


There's one


It's taking a minute to get there


OK, so it's like a triangle and then like a


boxing, OK, let's look at B.


and then what we're C and D, just a double check.


Yeah, I don't think it's C.


and I don't think it's D either cause it's like a


different shape


So yeah, I agree with you. I think it's B.


I wanna go back down and look at the and.


to me it looks like it's just a 180 degree rotation.


because


are opposite of 2 and 3.


and uh


there's only one unit measured in between.


for


both of these


Mhm


but it's only asking.


for civil it's nice and fork and ruin.


Yeah, so I don't think the


So


I think it's because of like you said, like the rotation and it's just like dilated.


Yeah


So it's just the difference scale.


OK


OK.


What shapes are similar shape A and what shapes are not.


I


OK, so same thing


just like different sizes again.


I think


just


yes


not conver


We don't want conru. We want some.


OK, we can just like go through every shape. So what do you think about one?


That one's rotated and it looks a little smaller.


or


Yes


yeah


So do you think that one could be um similar or congruent?


or not similar


similar


Yeah, I agree because it looks like a little


different. I don't know if it's just


my screen, but


and then what's the next one, too?


that


It looks to be like the same size as I.


but


You're really


it?


OK. Hey Chris, um.


Are you there?


Yeah


So it's like I have the one is not somewhere so far, right?


Uh


if you care


remember


too much about the subject, then I can always find love for children.


Um, yeah, we can try it. It might put you back in with me because I don't know how many tutors are on right now, but


Um


so do you wanna try to request one? I just don't want you to get it wrong.


Ultra


OK, I'm sorry


That's OK


hello


hi


I need help solving this problem. I'm having a lot of trouble with summation and how to solve problems that look like this


I only have 20 minutes to do this problem for now though because I have to go to my next class then


ok


You can break this apart.


any questions about that so far?


why did the 3 go to the other side of the symbol?


You can pull a constant in front of the sigma, which means you are factoring it out.


I will show you an example.


okay


See how that works?


I think so


There is a summation formula for 8+9+...+16, right?


for the sum an arithmetic series


ooh okay


or actually, n(a1 +an)/2


since it doesn't start at 1


n=9 because there are 9 numbers in the the series.   16-8 +1 =9


for the summation on the right, you are adding 4 to itself 9 times


so that's 9 times 4


any questions about that?


um I think that makes sense


are you all set with that question?


okay I think I see what's going on


there are summation formulas for sums of squares, sums of cubes, etc.


ooh okayy


okay yeah I think I'm making sense of it


thank you


You are very welcome.


I have another problem but I wanna try to solve it by myself. Thank you for helpingg


you are welcome.


You can also change the index to start with 1, but I don't know if your class has done that.


are you all set then?


are you still there?  Perhaps you have left.


Have a good rest of the day.


bye


i need help with my ixl 8.71 subtract 1.47


hi


how can I help you


i need help with my ixl


can you show problem in a table


do you want me to write it on the littile sheet that i have


sure


ok


it 8.7 / x


8.71 suntract 1.47


subtract


frist


8 - 1 is


yup


71 - 47


equal


ok hold up let me figure it out right quick


okay


it mean


you will do the number before the point frist


then you figure out the number beside after that


Good


so the answer is 7.24


so the answer 7.24 or no


ok


have any questions you want ask me


yes


this one is the last one


ok can you chat it I will write in a board for you


or if you want to write in a board


I work both


wait this one is easy do you still want me to write it down


sure I want to show you each step


for sure you understand it


right


0+0 is


Correct


how about 3+2


they are both 5 right


no you need to write 0.5


5 and 0.5 is different


i know i was saying like its 2+3 still five even if its turned around


Right


yesss


ok


good job


thank you


your welcome


hope you have nice day


you to


Hey


Halloween is tomorrow


Hello I have a couple questions I need help with


You excited? Are you gonna dress up?


And sure go on


I don't really do anything on Halloween


Oh


these are the first two I have a couple others I don't understand how to solve them at all


Are there answer choices for this one?


yes its multiple choice questions


about the side opposite or the side adjacent


What are the choices for the first one?


So for #2, we have to use inverse trig functions


ok how do I do that


Make sure calculator is in degrees


ok I have my scientific calculator


what do I input


oh ok


You see what I put?


yes


I got 54.5


so 54.5


where did 35.5 come form though


oh because its a right angle ok


To get x by itself


so just input it like this sin(41)


to get the answer


Find out what the value of h is


Jamie fallowing along so far?


yes this is really helping me thank you


You want to find the last one on your own?


ok


it is the last answer


I think


30.03 right


Yup


Any others?


no thank you so much for your help you've helped me a lot is there a certain time you're on here so when I need help in the future I might be able to get you you've helped me more than any of my other tutors


10 -1, 2-4

Sometimes I'm on linger than that


So you'll def see me again :)


so you're on every day


Yeah


Sometimes I'm on weekends as well


ok ty so much have a wonderful day


Happy Halloween kiddo


See ya again soon


ty you too


bye


I need help with the summation equation. In the equation I am working on, 16 is on the top, k=8 is on the bottom and in the middle is 3k+4


Hi Sophia: How are you today?


I'm okayy


If I understand your post correctly, you need to input x = 8, 9, 10...16 one at a time into the equation and add up their sums


I think so, but i'm not sure. Im having a lot of problems with summation


the weird symbol is throwing me off a lot


Does what I wrote make sense?


um did you just plug numbers into the 3k+4 part of the equation


yup, and then add the sums of each calculation together


wait I'm confused


Write each sum on the blanks plz


Ok, now keep on doing this with the other integers up to 16 and add these sums


Sorry, but I have to run, hope this helped!


They


How can I help you, Leo


If you would like that, you can just go ahead and copy and paste your problem here into the whiteboard so that I can see.


I want to learn something new


OK, so what


it is something new for you.


yes it is I  just came to fifth grade


Well


so the


fifth grade math, OK, so you need to come up with something specific because there's so many subjects here. I don't know which one that interests you the most.


yes sir


So be specific, be specific about one particular subject, please.


Solve for x: 3(2x - 5) + 4 = 19. ...


I working on that


OK, uh, sorrowful act, OK. Hang on.


OK, here. So let me copy your problem, OK, so it's going to be here, well, it's gonna be 3, right, and then 2 x minus 5.


+ 4 equal to 19. Am I correct? Yes. So this is what we call the left-hand side, and this is what we call the right-hand side. Am I correct? Yes, but, OK, now the first thing we need to do is that well we have to end it out the left-hand side so that eventually here by the end of the story here, so you got only one single act. So what you are going after is that the situation, the format like this X equal to something something. Am I correct?


OK. Once you've got X on the left-hand side and everything else on the right hand side here. So that is the solution, am I right? So let's go forward, OK. So the easiest one for you to go forward is that, well, first of all, you need to move this one here from the left hand set to left hand side, OK. Meaning what meaning here? Well, looks like here I need to


subtract 4 on the left-hand side and doing so, we have to do the same thing to the right-hand side, right, yes, so remember here just like what your teacher said. So this is an equation. So you have to put an equation and just like a scale, OK. You can do whatever you want to the left-hand side, but you got to do the same thing to do at tennis that and I like, so that the scale still balanced. It doesn't tip to one side or another.


OK, but so, so let's do it. OK, so let's give me 3 here, 2 x minus 5 + 4.


is it x=5


OK, minus 4, yes, so I'm introduced minus 4 here to the left hand side, it's OK as long as you do the same thing here to the right-hand side as well. Did you see? So it can balance out the my client, yes, so remember here we always, always have to treat the equation as a


as a, as a scale, OK.


OK, now, and of course, let's go forward here. So looks like this is 4, positive, and it's manageable. Of course, it goes without saying here. So this one is gonna be coming down to 0, am I correct? Yes, and here, so it's gonna be you end up


as a second step, you get 3 here and then 2X minus 5 here, OK, plus 0 remember here because we already reduced 4 minus 4 into just 0. And then this one, of course, 19 minus 4 equals 1615. Am I right?


Sounds good


But, and then after that here, well, so I don't think I have to write this one anymore because 0 is nothing, OK, right, so here, so we got something like this, 3, and then 2 X minus y equal to 15.


Yes, right, and then after that, what after that here, well remember here that our goal is still the same thing. So what I'm aiming for is that I have to have a situation in which that the left hand set equal to just only act here, get equal equal equal something, am I correct? OK, so what is the next step? The next step is that I would like to get rid of this history here. But, OK, how? Well, of course, that I have to define left-hand side by 3 at the same


time here. Remember here equation is nothing but a scale, whatever you do to the left hand side, it's OK as long as you do the same thing to the tenet, am I correct? Yes, so I hope, I think that this is the same way that your teacher talked about it.


OK. So go ahead, divided by 3 and divided by 3. Yes. So let me repeat one more time because this is very, very important concept here in algebra. This is an equation, an equation is just like a scale in daily life. So whatever you do on the left and then it's OK as long as you do the same thing to the right-hand side.


OK. So of course, from here, let's focusing on the left hand side first. This is 3, this is the, of course, you can just easily canceling out. A my product gone?


Yes, OK.


yes


OK. So here, the next step is gonna be 2 x minus 5 here equal to 1, 15 divided 3, of course it goes without saying. It's very simple. It's gonna be 5.


Am I correct


Yes, right, am I correct? Yes, 15 divided by 3 is 5. So 3, looking at the left-hand set, 3 and 3 canceling out gone, am I correct?


I cant see the problem


Yes. And then after that here, well, so it looks like here again here remember here I my goal is still the same thing as equal to something, something, something like that. So it has to be alone on the left-hand side, whereas everything else is going to the right hand side. OK. So the next thing is that I need to do the same thing here. I need to get rid of this one, OK?


OK. And then here, of course, that do the same thing here, there, OK, so I need to put in positive 5 on the left hand side. In doing so, because I'm treating this equation as a scale. I got to do the same thing to do about 10 cents. So we got here to X minus 5 + 5 is it? Yes, so this is something new that I introduced to the left and sense and then 5 + 5 is it?


Yes, sounds good. OK. And then after that here, well, again, the same thing happened just like the last time here. So this is negative and this is positive, of course, they are gone. (-5 + 5) becomes zero, right? OK. At the same time here, OK, at the same time here, meaning that it's going to act only my, so I no longer have to write the neg55, they are gone here and then 0 I I like because 5 times, excuse me, 5 + 5 is 10, OK.


Yes. Now, so here, again here, remember here my goal is x equal to something, something on the left hand side and the left and everything else on the right hand side. So I'm very close, OK. So the only thing that I still need to do is that, well, I think that I need to get rid of the two, and I like.


Yes, so here, of course, is funded by 2, it's by 2 X


X.


exactly


Uh, there's I know the answer.


Yes


Yeah, I think it's, oh


oh, you already answered it


Yes, uh-huh, X equal to 5. That's correct.


Uh


Look later and check. Later in chat, it shows that I put the answer, but I guess you didn't see it.


Yeah, the answer is 5, that's correct. This is what you've said here X equal to 5. That's correct.


Good.


Thank you. You helped a lot. Um


Yeah, you are correct


Thank you. You brought, you brought it in a lot of steps and showed me step by step how to do this. It helps a lot.


OK


Thank you.


The teacher just suggested it and like a couple steps and I can't really understand him that well.


OK, it might be possible your teacher is running out of time here, OK, so you have to be


well, maybe, yeah, I think, I think maybe the the best explanation that your teacher may be running out of time. So she doesn't see or he doesn't have time to follow through but one by one.


But I'm glad you came here so that at least


you see that all the necessary steps in order to arrive.


at the final solution.


Yeah


OK. Do you have any other question? I think that we still have some time, hopefully.


Oh, I have a bunch of to, uh, you might not. I have a lot of time cause


I'm doing my work


Yeah, but you know that, yeah, the system, the system that limits our confession only to about 24 minutes, so for some reason.


Oh, OK.


Yeah, so it's not about, I have also your, I mean, I have also a lot of time. You also have a lot of time, but the system cut off


about 24 minutes.


Well, that's kind of not fair


I'm sorry here. So it is not under my control.


Yeah, I understand.


Yes, OK. So in what state you are in Leo, if you may.


Uh


uh, I'm in Miami.


Oh, OK, OK. Sounds good. OK


All right


Thank you for this, this helps me out a lot.


Sure, absolutely. Anytime, anytime. I wish you good luck, Leo.


You were, oh, OK, you too. Uh.


OK, OK, bye-bye. Say hello to your pattern, OK?


I, I'll


OK


Thank you so much. Bye-bye. Good. Excuse me, I'm sorry. Have a good day.


It's OK, bye.


OK. It's a bad, bad, I'm bad.


Bye-bye


so i need help with


math


so the question is to find 1/3 of the total number of fruits divide the total number of fruits by


Hi Liam! How can I help you today


Can you put the complete question on here please?


if you can upload a screenshot or something it's good as well


done


i see


so here is an example


if we have three people here, and 12 cake


and we want each person to have the equal amount of cake


this means each of us will have 1/3 of the total number of cakes right


or fruits in your case


so how many fruits can each of us get?


but it didnt work


it is only numbers


no letters


1/3 is divide a thing to 3 pieces right?


so that each piece is 1/3 of the whole thing


say that we have 3 fruits in total, and to find 1/3 of the total 3 fruits, it is 3 times 1/3, or in other words, it is 3 devided by 3


*divided


let me know if any of those were not clear!


Hi Liam, are you still there? do you need more explanations for this? :)


I will end the session right now, but if you need anything else, feel free to come again!


Have a nice day!


Hi


hii


How can I help you?


Okay, i need help determ


woah


oops


determining if a figure has symmetry, axis symmetry both or neither


and i dont understand it


Ok


plane symmetry*


So what do you know so far abut plane and acix symmetry


quite literally nothing


Totally fine


so a line of symmetry is a line that cuts a figure into two parts that are reflections of each other


ohh


does what I just drew make sense?


yeah!


Perfect now do you know the different between a plane and a axis/line


not really


ok so a plane is 2D


so think of it as a rectangle but extending forever


and line is 1D because it only goes in one direction


like a rectangle has length and width


and a line only has width


does this make sense?


kinda?


What are you struggling to understand


its totally fine, this topic is tough


haha yeah


im kinda strugging to understand the difference between 2d and 1d


ok so a plane is basically a rectangle in all directions


a rectangle i considered 2D because it has two dimensions (length and width)


a line on the other hand does not have a width


and only has a length (which means only one dimension)


oh okay i think i get it now


so a axis of symmetry and a plane of symmetry are different because an axis is a line, and a plane is 2D


this means a axis of symmetry is normally cuting a 2D object


and a plane normally cuts a 3D object


Ohh


I am not sure how to draw this so let me find a picture


i have my homework pulled up i have 4 examples?/


sure


lets take a look at those


okk


great


so is this figure 2D or 3D


i think its supposed to be 3d


do you havea screenshot yo ucould upload?


let me attempt to do that


great! thank you


okk so im on my home computer and im like struggling to get a photo of my school coputer


computer*


umm totally fine


so considering this figure is 3D


which one do you htink the symmetry is Plane or axis?


it'd be plane?


no


wait


axis?


it was most likely be plane


oh


This is because in a 3D object the object cut by a line does not completely cut the object


ohh


See in these images the 2D plane is able to cut throguh the entire 3d Object


ohh!


Does this make more sense


yes it does


so when there is a 2D object, it is normally a axis


i put plane symmetry as the answer but its marking it as wrong


and then it is a 3D object, it is normally a plane


since it is marking it wrong i think it could be a special case


how come


it could be similar to the orange image


where even though its 3D it still only has a ont dimentional simmetry


this is because at the point specifically there is a place that drops down dimensions


i dont think we've learned point symmetry yet, its only giving me four options


what ar the four options?


plane symmetry, axis symmetry, both or neither


oh


then it could be neither because if there is not symmetry then it is neither


you were right


great


thank you!


so doers this make more sense?


yeah!


perfect I have to go now, and I loved working with you Alex


Good luck!


ithank you!


have a good night/day


You too!


Howdy !


Hi


So you've got some math stuff to go over?


Yeah trying to prepare for a quiz for next hour


Okey dokey.


Something you can post on the whiteboard?


before i get into that i have a question


have you heard of the fancy R


Nope.


how lovely, alright lol


I just googled it and apparently it can mean many different things depending on context.


Usually denotes the set of all real numbers in math stuff.


Vertex and x intercepts


Okay, so this is a parabola that opens up (since the x is squared and its coefficient is +1).


Vertex lies on the axis of symmetry which occurs at x = -b/2a


Sorry -b/2a


Okay so far?


yeah


So now you plug that x value back into the original equation to find the matching y value.


And there we have the vertex.


Ready for the intercepts?


So, the y intercept is easiest and we'll do that first.


Plug in 0 for x and you get 5 for y.


So (0, 5) is the y intercept.


Ready for the x ones?


indeed


Can I erase that blue text?


So the x intercepts are when y = 0.


So we set that equation = 0 and solve for x.


There are 3 ways to do this (other than graphing).


1. Factor


2. Complete the square


3. Quadratic formula (this will ALWAYS work) and is thus what I recommend.


Which way to you wanna solve it?


quadratic


Okey dokey.


This one is easily factored so I wrote that on the board as well.


So to use the quadratic, you have to make sure the equation is in the standard format of ax^2 + bx + c


Which is already is with a = 1 b = 6 and c = 5


Make sense?


yeah


now i have a question


lets say you start with imaginary numbers, like i for example


how do you get it into factored form


So what is the other factor?


Are you asking what happens if the discriminant (that b squared minus 4ac term) is negative?


i found an actual example


so like i have the zeros


-3, 1, -2i


Can I erase what's on the board?


-3, 1, 1-2i, 1+2i disregard the other one


So the basic idea here is that if 5 (for example) is a zero then (x - 5) is a factor.


right


So that's how you jump from zeros to factors.


im following


now as a polynomial?


You multiply that mess back out.


It's a bit soupy in this case, but that's the process.


can you do it


Hold on a sec...


I'm goofing a term somewhere (in the soup).


And that's the final answer.


very silly


but i follow


It's just messy.


But setting aside the algebra soup, did that make sense?


yeah


last one


Okey dokey.


how do you prove that 1+2i is a zero of x^3-3x^2+7x-5


The short answer is that you plug it into the polynomial and you will get 0 as the result.


This, again, after many bowls of algebra soup.


Like that...


a whole lot of


distributing


Yup.


how lovely


Yes - and not very helpful.


These problems confuse the learner over needlessly complicated algebra.


whats the final answer supposed to be


End result is that the student gets frustrated and doesn't learn the main concept they were trying to teach in the beginning.


The final answer = 0


is there another way


Not that I know of.


Let me cheat a bit and make some easy soup bowls?


yes please lol


That cubed term is equal to that


Now let me do the squared term


Okay so far?


ye


kk


So there it is, covered in a minimum amount of soup bowls.


making our brains hurt


I have to cheat like that, but if I don't then we get lost in the algebra and miss the main points.


Yup, my head exploded 10 minutes ago. :-)


lol


alright i should be good


Cool beans.


So best of luck to you and have fun with that fancy R !!!


lol tanks


hi


Hi


I need help with solving the zeros for all these 4 questions please


I will be glad to help.


the first question needs factoring.


there is a 2 at the beginning.


that makes it a little harder to factor.


I tried doing the borrow payback method but I forgot how to do the rest of the steps


I like the AC method.


multiply the 2 that is A and -2  that is C.


we get negative four


mhm


isn't that similar to the borrow payback method?


i think so.


our teacher didn't teach us the ac method he teached us the borrow payback method


I am not familiar with that method.


we could try the guess and check method.


do you wanna search the borrow payback method?


or we could work on one that doesn't have that first number?


i can do that while we start on the question next to it.


We need all of the terms on the same side.


I will.  let's work on this question first.


ok


wait here are the steps to borrow payback.


Steps for Borrow/Payback
Multiply the “a” value into the “c” value.
Factor the resulting trinomial (Trinomial Factoring)
Payback the “a” to both binomials in the answer. (In front of x)
Divide out the GCF from one OR both factors.
Check your answer using the box method.


multiply a by c


that's what I said, but in different terms.


so are they both the same?


yes


you did that step.


next step?


I did ( X + 4 ) ( X - 1 )


then what?


good


payback


how do I payback?


divide by 2


the a number


ok so payback by dividing by the "a" number


if there are fractions, we will multiply the denominator.


ok


so 2 x 2 = 4?


the first factor is ok.


we divided 4 by 2.


1 divided by 2 is 1/2


we need to multiply that factor by 2.


-1 divided by 2 is -1/2


yes


what will that become?


2x - 1?


yes!


it is factored.


to find the zeros, we set each factor equal to zero.


so ( x + 2 ) = 0 and ( 2x - 1 ) = 0?


correct


ok now what?


oh wait do we do inverse operations?


very good


so x = -2 and x = 1?


let's look at the second part.


ok


added one


that gives us 2x = 1.


what do we do about the 2?


divide?


yes.


that is the inverse of multiply


so divide both sides by 2 then what?


what does the pink writing show?


2x - 1 being divided by 2?


can you see the black writing?


oh wait it makes sense now


x = 1/2


yes


x = -2 and x =1/2


ok next question and can we also hurry this up a bit pls?


do you know about the quadratic formula?


we will need it to solve the questions on the right side.


we also need the equation to be set equal to zero.


or can we simply just change 3x + 6 to -3x - 6?


sorry, no


we can subtract 3x from both sides.


we can subtract 6 from both sides.


that is the inverse.


yes I mean that


good


its much more simpler and easier than the quadratic formula


we will still need the quadratic formula.


or do you have a different way?


some equations cannot be factored.


hold on let get the equation real quick


I wrote it on the board at the top right.


I wrote the quadratic formula.


would the equation be -3x^2 - 14x + 15 after doing inverse operations?


oh woops


sorry


I was looking at the equation at the top on the right.


would the equation be x^2 + 11x + 9?


sorry - 11x


kk


it would help for us to write what a, b, and c values are.


can we factor this by finding numbers that multiply to 9 and add to -11?


I don't think so.


not all equations can be factored.


that's why we have the quadratic formula.


there is one way called "completing the square".  it is a lot of math steps.


you mean DOTS?


what is DOTS?


Difference Of The Squares?


no


that is for binomials


oh ok


not trianomials.


yeah right


I plugged in all of the values into the quadratic formula.


I kinda forgot how to plug in the quadratic formula into the calculator its been a long time since I last done it


how do you do it?


It takes a lot of parentheses.


I choose to do the math steps.


what is (-11) squared?


yes


what is 4 times 1 times 9?


right


what should the number under the radical sign be?


we are done.


that's our answer!


you sure we solved the zeros for this question?


ok


next one


can we also speed this up a little bit because I have to go soon


are we working on the left one or the right one?


the bottom left then the bottom right


the one on the left can be factored.


we need it set equal to zero first.


so we need to do inverse operations with the right side?


is it 3x^2 - 2x - 8?


very good


now borrow


where did i get -24?


3 x -8?


good


So (X + 4) And (X - 6)?


yay to go!


now payback.


what do we divide by?


the a value which is 3?


yes


so we are gonna get 2 fractions?


only 1 for this question


oh yeah right because 6 is divisible by 3


do the inverse for the other one.


so wait we got 4/3 then the other one is 2?


what about the signs/


inverse ops again?


so x = -4/3 and x = 2?


very good work


ok next and last question


the last question will need the quadratic formula.


what else do we need?


is the equation set equal to zero?


if not, we have to do some work.


so equation is not zero so we do inverse operations


correct


so would it be 8x^2 - 44x - 40?


oh wait sorry + 40


I mean


those numbers are really big.


is there a GCF?


greatest common factor


Is it 4?


yes


so would it be 2x^2 - 11x + 10?


awesome work!


now what?


we need a, b, and c for the quadratic formula.


So would it be -(-11) +- (-11)^2 - 4(2)(10)/2(2)?


great!


so how do we plug in this in?


what is -(-11)?


what is (-11) squared?


(-11)(-11) = =121??


i think + 121


oh yeah


4 times 2 times 10


we walk through the quadratic formula using order of operations.


ok


almost done


can you see what we have on the board?


yes


what is the next step?


subtract 121 by 80?


good


yes!


all done!


x = 11 +- square root 41/4?


Yay!


ok cya


Hi need help with anything?


yes i have mid terms tmmr


ok anything you need to review


yes my teacher told


me i should review


cool cool so what topics do you guys have


we can do some practice based on it


Midterm Review Packet

What topics will be on the Midterm?
UNIT 1
UNIT 2
UNIT 3
1. Constructions
Circles (radius, diameter)
Perpendicular Bisectors
Angle Bisectors
Inscribed Polygons (Hexagons, Equilateral Triangles. Squares)
Using constructions to make statements about a figure

2. Transformations
Translations
Reflections
Rotations
Preimage vs. Image
Writing a sequence of rigid transformations

3. Angle Relationships
Vertical Angles
Linear Pair
Alternate Interior
Alternate Exterior
Corresponding
Same Side Interior
Same Side exterior
1. Congruent Figures
Using rigid transformations to determine if two figures are congruent

2. Triangle Congruence
Congruence Postulates
SSS
SAS
ASA
AAS
HL
3. Proofs
Triangle Proofs
CPCTC Proofs
Quadrilateral

4. Trapezoid
Parallelogram
Square
Rectangle
Rhombus
1. Dilations
Dilating Figures
Determining Scale Factor
Comparing Measures

2. Similarity
Using rigid transformations and dilations to determine if two figures are congruent
Similarity Postulates
AA~
SAS~
SSS~
Similarity Proofs

**NOTE: I will NOT ask you to perform constructions with a compass and straightedge.
	   Instead, I will ask you questions about HOW to construct or ABOUT measures from a construction.

What materials should I use to study? How else should I study?
Review classworks from units 1-3
Check answer keys on google classroom for all classworks
Do more problems for each delta math skill that has been assigned
Complete the OPTIONAL delta math review assignments (these are not due for a grade - they are OPTIONAL for your extra practice!)
Write definitions or explanations for each topic listed above to ensure that you understand the concept


this is what she said


ok tell me which one you least understand


the last unit


Similarity?


yes


alright lemme put a practice problem from the basics


ok let's say these two are similar


it means that their anges are the same but the sides are different


i see


i can try to show you what she told me to do


like she gave us a packet


ya that would work


wait finish what your were doing


if you have a photo you can upload that


ok ok


alright so basically the two sides are different right?


wait quick quesiton


are you guys doing proofs?


oh ok ok so then you already know the basics nvm nvm


ya lets do your problem first


ok so for #9, can you label the "graph" I made first


sure


with the heights and shadow length?


ok so the x is in the wrong location


it's the height of the tree not the


side of the tree


ya right there


sorry


no it's ok mistakes are good


ok so next we have to do the fraction matching


ya then we gotta cross multiply to find the x


ok good


so that would be your tree height


so we have to do the same for 10 can you make the graph and try that?


yup that's right


sorry im taking long


no it's ok


knowing the concept is the most important


olivia john


Olivia!


do you want to do the proof now?


yess


ya good job


the full name is vertical angle theorem though


I don't know if your teach wants the full name or not


last time i did the test she gave me fullcreidit


ok then it's fine


yup good job


any other problems you want to try


are you a student??


ya!


we're both students then


ayeeee


im scared for the midterms


do you have any advice


i get to use a notecard does yourschool let you


ok so for midterms (I just took one)


nope!


but for midterms you have to make sure to keep your timing right


wdym


because I real issue during exams is not being able to finish the test in tiime


so what you should do is have a good speed during the test to leave some time to check answers


do you want me to fail


no


so i rush😭😭


no don't rush what I mean is that make sure to keep pace


like don't spend too much time on one problem


skip it for now and get back to it later


lol i do this a lot


try to do the ones you know first so you have time for the others


okk


do you know what i should add on my notecard


and also write the thermos on your paper


its a small notecard


the theorems unless you remember every one


no i dont i will make sure ot add that


maybe the properties of the quadrilateral


i have a 97 in that class


oh wowww


that's my dreams in math


math is so hard now :(


what classes are you taking


im taking precalcuas im scared for next semester


sorry I can't say but I've taken precalc before


why


and you just need to have a good structure


part of the rules


huh


if you understand precalc well the next level is going to be easier then if you didn't


a lot of the next level is based on precalc basis


Olivia


if you're doing good now, then you will do well next semester too trust


it's all about the structure


no the mid term is ging to be hard watch when my brain forgets everything


nooo you got this just practice with a lot of problems and don't just rely on the notecard


practice creates muscle memory


thank you Olivia have a good reast of your night


yup u too!


good luck and do more pratice


Riverside


Liam!


hi need any help?


Yeah, I need help


Geometry


ofc do you have the question you need help with?


Yes, I share my screen.


I need help


I don't know.


I just


OK, hi, can you hear me?


Yes


OK, cool. So which question, is it a matching one?


Yeah


OK, which question do you want to start on?


Um


and


oh my God


Sorry. Um


we can start off the


The tree


All right, cool. OK, so first we have to find out the correct proportions of similar figures, OK?


OK.


Do you know what similar figures are?


Alright, so, um, do you know how to solve for the ratio first?


Yeah. Don't we have to do cross.


multiplication


Yeah, OK, so for this one, what are the two numbers that you know from the human?


Um, 5.5 ft.


Yeah, and the other one is 3, that's the shadow, right?


Yes


And because they're similar, that means the angles from the tree shadow is going to be the same angles. So that means the 3 corresponds to the 24 ft of the shadow. You get that?


OK, so first we have to find this, let's find if there's any numbers similar to the equation first. So 3 and 24 have to match, but the fraction


is on the, yeah, that one, that's perfect.


So you see how it's 5.5 over 3.


Yeah, cause the height of the weight.


Yeah, exactly, yeah, and for the other one, you want 3 equals 24 because they're in the same similarity, correct?


Yeah


All right, cool. So


now that you know that, which one do you want to do next?


Um, you can do this one.


So this one's a bit different because the it's


um rotated. So if you look at X from


the trapezoid ABCD, which one, which side does X correspond to?


from this one to this one or to this to this.


Uh, no, like, um, you see how it's uh X and then ABCD.


trapezoid


So you have to known here and two unknown here, one unknown in an one known for


uh the other one, FG


HJ, right?


FG


HA, yeah


OK. So knowing this


what is the side that X is on?


Um


X is on


this side


Mm.


OK. With this one.


No, like what side of the, uh, just looking at the, the, the shape it's on. So FGH


F sorry, F


F G H J.


Like the sides are gonna be corresponding like either FG HJH


G or K


Oh,


G


GH


Um, close, but it's, um, that one is similar to


JF. We're trying to find what X is on, like what's the side it's on.


to HG GH.


Um, not exactly. It would be FG because X


the X symbol is right next to the FG side. Do you get that?


FG


OK, wait, I thought it said like this corresponding like to the side or something.


Oh, no, we're not, sorry, that's from the other, the tree one. I just meant in general, what side is it like?


what side is it on? So how, how long is FG?


FG would be, would equal to x feet, right?


Yes


So I meant, sorry, I meant like that. So


what about the other one?


Like this one


A, yeah


and this and this and that.


Yeah, OK, so