Hi Chloe! What can I help you with today?


hello!


There is a specific question that i do not know how to solve


it's #4


Okay! Give me a second to try it out


i have to be able to state the transformations that occured in order, with the graph for each step


Okay, so first factor out the constant so it would be -3f(-2(x-3/2)) -1


the function f(-2x) represents a horizontal compression of the original function f(x) by a factor of 1/2 about the y axis


the function f(-2(x-3/2)) represents a horizontal shift to the right by 3/2 units


the -1 at the end is the vertical shift downwards by 1 unit


let me try that out with the graphs


ok so


like that?


wait


the vertical stretch of 3


and reflected upon the x axis too right?


yes the third graph would be like that instead


does the vertical stretch happen before or after the vertical translation?


because i always mix up the otder


It happens before since the -3 is attached directly to the function while the -1 is on the outside so its after


oh ok


thanksss


np!


Hi. I have a question that I wrote it on the whiteboard. I'm starting to write my work out so you can see it


Hello


I see it


its really the finding the domain part that's confusing me the most with this particular problem


The domain is what X values are valid


yea. so I know anything lower than -2 cant be right


see board


ok


why did u flip the sign? x cant be less than -2


-1 gives you an invalid answer


Nvm. it can be bc then the numerator would also be negative and it would cancel out


see graph https://example.com/math_graph


correction


Can you see the graph?


yes


does the domain make sense?


but I think I'm supposed to solve this purely usingalgebra


Precisely


algebraically denominator can not be zero or negative


I can see that x has to be less than 2


cool


is that correct?


looks good


ok great! I have to right now but thanks for helping me today.


bye


Hi, how can I help


Hi I was just wondering how to do the functions, because im functions% understanding it


sure, do you mean like how to graph functions or what a function is, for clarity


like the tables, and how to determine what happened to the function from an equation


do you have an example we could work from?


i do not


Ok, lets see


Can you make any predictions on what this function could be?


is it a shift


Not quite, think of your main types of functions


Exponential, linear, polynomial, etc


are there any patterns you notice, patterns are something fairly relevant for functions


quadratic? because of the perfect squares


Yup!


I dont really remember going over these in class, because we automatically went into horizontal shifts, vert shifts, reflections and stuff like that


Ok, lets try one of those


What kind of technique/shift do you have to apply to y=2x to get the function there


so im mainly struggling on the stuff when the teacher gives us an equation, and the parent funtion and then we have to use the equation to determine and graph the new function


ok


Ok, how would you graph that, try drawing on the board


Yep right 5, and what other shift


Yep, I agree, those are the shifts


Is there anything specific I can help with, if not, you might be best served just finding some of your hw and reviewing the problems


I just want to practice more of this type of stuff, because i dont really feel like im too confident in it yet


sure, we can do a couple more problems


try this one


so up 1


yep


and then would it be a shift to the right


That sounds right!


what about this one


oh i have never seen anything like this, let me try it though


Sounds good


so down 10


yup


left 3


Yup, nice job!


i feel like there's other steps, but i dont really recognize this


For this one, its a function you probably aren't familiar with, but the shifts are the same


i feel like its the cubic part i dont understand


could you still ecplain it though


sure, in this case, this is the cube root of the square function


That's approximately what the base cube root function looks like tho


oh, i have never seen that, but okay, what would happen after that then


the shifts are the same as all other shifts, the graph itself approaches infinity as x approaches infinity and the opposite in the negative direction


Hi, are you still there?


yes i am


hii


hii! how can i help?


I need help on my math work


alright, let's take a look


okay


I put it on the board next to the chat


i see it


ok so there's a rule to rotating points 90 degrees counterclockwise


your new point would be at (-y, x), using the x and y coordinates from your original point


or in this case from point b


you can kind of picture the rotation like a circle


hello?


unfortunately i will have to end the session in a few minutes if you don't respond, it's Tutor Provider policy


ill give you 2 more minutes, but unfortunately that's all i can offer if theres no response


alright, im wishing you luck on your math!


Hi! Are you good with Excel?


Hi Alex! I am not very experienced in excel. What kind of help do you need?


Or rather, what are you trying to do in Excel?


Its stats related but nobody is taking my session at the moment


Let me screenshot it


Maybe I can help


Ok give me one sec


Okay! :)


here it is


so so far i did the A part already


i wish i could screenshare but it wont show so we'll do this


So you want to click on the empty blue box next to mean, for example, and start typing =AVERAGE()


yeah but for hat cell


wait let me show you what i emailed my techer


Then, you'll type something like =AVERAGE(A2:A81)


but replact A2:A81 with the range of light bulb values


The row and column of the first data point and the last


"There are 80 values, but A2:A80 is only 79 values. You are missing the bottom one.
"


Is there a value in A81?


The reason why I put A1:A80 is because A1 is the title of that section. "Sorted Lifetimes (hrs)


That's good! But if there's 80 values, then there should be an entry in A81


so how do i do that


bc then it'll count the title


Could you clarify if there is an entry in A81?


A1 is sorted lifetime


Okay. Is the column Light Bulb Lifetimes (hrs) column A then?


yes


Okay! In the box next to mean, we want to compute the average of the column


We can enter =AVERAGE(A2:A81)


Because the 80 values should be in A2 to A81


Ok


Ohh I do both


either column A or B should be fine


Ohh I have to do it to Light Blumb (Lifetimes hrs)


because they are both the same data set, just sorted differently


However, you need to go up to row 81 to get all 80 values


since the data set starts at row 2 due to the title


That's what your teacher was talking about I believe :)


Ok so type in for mean A1:A80


Not quite! We don't want to include A1, which is the title


We want the first 80 numeric values


which is A2:A81 :)


Exactly thats why I did:  A1:A80


let me show you the cell


A2:A80 is the first 79 values


A80 is not the 80th value, just row 80


the 80th value is in row 81


look


theres no number in 81


Oh okay! That was probably a copy and paste error


ok let me start over then on a new excel sheet from the original


Can you try redoing part A, making sure you copy all the values?


fixed it


i fixed it


Awesome!!


so do


Yes!


Yep :)


uhh what do i do for midrange


there's no formula


Can you add MIN(A2:A81) and MAX(A2:A81) and divide by 2?


oh that's what i do?


Since column B is sorted


the low and high are at the top and bottom


ok but how would that look formual wise


I believe Alex


oh its =(MAX(range) + MIN(range)) / 2


mhm


That works too!


Alex


yep :)


now i have to subtract


Yeah, just use the letter of the column and number of the row to specify the values you want to use in the equation


how would i do that


ok


It's gonna be similar to how we did things for midrange!


Ok done


Nice! :)


ok i completed the purple


Good job :D Do you have any other questions?


im updating the new stuff


done


now i need help with the orange


Okay! Do you have an idea how to get started?


So I have to use the 5 stats to summarize the data set


Yeah!


So like what would i say


bc idk what to say honestly


I would reiterate in your own words what the statistics you calculate are saying.


For example a mode of 8 means the most common value was 8.


You can also write about what the statistics say about the spread and skew of the distribution if that feels appropriate


ok


ill free write and then can you help revise it


Okay!


the data kinda centers around 1100, most of the values like fall between 900 n 1300. the mean n median r close so the distribution looks pretty symmetric. the mode 1050 so theres like a bunch of data around there, n the midrange 1127 shows the spread is balanced but a lil pulled up. standard deviation is 115 so the data got moderate variability.


That looks great!


Well its kinda informal


How's it going? :)


im saying the writing is informal


Okay! How's the writing going?


lets skip and do #4


so how would i do that


You can click and drag your mouse to select cells.


so select the full A1:A81


i mean 81 omgg


If you look at the sorted column, it easy to see where the first value within the range you want start and where the last value ends. You want to select those value within one standard deviation of the mean


Then you can change the text color somewhere up top


wait so do i just change it to purple


and it'll change the ones that need to be changed to purple


or do i like have to go to the "A,Z" column


If you change the text color to purple, it will change the text color of the selected cells.


Does that answer your question??


yes so i selected A1:A81


but im asking if i only need to just change it to purple


i wish Tutor Provider would let me screenshare sometimes that button shows sometimes it doesnt i dont understand why


Problem 4 is asking you to change the text color or cell fill color of the values in the sorted that fall in the range of the purple cell block, which is one standard deviation from the mean


ohh


so i have to change the color manually


yes :)


only for the sorted lifetimes section right?


Yeah!


ok is it ok if i send u the numbers when done and then you verify?


if theyre right?


Sure!


Just a heads up, I have to leave at 2:25


kk


906, 911, 913, 925, 944, 958, 969, 979, 998, 1006, 1009, 1022, 1031, 1048, 1050, 1051, 1052, 1057, 1058, 1060, 1067, 1073, 1075, 1078, 1080, 1083, 1091, 1093, 1095, 1096, 1122, 1127, 1136, 1142, 1149, 1155, 1165, 1167, 1173, 1179, 1188, 1202, 1208, 1208, 1227, 1239, 1240, 1245, 1257, 1265, 1284, 1285, 1288, 1307


Very close! You want to make sure all values are less than the upper bound, 1304.17. If they're greater, they fall outside one standard deviation from the mean :)


where did you get 1304.17 from


906, 911, 913, 925, 944, 958, 969, 979, 998, 1006, 1009, 1022, 1031, 1048, 1050, 1051, 1052, 1057, 1058, 1060, 1067, 1073, 1075, 1078, 1080, 1083, 1091, 1093, 1095, 1096, 1122, 1127, 1136, 1142, 1149, 1155, 1165, 1167, 1173, 1179, 1188, 1202, 1208, 1208, 1227, 1239, 1240, 1245, 1257, 1265, 1284, 1285, 1288


Mean + Std Dev in the purple blocke!


That looks good :)


my mean 1100


oh nvm


i see


so ill highlight, 906, 911, 913, 925, 944, 958, 969, 979, 998, 1006, 1009, 1022, 1031, 1048, 1050, 1051, 1052, 1057, 1058, 1060, 1067, 1073, 1075, 1078, 1080, 1083, 1091, 1093, 1095, 1096, 1122, 1127, 1136, 1142, 1149, 1155, 1165, 1167, 1173, 1179, 1188, 1202, 1208, 1208, 1227, 1239, 1240, 1245, 1257, 1265, 1284, 1285, 1288 PURPLEE


looks good!!


and that is 54 values?


I'm not sure... you can take the row number of the last row you're changing minus the row number of the first row you're changing and add 1


let me look


cell 15 and cell 67are highlighted


so you do 67-15=52


and add 1


oh 3


you can also count to double check!


it wants to know how many out of the 80


Yeah!


yep its 53


Nice! I have to head off now


alright, thans bye! :)


Great work today :D


Hello


hi could i get help with this assignment


Yeah, sure, I can help you with that


So we'll have to break down the overall equation into two parts.


I'm gonna type it here and you should be able to see it in a bit.


Do you see it on the board


OK, I have posted on the board and also shared an explanation.


Please let me know if you have any questions.


Are you still there


hi


Do you have any other questions


hello?


Yup.


yes i am back


how do i do this because i know nothing about algebra so i want to figure out how to do this


OK


ok so it will be x-3^2 because x^2 -6x would be 3+3=6


like how it go to x + 3


Yeah, kind of, but let me share the formula.


Do you know the formula for A + B, the whole square?


Put it on the board


So A minus B is there. I'm gonna add A + B as well.


So basically that's what we apply for


the X minus 3, the whole square. You should have your answer.


(a + b)² = a² + 2ab + b²


yea


I


That's correct, yeah


There's a trick in this question because the last digit is + 14.


uh, that, that is what can confuse some kids, so essentially,


uh you get 9 by swallowing the X minus 32.


by solving.


So the 9 + 5 would give you the 14.


Did you get that last part


So it will be -2AB when you're squaring XA minus B.


For A + B, it'll be +2AB.


Any other questions?


the x-3^2 would be 3x3=9?


Yes


so then it will be 9 and then the 5


but do we add the 5 or subtract the 5


correct.


So the answer is option C.


wait no i was asking a question


The answer to your question is, uh, 9 and then the 5 gives you 14.


We add the 5 only because that's one of the options and that will give you the 14.


He.


Are we clear


Did I answer your question


but how do we know if we subtract or add the 5


If you subtract 5


then 9 minus 5.


would give you 4


But if you look at the question


it is x squared minus 6 x + 14.


So the plus 5 is coming from option C.


(x-3) ^2 = (x^2 - 6x + 9)


(x-3) ^2 + 5 = (x^2 - 6x + 9) + 5


ohh ok


because we alread subtract the x and the number


and then we just add the 5


yes


good work.


ok so how do we know if its C or D


because the Q has -6X


ohh we subtract the x and 3


and not +6X


ohh so it would be


Yup.


Excellent job


I'm glad to see that you're trying to understand the concepts.


and you have it all


ok can we do another one cause you explained it in a way for me to understand


OK, let me delete the previous.


answer


Oh, you did it. Thank you.


So you see that


the, in all the options,


the R is in the denominator.


So our goal is to solve the above equation in such a way that our goes into the


denominator


So let me show you how.


So when I solve the equation.


on the left-hand side


you get QX + 5 X.


On the right-hand side


You have 3Q


Any questions so far


why we do 5x and we didnt do 5q?


OK, good. So you caught the error


I just wanted to make sure that you understand it. So it is 5Q.


So now let's solve it further.


oh so it is qx + 5q and not 5x


We have to isolate the eggs.


Isolate the X


Do you see the screen right now


We, we took X out.


and put Q+R in the brackets.


why we take x out?


because that's the question. The question is saying,


which equation represents the given equation when solved for X, so we are trying to find out.


what is X equal to


Do you understand that?


ok its asking when solved for x


correct.


If you wanna use the mic and speaker, it may be easier to kind of.


walk you through that


so we have to figure out how to solve for x


Yeah.


idk how we solve for x because why are we breaking apart the equation?


You're not breaking apart the equation. I was just trying to explain it to you so we solve each side.


of the equation, uh, but you can


just um


keep it as left-hand side and right hand side.


because those two are the parts of the equation.


ok so we have q+r in paranthesis


yes as x is common to both


why we do x(q+r) two times


what do you mean?


like we did these two both times


There two different lines


the 2nd line has 3q-5q =  -2q


nothing is changes on the LHS


yea how we get -2q?


i explained it above


yea so you did 5-3


and then it got -2


dont forget the q


ok so it will be x= -2q/ ( q + r)


i think i will just be confused like doing the LHS and RHS


what is a LHS?


Left-hand side of the equal to sign.


Do you have a mic


yea but im in public


They're fine for me if it's fine for you.


It's easier to explain


The left hand side and right hand side is just a way to make it simpler. So if it is confusing you, then you can ignore it and just, uh, you know,


solve it as is


yea  i cant hear it


and ok


Are you're not able to hear me


Hello Emily


Emily


hi! how are you today?


Good thx


How can I help out


i was wondering if you could help me with an algebra assigment?


Sure thing


I don't get it at all, we had to teach ourselves but I don't get it


I hear you


Reviewing the question


I will show on board the steps


Please ask questions as I go through the steps


sounds good


clear step 1?


you plugged in x right


yes


k


g(17)=272 clear?


Is step 2 clear?


Are you there?


sorry


any questions so far?


no


So 2 a is done


We will do 2 b now and then go back to 1


okay?


done 2 b


any questions re. step 2b?


wait


is g(h(t)) the same as g(f(x))


wait I read that wrong nvm


Same concept


ok


h(t) is like f(x)


function of t or function of x


same concept


oh ok


how would you do 1


uhhh


step by step


what does t represent


the number of seconds


yes


so what does p(t) represent


the number of push ups in the number of seconds


yes and t=?


yes so a person is the number of push ups one can do in 45 secs


makes sense?


great


so what is C(p) mean?


the number of calories burned doing a number of push ups


is how much time?


in how much time?


45 seconds


super


So here is the interpretation of C(P(45))


c(p(45)) represents the number of calories burned from the push-ups a person can do in 45 seconds.


I will need to leave in 5 mins


I can send you a video on composite functions if you want


yes pls


sure, working it


Please review


bye Emily


bye


thank you


welcome


Hi Leo!


hello i have


a assignment


Sure, just share the question you need help with


here could you demo 1-2 and help me do the rest?


Ok


The first step is taking the coefficients of the dividend


Okay


Then for the divisor you need to do x+6=0 and solve for x (basically find the root)


I see


For the first term, we just take it straight down, no calculations required


then ?


For the second term, you will need to multiply 1 x -6


Got it


Then add the 1 and -6


Then repeat the process


So now we would do -6 x -5


Now the results are at the bottom


The last term is always the remainder


oh okioki


And the other terms are applied to increasing powers of x starting from 0


so whts hte fa


So for -5 it would be -5x^0 which is just -5


Then 1x^1 which is x


If there's any remainder, you would write that over the existent divisor


Since the remainder is 0 it makes no difference


Hmm


then the next numberr??


Which number?


x+2 so i can do 2 --2


Ok


Do you understand this?


yup


That's great!


Do you still want my help for the other questions?


what why is 2 -2 when in x+2 is x+2


you change signs?


For the denominator (i.e. divisor), you're supposed to solve for the root of x


So in this case you would do x+2=0, which would give x=-2


ohhh I see


wait


plz check


if you have any corrections feel free to correct in the thing i did


What's this?


4 as we bring the first one down(?)


Yeah, that's correct, it was just a bit hard to read


then abt abt -3-12-32


The final answer is wrong


Wait I'll write in red


Understood


whast the fa


Perfect


Sure


The solution is below the worksheet


Ok


can you check


Yeah


okay next


oki please checkk


You should put the values in descending order of powers of x


So 3 should be first not lasr


oh


plz check


can you write it with the variables?


Yes that's correct


can you do (2x^3 - 9x^2 + 4x + 12) / (2x-3)


also check for (2x^3 - 9x^2 + 4x + 12) / (2x-3) i did the fa


Yes it's correct


also can you do (2x^3 - 9x^2 + 4x + 12) / (2x-3) plz?


It's the same concept, equate the denominator to 0, solve for x, then apply synthetic division


i dont get it plz helpp


For the divisor, you need to solve for x in 2x-3=0


And then the rest of the steps are the same


huh i dont get it tot


can you solve (2x^3 - 9x^2 + 4x + 12) / (2x-3) plz


huh


It's the same steps, you're just multiplying and adding fractions instead of whole numbers


plz can you do itt??


dont get it??


I've written it in red


I'll explain it to you step by step


First for the divisor, we solve for x in 2x-3=0, which gives x=3/2


lets do it together


I'll solve it in the gray box


Okay


Do you understand so far?


yup


3/2 x 3 = 9/2


3/2 x -9/2 = -27/4


oh okoki


oh okiki


3/2 x -43/4 = -129/8


That's it


oh okioki


is it correct??


The denominator should be 2x-3


For the last term


huh


We always use the denominator of the original question


thank youu


No problem!


Happy to help


hello


Hey!


I put my first sheet on board I’m on 17 I’m doing every other odd until 71


You mean finding h(1) ?


I just wanna make sure my process is correct


What do you get for h(1)?


So I converted 1/2 to 0.5 and done 0.5-10=-9.5


yes, that's right


Ok so then I’m ready to do 21


that involves graphing


Yes


Did you graph it?


Not yet cause I’m trying to find out where  to start


You could start by plotting the top function. You could start by finding f(1))


i uploaded some graph paper


Mr. Evans t do you mean like so 2x graph that?


Yes, but only for values of x that are greater than or equal to 1


it's a good idea to graph the endpoint, which in this case is x =1


That point is not in the right place


What point?


I guess that I am not sure what you are doing.


Me either😂


I’m just being honest


what is f(1)) ?


not sure?


yes, that is the equation to use for x =1.  So what is f(1))?  do you know what I mean by writing f(1))?


No I guess


the notation f(1)) means to plug in 1 for x.  the notation f( ) means that you plug in whatever is in those parentheses ( ) in for x and that gives you the value of y


so in this case, where f(x) =2x, f(1)) =2*1 =2


Ok


so then the point you would plot for that would be (1,2)


you plotted (2,1) not (1,2)


hello?


Hello Sarah, what do you need help with today?


hi


Do you need help with this question on the board?


Do you have any thought on some first step we can take here?


yes


Is there an equation form you will like to use here? Like the slope intercept form?


That looks good to me!


Great job!


ok


Do you need any help with this question? Feel free to try it yourself first


Is there a first step you can think of?


not really


That's totally fine! Let's start with the problem, they gave us a graph instead of two points (like in the last problem). Is there any information we can get from the graph?


the two points


Exactly! Can you start with writing down the two points?


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


great job!


now we have two points, can you try to find an equation?


good job on calculating the slope! I do see one thing, please double check how you simplify the fraction in the last step here


How is it going so far?


Let me know if you have other questions! I will end the session shortly if you don't need any more help.


Graphing lines on a coordinate plane


Hi how can I help you today?


Hello


Nice to meet you


Hope you're doing well


Nice to meet you!


So I wanted to understand how to graph specific lines on a coordinate plane


Help me?


Okay sure I can help you with that


Let me show a picture


Okay take your time


See the question labelled 4?


yes


That


do you have any idea about how to graph it?


No


so does it mean if we randomly take a x value and it is corresponding a y value


so if we know x and y value then it means we have a point


so that we can draw a graph


is it make sense?


Uh


example.com/graph-image


Alex


this equation has an x and a y right? means that for each value of x, you can calculate a corresponding y value


Yeah


and we can plug them into the equation to find the matching y


What value is for the x and y?


x is the independent variable that you choose, and y is the dependent variable that you calculate using the equation


actually x doesn’t have a single fixed value. You choose different values of x to calculate y, but usually we pick x values within the range shown on the graph


such as x=0 x=1 x=-2


Okay


can you choose a x value first?


and we can calculate the corresponding y value


Any x?


uhh the range of x on this graph is -6 to 6 right?


so we just need this range of x


Yup


you can calculate each of them of course


from -6 to 6


My brain doesn't work
It's already like 10 here....
Please explain


Sorry


its okay, for example y=x + 2
pick x = 0 → y = 2 → point (0, 2)
pick x = 1 → y = 3 → point (1, 3)
pick x = 2 → y = 4 → point (2, 4)
and plot these points and draw a line through them


Ahhhh


I got it now


Okay can you try to calculate y value first?


choose a x value and plugging in the equation


Can you look at the question on the board??
They ask y=3/4x+4


So the y intercept is already 4


Oh yess


if we plug in x=0 we get y=4


and we know a point right now!


The slope value is 3/4


is -3/4 right


hi are you still here?


Yes I am


The phone just glitched


Don't know
Whenever I use the app
It just stops responding all of a sudden


Sorry


It's written -3/4


Yea


its okay that happens sometimes


So then?


Hello!


How can I help you today?


I need help with a homework assignment


I can help with that, just so i know, how many questions is it?


it's 34 questions total but I've already answered 10


ok lets try to finish all of them


would u mind pasting a couple in?


so we can start on those?


yes


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


yea for sure


lmk when your sdone


ok


I'm on 11. I was confused what it meant by "find the measure of each angle


ok so basically


your trying to find the measure of each of them so first you want to find x


how would you find x?


if you dont know its fine i can help


I know how to find x but I was just wondering what angles I am supposed to find


your trying to find angles QRT and TRS


you have to plug x back in to get each one


I think that QRS equals 180. is that part of the answer or no?


I know I have to use that to find the other ones


that is not part of the answer but your on the right track to finding the answer


so I only need to find QRT and TRS for 11?


yes


do you know how?


ok perfect


do it and lmk what u gte


get


so once I find those 2 that will be my whole answer?


ok


QRS does = 180, right?


angle QRT=47 degrees


angle TRS=133 degrees


those are right, correct?


ok let me check ur answer


yes those are right


good job!


now try 12


so once I write those 2 down question 11 will be complete


Yup


which angles do I have to find for 12?


BAC and CAD


so I don't need to write down BAD?


no BAD is already shown to be a right angle


because of the little square in the corner of it


yeah, I know that it's 90 degrees, but I don't have to write that angle down right?


nope


its asking you to find the angles thathavent been found yet


in this case those are BAC and CAD


ok


so once I have  those 2 written down 12 is done?


yes


let me check your work


what work?


oh i thought u did the questions already lol


my bad


keep going


I did 12


what did you get for each agle?


angle?


BAC=58 degrees


CAD=32 degrees


on 13 does it want me to find UVW and XYZ


You got 12 right, good job!


on 13...


yes it wants you to find UVW and XYZ


ok


on 14 it wants us to find EFG and LMN right?


yes


what did you get for 13 tho?


Yea ur right good job


did u finish 14?


what did you get?


EFG=161 degrees and LMN=19 degrees


yep ur right!


would u like to paste the next couple questions in?


also how many questions are left?


is it all due tomorrow?


Technically it's past due but the teacher accepts late work for full credit


ok lol


well try to get as much done as possible


paste in the next couple questions pls


I have to go take a shower now. Can you stay on the line and I will come back when I am done?


yea sure


how long will it take tho?


no rush lol


I'm not sure


oh ok


becuase I have to leave at 10:45


so can you try to be back by like 10:35


what time is it for you currently


in like 10 mins lol


just try to be done in 10 mins


ok. I will try to get back as soon as I can


I will let you know once I am bacj


*back


yea for sure take your time


hii are you back yet?


just asking cuz i have to go soon sooo


im going to leave the session in 10 mins if you dont come back by then


ok sorry im going to have to end the session, bye have a nice rest of your night!


I'm back


oh lol


ok i think ill be able to do like 5 more questions with you


and then i have to go


ok


I'm on 15. What are linear pairs?


its basically asking what angle and angle 1 create a line?


how many answers are ther


one


angle 3?


good job


next one should be easy


so the answer for 15 is just "angle 3" and then that question is done?


yep


now for question 16


whats the answer?


is there only 1?


yes


yes good job


that is the final answer for 16


now do 17


"Yes because they are across from each other."?


that is the full answer for 17?


ok


now try 18


are 2 and 5 vertical angles?


no they are not


although they are across from each other you would also need to add angle 3 to angle 2 to make it equal to angle 5


would I say "No because they are not equal."?


how many questions are left?


after 18 there is 16 more


ok so i have to go but i think you will be fine with the questions, you know the informartion very well!


sorry that i have to leave, you were great though.


you have to go now?


actually i can do like 5 more questions and then ill go


paste them in lol


oh ok


thanks


yea ofc


actually sorry i have to go lol


u got this tho, you umderatdnt hat info!


understand


oh. you have to go now?


yea


sorryyyyy


its ok


thanks for all of the help today


yea ofc please remember to favorite me and give me a good rating!


Hello! How can I help you?


Hello, I need help with the word problems


Ok!


Two


Text them out to me if you don't mind?


1. How many marbles that are not blue could be added to the back so that the probability of choosing a blue marble becomes 1/10.

You have five red marbles, four blue marbles and three yellow marbles


Ok! Lets start out with a statement


How many marbles do you have in total and what color?


2. Your team is in charge of games at the CMP amusement park. One of the games involves a robotic arm that randomly grabs a stuffed animal. You need to set up the game so that the probability of a customer grabbing a teddy bear is exactly 1/2 how would you set up the bin?


Is it fine if we get to the second one later?


Yeah sorry


We have 12 marbles in total


Yes!


and how many blue?


4 marbles


yes. could we develop a fraction of blue / total


Sure


What would that be?


And can we simplify that?


Uh I think so


if we divide 12 by 4 what would we get


yes


so the fraction would then be 1/3


Now if we were to make that fraction 1/10 would we be adding to the numerator or denominator


Numerator


Well, not really, since we would be making the number smaller


for example, what is smaller-1/5 or 1/10


Uh the -1/5?


So sorry, i meant 1/5 or 1/10


Oh


It’s okay


So now what would be smaller


Yes


So, using that same logic, to make 1/3 to 1/10 what would happen?


Would the number get bigger or smaller


Bigger


Almost!


since you are getting a bigger value of the denominator, the fraction would be getting smaller


remember how 1/10 is smallr than 1/5


YEAH


So then 1/3 would get smaller to get to 1/10. Do you get it now?


No :<


Ok, if you had a pizza, what would be a smaller slice


1 slice out of 8 or 4 slices


Yes!


This shows how 1/8 is smaller than 4/8


Now do you understand?


Okay, with this being said, to make 1/3 to 1/10 are you getting bigger or smaller


Smaller


Yes!!!


So if 4/12 is 1/3, 4/? is 1/10


That is basically what we are figuring out


To start, how many times do you have to multiply 4 to get 12


yes


So how many times do you have to multiple 4 to get 1/10


since you did 4 times the denominator (3)


to get 1/10 you will do 4 times the denominator (?)


Do you understand how to do this?


No :(


Ok-So since the denominator was 3 for 1/3, if we multiplied 4 times 3 we got 4/12 (which is the ratio of blue to total)


Using this same principle, if we multiply 4 times 10 we will get?


YES!


But thats not it


Since the question is saying how many marbles to add, we would do 40-?


what would we subtract from 40


YES!!!!!!!!!!!!!!!!!!


So what is 40-12


HOLD ON LET ME DO THE MATH FOR IT


lol go ahead lol


Almost!


here lets break it down a bit


what is 40-10


THEN do minus 2 more


YAYAYYAYY!!!


Thats the answer!


Now we can get started on our second problem: 2. Your team is in charge of games at the CMP amusement park. One of the games involves a robotic arm that randomly grabs a stuffed animal. You need to set up the game so that the probability of a customer grabbing a teddy bear is exactly 1/2 how would you set up the bin?


So what do we know straight from the beginning


(What is the probability we need?


YES!


This would mean that every two times someone used the stick, how many stuffed animals would we get


Yes


So to make a machine you would need to ensure there is half teddy bears right


Okay


So if there were 50 other stuff we would need how many teddy bears


No, in this case it would be 50 since it is the otehr half


OH


So in conclusion, we would need to make the machine have as many teddy bears as other prizes.


OKAY


Anything else you need help with today?


I HAVE A BACKSIDE TO THE PAGE :(


Ok give me the first question and we can take this on together!


to the first question, what is the ratio of 4/12


What if you return to check on the bin and found that there was four teddy bears left and 12 other animals what could you do to add or remove from the bin to return the probability of selecting a teddy bear to 1/2?


Yes!


so since 4/12 is 1/3


To make it 1/2 we would have to remove how many other stuff (not teddy bears)


Hi


Hi, what do you need help with


I need help with some math idk what its called


For sure, can you show me it?


what part do you need help with?


Number 5


does #5 say g(x) = 3/2(x)+1 when x=8


Yes


but it looks like the answer you got is correct, do you want me to explain it?


Yes, I copied what my teacher wrote on the board


can you show me how you are currently working it out on the whiteboard?


or I can give you some pointers to start it


Some pointers


it seems like you understood question 4, am I right about that?


Question 5 can be looked at in the same way, just like 3x is 3*x question 5 can be looked at like 3/2 * x


does that help?


I got it


Great!, do you need help with anything else?


Yes ill take a picture and put it on the board


Is this the same situation as the last problem?


No


it seems like you got the right answer though


I copied what my teacher wrote on the board we are supposed to study from it


I see


so for these types of problems you want to isolate y on one side


Why does it say by over y


I think you meant to write 3y/3 not by / B


Oh ok


now does it make sense to you or should I continue explaining?


Can you keep explaining


For sure


Like I said above in order to solve this problem you need to isolate y on one side, to do this your teacher subtracted 4x from both sides


After getting 3y=-4x+12 you still need to get just y


to do that your teacher divided both sides by 3 making 3y=y and -4x+12= (-4x+12)/3


does that make sense?


Yes


Wait how did she get


because she had 3y=-4x+12


she divided both sides by 3


to get  (-4x+12)/3


It doesn't show thst step


I think your teacher combined the step of subtracting 4x and dividing by 3


Can yu show me down beloa


Definitely


Does that make sense?


Yes Im still reading it


Wait why did yku switch it


You


switch what?


Switching it doesnt change the problem at all, its just that generally the x goes in front of the constant


Why


Plus 12


Instead of subtract


Remember that the starting equation is basically +4x+3y=+12
so by -4x from both sides 12 stays as +12 not -12


Ok


ThankYou for clarifying


For sure


do you need clarifying of anything else?


No


Im still reading the graph you drew


I mean the equation


Let me know if you need more clarification on any step


Why dont you subtract 4y from the 12


Remember


From each side


I mean 4x


I did subtract 4x from the 12


But there's not


An 8


you cant say that 12-4x=8 unless you know that x=1


for example 12-4x=0 when x=3


Isn't x always 1 of its just there


Isn't x always 1 if its just there


No, x can represent any value


think of it kind of like a placeholder


x can be any number


Ok


do you want me to give you a practice problem?


No im ok


okay, do you need more explanation on anything?


ThankYou for helping me


Ill give you a nice review


Glad I could help, have a good rest of your day


thank you so much


Have a good day


You're Welcome


Hello there!


How may I help you today?


Hi! I’m just now learning about proofs and it’s kind of confusing.


Okayy like triangle similarity proofs?


Like paragraph proofs or like 2 column proofs


could you provide an example?


Since <A is congruent to <B Since ∠A and ∠B are complementary, their measures add up to 90°.
Because ∠A ≅ ∠C, ∠C has the same measure as ∠A.
Therefore, ∠C and ∠B also add up to 90


okay so for this


you need to prove that C and B add up to 90 yes?


Yes


okayy


and you want to explain it in both paragraph and column?


okay first lets write out how it would be true in math


so we know that angles A and B are both complimentary


so that means that both added is 90 degrees


lets draw that out


okay so in simple math terms


we can write this as A+B=90 right


Okay!


so noww


next thing they give us is that


A is equal to C


so that means A and C are interchangeable right


Alright!


so that means we can swap out a with C


hence C+B can also equal 90


so now we take all of this


and for paragraph mode we write a  summery of our thought process


do you want to try with the things I said?


Sure I’ll try!


okayy you got thiss


Since <A and <B are complementary, the sum of their measures is 90°. This means m<A + m<B = 90°. Because ∠A is congruent to <C, the measure of <C is equal to the measure of <A, or m<C = m<A. Substituting m<C for m<A in the equation gives m<C + m<B = 90°.


yessssssssssss


thats how you do ittt


you got the paragraph version down


Thanks!!!


Now we should try the column one tooo


okay so for the column one its gonna be very similar


can you use the whiteboard?


Yes!


okay so what you want to do


is remember your thought proces?


you want to put it step by step


so what is the very first thing we identified


That the angles of a and b were complementary


right


and what does that mean


They equal 90 degrees


yepppp


so what we do is


in the step column


we write the mathematical version of that


so the


is what we write in the first column


don


don't forget the = ninetyy


I can’t write ugh!!! I’m on my phone so it makes it look big


oh its okayyyy


you just type it in chat


Okay A+B=90


and how did we find out that the A and B is complimentary


That was already given


yeppp


so in the proof we literally just write given


next what did we do


We said a and c were congruent


right


so angle A is = to angle C


and how did we find that outtt


That was given too!


now here is the trickey part


how does knowing that


A and C are congruent


mean that the measure of A and measure of C are equal


don't over think itt


Uhhhm I’m not sure 😭


what's the definition of congruentt?


Equal


so we know that the measures of both of them are equal because that is the definition of congruentt!!


its super straight forward


ohh ok!


we tend to skip that step because we automatically know that congruent means equal but unless they straight out say that measure of both are equal we have to mention that the measures are equal according to the definition


oh ok!


yeppp


so after that what did we do?


after saying that A and C are equal to eachother


We said that C and B had to equal to each other as well


noooooo we said that C+B is equal to 90 remember?


we shouldn't usually assume things when it comes to this stuff. Unless they say it outright or we prove it somehow previously we shouldn't say it.


Ohh okay sorry


its okayyyy no need to apologize its a common mistakee


even I do it sometimess


I think I understand now from doing this so thank you so much! That helped cleaned up my mistakes more


no problemmm


do you want to finish the rest of the process or do you think you got it noww?


The last part would just be the definition of  complementary angles right? Or no?


next you just have to say that C+B is equal to 90 and thats because of  the substitution rule. The substitution rule is where you go like if two numbers are equal then you can swap one for the other


And then substitution for C+B=90


yesssssssss


and once you get to the thing you want to show you are gooddd


this is what the 2 column table would look like


Okay!! I don’t think I have any more questions. I really appreciate the help.


This cleared a lot up.


no problemmm if you want any more guidance make sure to make another request and one of us will help you out!!!!


You did great learning this dear


Thanks! You did great helping me understand! Hope you have a great rest of ur day.


You tooooo!!!! have a great dayyy


Hi, what can I help you with?


Do you have any questions you need help with or concepts you want to go over?


Hi! I uploaded photos of the problems that I don’t know how to solve. I’m hoping for some help learning how to find the answers.


Can you see the pics I added? Or should I add them in this thread?


I can see them. It looks like the answers are already there but we can go over them.


Yes… the answers are there… classmates gave me answers but I don’t know how to get there.

I was really good at algebra… but have had a hard time getting going with geometry this year


Ok, don't worry. I can help with these questions.


Awesome. Thank you


Does this look familiar?


This is a vertical angle. When 2 lines intersect, the opposite angles will always be congruent.


I’m not seeing a pic… or diagram. Should I get the app? Is that a better way to chat?


I am drawing on the whiteboard just below the problems.


You should be able to see it if you scroll down but let me know.


Okay…I see now. Sorry!

This is my first time using this platform…


Does everything I wrote down make sense?


These are just vocab terms to remember.


Yea they make sense


Do you want to try solving this one?


We can start by finding the volume.


Try solving it on the whiteboard so I can see your work and help if you get stuck.


For the pyramid and prism?


Yes


Okay


Do you need help?


I recommend using a calculator


It’s not letting me scroll down to have more room for my work


Oh, I see what you mean


Can I rewrite it a little bit smaller?


Yea I know how to scroll down more


Now


I'm also a little new to using this. How do you scroll down more?


Ok, now we need to find the volume of the pyramid and add that to 41472.


You click the button on the far left and you just use your finger or mouse too


How do you find the height of the pyramid? I know that 25 is the slant height but I don’t know how to get the height of it


we know the base must be 48x48 because it is on top of the rectangular prism


Yea


Unfortunatly, I am still unable to scroll down so I will do the work a little higher up.


I put the formula of the pyramid above.


We just need to find the height now.


Do you have any ideas on how to do that?


I have no idea


25 is the hypotenuse of another triangle


Do you see it?


Yea what’s the hypotenuse again?


The hypotenuse is the longest side of a triangle.


Do you know the pythagorean theorem


Oh okay


Its like the diagonal


And not really


This formula is true for all right triangles.


Okay


c is always the hypotenuse and variables a and b and interchangeable.


The hypotenuse is 25 right?


Yes


Now we need to find length a and b


okay


Is length b 24?


Now we can apply the formula to solve for a


Can you solve for a?


Yea let me try to do that right now


Is a 7?


Okay I will put it in to the equation now


Is the volume of the pyramid 5,376?


Okay then I’ll add it to the volume of the rectangular prism


It’s 46,848


Great work!


Do you want to find the surface area now?


Yea


Is it ok if I erase the work?


Yea let me take a picture of it real quick


Okay you can now


Any ideas on how to start?


Do you find the area of each side and add them? I feel like I remember a little


Yes, we can start by finding the area of each side of the rectangular prism and do the same with the pyramid


Okay


Remember, we are using area not volume


Yes


Is the surface area of the rectangular prism 3,456?


How did you get that?


I multiplied 18x48 which is 864 then I multiplied that by 4


Ohh wait


I think you are forgetting about the bottom


I need to find the bases too


I’ll find that too now


You only need to find the area of one base because the pyramid is on the other one


Now I got 5,760


Yes, thats right


Now, lets find the SA of the pyramid.


Don’t you do the base x height and divide that by two?


Is it 4,704?


I did 1200 then divided that by two which is 600 then I multiplied that by 4 which is 2400 then I added that to 48x48 which is 4,704


You actually don't need to add that to 48x48 because it is not on the "surface" so it is not part of the surface area.


It would just be 2400


Ohh okay


Yes, so that is the surface area of the entire figure.


Okay


Sorry but I only have time for one more problem. Which one would you like to do?


Can we maybe do the rectangle one that is question 7?


Ok


We will need to use pythagorean theorem again for this problem


Do you any ideas on where to start?


not really


Lets try to find all the side lengths of this rectangle


Can you use the grid and pythagorean theorem to solve for side AB


Yea


I got 20?


I’m not sure if that’s right though for the side


Lets go through this together


It looks like you found c^2


if c^2=20, then what is c


Do you square root 20?


yes


Can you try finding CB?


Is it 4.47


Or do you just leave it like square root 20


We should keep that as square root of 20 because it is technically more precise.


Okay


I got the square root of 45


Yes, thats correct.


Do you multiply them now?


Yeah, now we have to multiply them.


You can just do 45x20 and put a square root over the answer.


It’s 30


Great, lets find the perimeter.


Do you add them now?


Should I do 20 + 45 +20 + 45 then square root it?


When adding square roots, whatever is inside the square root needs to be the same.


For example square root of 7 + square root of 3 can not be added together.


Oh okay


So how do we do this?


we need to simplify the square roots first


Do you know how to do this?


No


Since square root of 20 = square root of 5 x 2 x 2, we can take out the 2.


Why do you take out the two?


This is how we simplify square roots. Hopefully we can simplify square root of 45 to have the same root.


do you want to try simplifying square root of 45?


I’m a little confused


Yeah sorry this is a more confusing topic.


Let me explain it again.


Okay


When we have a number inside of a square root such as 20, we can break it up into its factors and take out numbers that have a pair.


20 = 5 x 2 x 2


Oh


Since 2 has a pair, we can take the 2 outside of the square root


If we were finding the square root of 4, 4 = 2 x 2, since 2 has a pair, we can take the 2 out of the square root.


We are basically just square rooting a certain part of the number and leaving the rest inside.


Can you try doing this with the square root of 45


I’m sorry I don’t know


Ok, lets do this together.


What are some factors of 45


Can we break up 15 even more?


Since 3 has a pair, we can take that out of the square root and leave the 5 inside.


So it would be 5 then the square root of 3


Oh wait


The opposite


Yeah


3 then the square root of 5


Now that we simplified the square roots, lets get back to the problem.


Okay


Now that the square root is the same, we can just add 2+2+3+3


If you put 10 root 5 into a calculator you should get 22.4


Ok, I need to go now


Yes


Great work today!


Thank you so much


hiiii


Hi!


How can I help you?


hallo!


I have a math midterm tomorrow


and my teacher posted the study guide for it


I was wondering if we could go through it together


Yeah of course lets do it!


Chloe


Its just these 5 questions correct?


in total there is 22 questions but there are sections and this is the first section


Oh okay cool


Alright so lets gets started then


Alex I am ready whenever you are


Sam so what do you think the answer to the first question is


Or are you unsure


i think I know it


since point a, d, and e are on the same line I think that would make it a collinear point


Yes!


Collinear means the points are on the same line.


So yes that would be correct


Okay lets go to the next one


What do you think this one is>


lemme look into it


Okay!


I'm not sure about this one because I think it could be a variety of different answers


Just give me a guess and then I'll explain the correct answer


well can I tell u all the answers I think it is and with the explanation?


Yea sure


I think the intersection of the plane is line BD


because the two planes share the points b and d so the line that goes through both of them is line BD which makes that their intersection


or it could be line DEF


So close! The answer is line segment BD because


BD isn't a line


because the intersection of the two is a line where they meet. the shape is a 3D shape and plane P is one of the flat surfaces. the plane with points A, B, and D is another flat surface. the line where they cross is the line through d, e, and f


ohh


Yeah


so my first answer is correct?


Well you said line but the answer is line segment


ah I see


that makes sense now


Alr I have to go now unfortunately!


Try with another tutor!


Hello How are you?


Hello!


I’m alright, how are you?


I am finr tnx


How can I help?


I’d just need help solving this problem, and graphing it. :)


OK I will read it Pls wait


OK after the relation, are those instructions how to actually enter the answer in the computer?


Yes I just need to graph it once I have an answer


OK


have u solved any othre inequalitieis?


I have, but this one confused me with its many variables


I see


Are you able to write on the whiteboard?


Yes


OK pls write the inequality as it si then we will work on it OK?


is*


good


Is there a minus beofre the 3d on the left?


ok


we will try to remeber tht


OK any idea what we shoudl do first?


Add the negative 1 to 11, and 15?


let me think


Or positive I suppose


do you mean add 1 to each "part?


OK that is good


but I htink I have a bette idea OK?


better


we might want to get d alone in the middle would that be good?


Yes that’s another way, so for that we would add the 3 to each variable?


do you add 3d to each?


Yes


yes that is good


can u do that ?


rember we have a minus at far left


Right so that means they would cancel out correct?


yes


so 4d in the middle and no d anywhere ea;ase


else*


do u agree


I agree


OK can u write that on the board?


Good but beofre the 15 I think you need <=   not <


I will write


See the "pink"?


Yes right sorry


OK


Now what about the 11 in the middle?


We subtract that on both sides


yes subtract 11 "everywhere"


pls do that


excellent


now how can we change 4d to d?


Last thing to do would be to divide everything by 4 correct?


yes


Now a comment


since 4 is positive that is fine


IF it were negative it would reverse the inequality DO u know that?


Yes


wait


it does not reverse


since 4 > 0


What do you mean?


I will write


my writing is ot so good but do you see what I mean?


Yes but shouldn’t the sign change since we have divided by a negative?


Yes but we divided all by 4 ad 4 is *not* meg


neg*


see what I wrote


My commenbt was correct but I htink it was confusing


Alright that makes sense


OK so I think we have the answer


Now can you grpah it?


Like that?


wait I will scroll


yes


and what kind of dots at each end  open or closed?


Closed


I agree


Did you see the cnfetti?


Yes!


Thank youuu


good


OK might you have a TI-84 cal;ciultor?


Unfortunately not


OK no problem


I think they can grpah inequal


But thii fine


you did vey well


very*


sorry I confsuded you about the sign


No problem you explained it very well!


Good thanks


Have a lovely day!


You too BYE BYE


Hi Liam


Hello could you help me understand inverse trig functions


like with derivatives and implicit differentiation


OK. Do you have a specific question or problem you'd like to work on?


I guess just understanding in general but let me pull one up


have you taken calculus?


Yes.


Okay, im in BC not AB but that was the only option


No problem.


The problem shows how to find the derivative of the "inverse tangent" function.


i know the derivative of the inverse tan and the inverses of trig functions and are familiar with that


okay


So you need help with "implicit differentiation" ?


no just this concept like why change sec squared y to Noah squared Tampa and how then did it transform to x


why does tan y =x


Let's start with sec^2(y) = tan^2(y)+1. It's a trigonometric identity. I can explain if you wish.


i am familar with the concept


i dont need help with that


So you need help with tan y = x?


i guess yes


like i understand when im looking at it but when im doing an actual problem im scared im going ot mess up


let me replace it with an actual problem


OK.


so finding the derivative


I think you mean something a bit different. I'll write.


Is this what you meant?


yes apolgies


is all i do is plug in x/2 into the derivative of inverse sin


Yes. You also need the chain rule.


I can show you if you wish.


i know the chain rule


is it purely just 1/ the square root of (x/2)^2-1) switch the 1 and x/2


It would be: 1/√(1-(x/2)^2)*(1/2).


adn the 1/2 is from the chain rule?


Correct.


okay i think i get that it seems simple enough


Awesome!


could i ask one more questions?


Sure.


You'll need to use implicit differentiation to solve this problem.


okay


would the first step be e to the y - e to the y^2 * 2y*dy/dx=1-3x^2


Yes. Then solve the equation for dy/dx = ?


You forget one thing.


*forgot


The first term would be (e^y)*dy/dx.


oh oh is it e*dy/dx - 2ye to the dy/dx


ah i see


and -2yeto the y^2 *dy/dx is because of the chain rule?


Yes.


I wrote above your uploaded page.


okay thanks!


so whenever you have e the power (in this case y ^2) will be what we are using for chain rule?


like it would be f of the deravitive of f(g(x))*g(x)


Yes. [f(g(x))]' = f'(g(x))*g'(x).


I'll write more details to explain.


thank you


but what woluld the derivative of f be


If you have e^u, for example, then d(e^u)/dx = e^u*du/dx.


That's because the derivative of e^x is itself e^x.


I think that's all i need help with


OK. We can end the session. Have a good evening.


you too thank you


hello! how can i help?


hi


i just want to learn the topic of double numberlines more


okay! can you give me a practice problem


yes


wait im not sure


i cant think of a problem


do you have like a problem


ok let me draw


this is in my workbook in math class


okay thank you!


yw


do you see it?


of course!


so i think the answer is 0.5


correct


:confetti:


lol


i think the next one is 1.5


yup!


okay


i just drew a problem out


can you find the tick mark values?


no


i need help


heres the formula


so final is 8


and start is 5 because that is what we are given


yes


how many spaces are between 5 and 8?


correct!


so can you simplify this fraction?


so what value would the blue question mark be?


ohh


oh wait


3 3/4


not quite


remember you have to add 3/4 to the left value


so what is the value left of the question mark?


5 3/4


correct!!


okay with that, can you finish the rest?


hmm wait


i think its actually 3/5


look


oh


sorry, its actually 3/5 so that means the blue question mark is 5 3/5


yes


its okay


ok done


good job :)


yay


ok i think i get it now


okay great!


would you like to learn something else?


Ben have a great evening


okayy


i am going to do my math hw now


ok byee


you have a good evening as well


Hello!


hello!


so ill give you a list of the topics on my upcoming test that i stuggle with and we can go over them


Sounds good :)


turning different forms of qudartic equations into others forms (ex, standard to intercept), factoring, taking the square root, completing the square, graphing different forms of quadratic equations, and solving quadrtic word problems


Ok:) lets start with the first one!


alright!


How do you think we would change this to intercept form?


could we factor it?


Yes!


How would we factor this?


we could do the X method, so 1 x -8


then the numbers that sum up to 7


so -1 and 8?


How would that look in the equation?


im not sre how to incorportaite it intot he equations


ohh ok


You just do (x+#)(x+#)!


okok


now what would we do?


because i can maage to get to this point but never to the full equation


That is it! It is in intercept form!


ohh oops i got confused with vertex form


And out x-intercepts here would be at 1 and -8!


ok well then how would we go form intercept to vertex and from standard  to vertex?


Lets start with standard.


First we get all of the x to one side


Do you understand how we got here?


yes


Then we complete the square!


but i thought you said you need the x to one side, why'd you take c?


all of the x's are not on the same side


and I am going to change a number in this equation to make it nicer to solve.


im confused, arent all the x's on the same side still? 8 was a constant so it doesnt have an x, right?


so now we just have x^2 and 4x the only x's


Yes! you do want all of the x's on the same side!


ohh ok


Do you know how to complete the square?


taknig half ot the b term, square it and add that to both side?


Yes!


so +16


Try again!


oh oop i was looking at 8


ok so +4


Then we can factor it!


ok so we have (x+2) becuase 2 is the b/2 right?


WE have the x+2 because it is what adds to 4 and multiplies to 4


ohh ok so if we use the X for the equation on the right those are the X's we'd get


but would my reasoning also work or no?


That is also a way to think of it!


ok so then to complete it to vertex form we would just subtract 12?


OKOK i get it now


If we were to graph this, what would the vertex be at?


(-2, -12)


ohh ok


Do you want another problem?


yess


Change it to standard form.


Excellent!!


yayyy


Want another one?


yes lets do like 2 more before we move onto the next topic


The good thing is, we are covering most of the topics right now!


Change this to vertex form!


Not quite!


oh i think i know where i went ewrong


The first thing we want to do for this one is make the x^2=1


We can factor the 2 out of the x


yess exactly


can i jjust divide the equation by 2 and like never see that  again?


or do i have to group it out wih the parenthesis


You have to group it out


ohh ok


Because then on the other side you would have y/2


oh yes youre right


What would we do from here?


(-4/2)^2 then add to both side


so +4


Yes!


But notice how we are adding it inside the parenthesis


so we can not just add 4 to the other side


We have to add 8


Because in this case, we are adding 8 to the overall equation!


oh ok


-10+8 so y-2= 2(x^2-4x+4)? what would we do with the side that has the parenthesis


We would factor it!


ok so y-2= 2(x-2)(x-2)


In then we can square that because it is the same thing twice!


so y-2= 2(x-2)^2


and we would just leave the y-2?


Then you add it back


Then that is vertex form!


ohh ok


What do you want to do now?


like as for topic wise or what i want to do within this changinf forms topic?


what would you like to do next? Do you want to stay on this topic or move on to a new one?


i think we can move onto a new one


Ok :)


What topic do you want to do?


could you give me some more quadratic equations to firgure out how to solve using either of the 3 methods? Unfortunately I'm not allowed to use the quadratic formula in class so its just completing the square, square rooting, and normal factoring


How about you try to solve this one?


im sort of stuck here teacher


We are trying to solve for x here


So out first step is to make it equal to 0


oh yes yes


The we can factor it!


Yes


What is the final answer?


x=+2 x=-6


Yes!


How about we do one more?


yes sure


After this one I have to go.


x= 4?


When you square root, you have to do the positive and negative number!


ohh yea


Hey you really helped me out today, thank you so much!


No Problem


I was wondering is there a way that I can like request you as my tutor further on?


There might be.


I am not sure how you do it, but I think there is a way to


I think it is something you can find after we end the session.


Oh ok, well thank you so much


have a good day!


you too!


hi


hi :)


how are you doing?


good and you?


good thanks. need some math help?


yeah


do you have a question you're working on?


I have like 20 questions but we could start with a little first


they are segment addition postulate


can you post the first one on the board?


ok


gimme a sec


ok im ready


done


ok, so line is HF and is G the point on it?


and GF = 1 ?


yeah i will put a screenshot


ok thanks that will help


do you see it


yes, thanks


so the whole line HF = 10. ok?


oki


and the little part GF = 1


so now you need to find the part HG


any guesses?


yes! exactly!


good job


wow that was actually easy\


yeah right?!


do you want to do another?


yea you can clear the board and i will get another screenshot


ok


done do you see it


so this time the whole length is 13


and the little part is 1


so what will ST = ?


you got it!


excellent


it has a fancy name but these are pretty simple


oh ok


so i will get a different one


ok, so now we have 3 segments


and they will all add up to the total of 26 ok?


oki


so first what is 9 + 11 ?


right! and the total is 26 so the KL will be ?


not quite, KL is the last little segment


it will be 26 - 20


oh


what is that?


yes! excellent


any more?


so KL is 6


yes


ok this one is a bit different


is it subtraction now


yes!


we are trying to find HI


what do we need to subtract?


not quite


look below the line HI


what is the distance GI ?


we have to subtract 3?


no, there is no 3


oh 2?


we have to subtract 2 from the distance GI ( 7)


that would be 10


no, subtract 2 from 7


oh


gimme a sec


ok


let me know when you're ready


ok hold on


ok im ready


ok, so what is 7 - 2 ?


yes! so that's you're answer


oh ok


want to do one more then I gotta go


are you still there?


I'm going to drop off now


keep up the good work!


Hello


hello could u help with this


Sure


Do you know what supplementary angles are?


3 and 4?


yes


3 and 4 are supplementary


3 and 2 are also supplementary


which means that angle 3 and 4 add up 180 degrees, and same with 3 and 2


is that all


2 and 1 are also supplementary


and 4 and 1 are supplementary


so their all equal?


3 and 1 are equal


and 2 and 4 are equal


what do I do after that


if angle 3 is 36 degrees and angle 3 and 2 add up 180


then what is angle 2 equal to


2 equals 144


do I do that for the others


just keep repeating


thank you


this is the work


yes


Hello!


you help my friend


he said you are a good teach


can u help


I'll try my best


can you please zoom in the pictures, they are a bit blurry for me to see the questions


I worked but it is wrong


ok


a bit more please


is this good


k


please give me a moment to analyze the question


is that what it says


ft/square root of 2


ft/s^2 right?


yeah


okay got it


that is the function for the height of the firework


now the axis of symmetry equation is y= -b/2a


and we can interpret it into the terms of t


like f(x) = ax^2+ bx + c


to find -b/2a


those are our a,b and c values


oh ok


so that means at 4 seconds, the fireworks reaches the highest point


so the first answer is 4?


so to find the value of the highest point the fireworks reach, we need to use the original equation and plug the value of t=4 in


oh


axis of symmetry is 4


the vertex is what we are finding now


k


do you want to try solving that equation?


it will be at the bottom of the board


no pls


my brain is cooked from all this work!


no problem


this is a lot of work, I don't blame you


so that will be our vertex


(4, 257)


does that make a little better to understand?


yes


that is great


do you have any other quesitons?


no


great


but do u know what I put on the last part


which one?


the max is 4


the height is 257


the maximum is 257


and that is after 4 sec


right?


we reach the highest peak at 4 seconds, which is the height 257


on the first part


it says 2 sec is the same height as blank sec


as it is after*


it will 6 seconds


oh


ok thank you


you the best


I wish u get payment


because u good at it


because the 4s will be the highest peak and 2s before peak is : 4-2 s and 2s after peak is 4+2 = 6s


Thank you for your compliment


bye


thank you for being a grateful student


hope you have a great day


gtg and do work


alright


thank u again


bye bye


Hello! How can I help?


Hi I was wondeirng if we could use ourmics for solving my study guide?


sure


Hi, can you hear me?


Yes, ma'am. Flu


Hi


So


Oh.


um, I'm not really understanding my, I'm in preche right now, but I didn't really understand this unit, um, I was hoping that we could go over my study guide together and like try to like maybe see if we can explain like how to do, like how to answer like the questions basically, if that's OK.


Of course


OK, this shouldn't be that hard. Don't worry about it.


Thank you


Of course. OK, so the first thing that you need to learn, at least when it comes to graphs is


what is given


What were the main characteristics of it. So, a graph, if it looks like it's just a line.


the equation corresponding to that graph has to have the power of one.


in the X


OK


OK? We're only doing 2 Ds, so on the X, the power should be just one.


Out of A, B, C, and D, how many graphs look like a line?


Um, like a straight line or like.


Yeah.


For the diagonal straight, just a line.


uh, A, B, and C


A, B, and C


If if you zoom in, there's there's like a little bit of a curve at the start for B, right?


Oh yeah, so just A and C.


Just ANC, yeah


So


ANC looked like lunch


Mhm.


Out of your options


does X have?


OK, you don't know, you, you know what an exponent is, right?


Yes


Yeah, so all of, all out of all of them.


there are only two options that have


X's where the highest power is one.


Could you tell me which one of those it is? A, B, C, and D


The ones that have exponents.


Yeah, the exponent for the X has to be one. Which one of those have one?


uh


A


The, OK, you said this one, right? Hold on one second.


So A is why equals x² + 5.


Mhm


What is the power on the X?


That's not one, is it


No


Yeah, it's OK. Don't worry about it. So, that we just keep looking for the other ones. Um, let's check, check the. So a square root is essentially just saying the power.


is 1/2.


So I can write this as X minus 5 to the power of 1/2.


So even though I can't really simplify this.


At X, the power of the X has to be one half.


OK?


OK


Yeah, the power of the X has to be one F.


Mm


This is not one either. I need it to be exactly one.


OK.


Um, let's do m-8X + 5.


What is a power over here


It's one. If you can't see it, it's one because we don't have to write the power one every time. It's like saying one of the power of one, instead of just saying one, you know it's stupid.


So


this one has a power of one.


Does D have a power one


Yeah


Yeah, perfect. So we have, we found the two lines basically.


Line, linear, power of one. Just remember that, straight off your head, OK?


OK. One more thing that you need to know.


There is this thing called domain and range.


Mhm


It would look like, hold on, and to say this is 0.


Let me go on real quick


This would look like this.


and this


stretching from negative infinity all the way to positive infinity.


It would look exactly like this


However


OK


if I draw, if I ask you to draw y equals X.


Do you know how that would look like


Um


cause you said if Y equals X it would go up, right?


Uh, it would look like what I draw, yeah, it was what I drew, sorry.


Mm


I don't know what why it calls negative X would look like.


It's OK


All negative X means it's going to be flipped over the x-axis, OK?


And X, this is Y.


If the X is being negative, I'm going to be flipping on the


X-axis. So, yeah.


I would actually just imagine this is a mirror, OK?


Mhm


You're flipping this down


So this would actually look like this.


it would go from the X to the Y, right?


Like


what do you mean the axilma


like instead of, you know, how it, like, the, the, sorry, just to remind myself, the why


is the


is it domain or is it range?


range


OK, so why it's range and X's domain. Like you, like for the


why it's going from the


R


like the line of the range, like


I don't know how to explain it, never mind.


It's OK. The range should be negative infinity to infinity.


And the said even the domain should be negative inf infinity. Essentially, what domain and ranges is, can I plug something to break math. That's all it is.


So if I have square root of -1.


Can you, OK, hold on


Um


what OK


I need you to tell me what is the value of X?


Can you solve for x real quick


You can solve it on the board if you want


Isn't it just one


OK? You, you got one by just what squaring one.


huh?


You, you, you, you got one by squaring both sides.


Well, isn't X like just automatically 1?


I'm, I'm, I don't, do you, do you, did you look at my equation around on top with -1 equals square x.


Uh-huh.


I'm asking you to solve for x.


I don't know how to do that.


OK


Uh, did you want to go through solving an equation?


without that?


Uh yeah


OK.


So, OK. If you have X + 1 equals 5.


How would you go through solving for X


I wrote it on the bottom if you can't see that.


Oh,


well, you wanna get it eggs by itself.


Yeah


So you would just do, since it's adding, you would just do minus.


1 and then minus 1 and then X


equals


5 minus 1, which is just 4.


All right, good. How would you do X² equals 4.


Um


well, you wanna get rid of this weird and since this one's multiplying, you would divide


by 4


I think


No.


No, wait, you would divide by X


right


No


no


shoot, uh.


Yeah, that's, we talked about square roots just now.


yeah


just think about it. Uh, what can I multiply by itself to give me 4?


one


1 times 1 is 4


Oh wait, no, 4 times 1


No, I said one something by itself.


02 x 2


OK, yeah. So if I do this, there's this thing called a square root.


Mhm


That should give me plus or minus 2. Just, just understand this. Negative times negative should give me a positive


So when they ask me for this, there's two solutions. It's 2 and 2.


OK.


OK


There is this thing called a square root.


The that which


Wait, sorry, I'm, the, there's some reason green is. I'll be right back, sorry.


Sorry, you were saying


I just wanted to, I just wanted you to know that there's, that there's thing, there's this thing called a square root, OK?


A square root and quite literally undoes a squared.


So if I ask you to solve for X, you need to be thinking of square root.


Still, I'm still surprised you haven't heard, you have heard of this, right?


I have, it's just, um, really bad at math, so I just forget everything that I learned.


It's OK.


OK. So let's just say


OK. If you have X² +


1 equals 9.


Hm.


Come on.


OK. Do you know what a functions


Yeah


Well, what's a function


Um


isn't it when you like


have like the graphs and stuff.


Sure, but OK, function is pretty much something where you can plug in a number


and you can get a result


OK?


Mhm


So in this case, for all your


questions, I can write a function instead of Y.


I can write F of X equals X² + 5.


To get back to your point


we're working with a graph, and X can be anything.


It can be 7, pi, E, anything and what you can be whatever you want.


The concept is you can plug in whatever you want, and it will give you a result. You're graphing the result on the vertical axis. OK?


When you grab that result on a vertical axis.


and when you graph the horizontal or whatever you're plugging in on the horizontal one. You will get a shape.


That shape is maybe a parabola or a line.


Thing is


if the X has a power of 1, ever if the highest power of a function is one. So if you have a lot of X's, you just look at them, the highest power is one.


then it has to look like a line.


OK


Has to look like a lot


So, out of your two options in your case, there's CND


One of the both of them have to be corresponding to the image A or C.


OK?


There's also this thing called reflections, a negative sign reflects something.


OK.


So in this case, if I said Y equals x.


Uh, let me just graph it real quick


Hm.


Sure


I said why equals x.


So give me a list of points.


OK, just, just tell me a random point for x and I'll, I'll write that down.


Um


OK, let's start with 5


Just keep giving me points


OK


um


All right.


Yeah, sure.


OK. So what, OK, what this means is, why?


equals X


So when X is 5, what, what, what, what would be the value of Y?


also 5


Good.


If XS 13, what would mine be?


25, so on


So, I'm gonna write down 5, I'll write down 13.


If this is 5, this has to be 5. This is 15, this has to be 15.


So this essentially


would make a perfect line.


Does that


answer


what a linear equation is. Does that answer what a line would look like and how you would find out what it would look like.


Uh yeah


OK, good.


Now


if I just told you


I don't wanna, I don't want to graph Y equals X. I want to graphy equals X.


Mhm


Well, exact same points, right? 5, it would become -5.


-13, 16, and so on.


At this point wouldn't be here anymore.


Let me just raise this, yeah


If you have 5


you would have -5. So this one would actually be


right here


right here, right here, right here.


This would be the one


See how it's flipped


Uh-huh


Does that make sense


Yes


What axis is it flipped over?


Um, the range


Um, I asked the access, can I either be X or Y? Don't tell me range.


Why


Flipped over the wine


No, I, I guess it kind of is, but, uh, in, in this case, it's actually flipped over YNX, so you're not wrong.


But what I was looking, what's that?


you said it's YNX?


In this case, it's Y and X It's an odd case, but


Y.


yeah, you're, you're not, you're not wrong. But what I was looking for is a text.


or why is it YNX?


OK, you see this line?


that I just drew on let me put it different.


Uh-huh


Do you see what I'm drawing there, right


Yeah


The blue line, you see it


Mentally flip it.


from the middle, flip it from this point.


Take this part


and put it this side. Just, just flip it.


Does it look like the back line


OK, now flip it upside down. What does it look like?


Oh, it's still the same


Yeah, it looks like the black line. And if you flip it


it looks at the black line, if you put it this way, this looks like, looks like the black line.


So I'm trying to say is


you don't need to remember this, but no, you did this part you do. If there's a negative on the X, it would flip on the X-axis.


This thing right here


OK?


Mhm


So, which, let me just zoom in on the graph.


Mm


Can't really OK


right


OK


All you need to know


is a regular g uh regular graph with Y equals x, and the X is positive. If there's no minus, OK?


It should look like this.


So what should a negative look like? It should look like this. I'm gonna make this.


Yeah, there we go


OK.


Based on that information.


what should this one be? What should C be?


We know it can either be A or C for this one.


Got be this one or this one.


It's


because they're both lines


C


Why is it C


cause it's going upwards.


What's the sound the X?


Oh, it's negative. So it's actually going the opposite way.


So, which, what is the answer?


A


So what you need to be thinking of is looking at the sign


is a negative? OK, then I know it has to be flipped.


There's only one answer where this has flipped.


It has to be it.


Another thing that you can do


there is this thing called Y intercept. Y intercept is if you take X to be 0.


whatever answer you get has to be along this line.


So if I take Y equals 8 x + 5.


OK.


If X was 0


what would Y be


If what sorry


If X was 0.


what would I be


Why, they use this equation plug it in.


You don't need me to write this down. If you, if you take X, just plug in 0.


What do you get


I don't understand.


OK, you see this X


Uh-huh


That X can be anything


Yes


If it was 0


what would the answer give you if 8 times 0 + 5. What would that equal?


It's because I don't have my calculator right now, so I'm gonna, sorry, I have


I'll need to calculator


It's 8 times 0


What is 0 times -1


So 00 + 5.


Did did you need a calculator? No, you trust yourself. Yeah, you got this.


If you don't, if you, if you, if you keep telling yourself that you don't, you need a calculator. I mean, you're never gonna get it. You gotta use it. You, you got, you have talent. You gotta use it.


What I mean is if you plug in zero, the entire term cancels. You should be able to do it. Come on.


If you have


they'll all get what answer do we get? We get 5, right?


Yeah


So we should get the point.


0.5, because when X is 0, my Y is 5.


OK.


OK


The, what would this, the, for number C, the graph looks like it's, it's touching the, it's touching this.


below the zero, right


So my Y value over here when it it is intersecting with


this axis has to be negative, correct?


Yes


So


can C be the answer?


We just figured out that the wine inter intercept is 0 and 5.


The 5 is positive.


On C


when the graph is intersecting with


the Y-axis, which is the vertical line.


It's set a negative value.


So then it's not


I mean, uh


yeah, it isn't, but I, I, I want you to understand why.


I don't, I don't want you, uh, I don't want you to just say no because the first answer was incorrect. Do you actually understand why?


Well, it's because it's flipped because it's negative.


I guess. Yeah, but I I I want to, I want you to use the Y intercept when what that means.


Mm


Over here, see this?


Yes


The line, the diagonal line is touching the vertical line.


at a point that is greater than 0.


in the 5 is a number greater than 0.


So it's, this one's gonna correspond to A because there is nothing in your graphs where a diagonal line is touching something more than 0.


where in this case it should be 5.


What would D be? Well, what's the graph for D?


What do you mean


But which one of these options is the


I'm sorry, I, I just really don't understand.


It's OK. Uh, I'm gonna be honest, I


I don't really know how to help.


It's not your fault. Like, I'm sorry, it's like


I genuinely don't understand, so.


Are you crying? I, I'm sorry. I, I just don't know how to help.


No, it's not your fault. I've been struggling with this classic for a long time.


Sorry, I didn't wanna cry. It's just they.


I know, but are you taking this class before?


No, right.


no


Are you taking algebra one


I took it, um


myself. I was a whole year.


um


behind in mass up until like this year, and I took algebra 2 online, but


I didn't like understand it very well either.


and then


OK. I'm gonna be honest right there, right?


Algebra one


algebra 2


geometry, are the most fundamental things that if you don't understand them,


I would honestly say take it again before you take this. This class is not easy.


I took it 2 years ago


I'College X right now. I took, I took it two years ago.


It's I mean, for, for me, I, I'm, I, I like math. It was fine for me, but


if you don't understandalgebra 2, it will only get worse.


OK.


You're gonna be taking derivatives of these functions. You're gonna be looking at the stuff that I don't even want to get into.


Trust me


Do you need, uh, I would say look integebra one.


You start looking at algebra 2


and taking it online is not gonna help.


Uh I, I'm sorry. I, these are some basic fundamental things that I would love to teach.


cause I, I do have a passion for teaching, but if you, if you're crying, it's


I, I don't wanna get into it.


No, it's OK


So I'm sorry. I hope you I hope you get better help than me.


No, it's OK. Don't worry. I have a tutoring session either way and like a little bit. I was just hoping to like, see if I can get some other help.


OK. Well, the only thing I can say is, when you look at the function, function is anything where you can plug in something and get a result.


In this case, you're plugging in a value for X to get a response and why.


So in this case


if it has the power of 2, it looks like a parabola, OK.


You have like, I do not.


OK. 2 means you. So in this case, A, because the power is too would be a parabola


C and D are both lines, so the power of one


has to be one of those lines, square root looks something like this. So the answer should be B.


OK


These basic things I really hope you look over with your tutor. I don't wanna just give answers out here either I wanna teach, so.


Mm


hopefully you get better


Thank you.


Thank you


Have a good day


You too


Hi, what do you need help with today?


Hey, I need help with polynomials, specifically factoring, long division, Horner's rule (synthetic division), remainder and factor theorems, zeros, and rational functions


Do you have any specific questions that you want to go over from class practice?


not really, i kinda just need a lot of help with all of it i have a makeup test on it tomorrow


Ok, I can create some problems to solve. Do you have audio so I can talk through the problems?


i do not


Ok, I can write out the problems and type the explanation


okay, thank you


I will solve this using synthetic division


First, you find the zero of x-2, which is 2. Then you take the coefficients of all the other terms in the equation and write them in this format. Does this look familiar to you?


yes


First, we brought the first coefficient down and did not do anything with it. Then, we multiplied it by 2. This is what would be added to the second coefficient.


Then, we bring down that value and multiply it by two and add it to the next coefficient. We keep repeating this process until the end. 7, the last number on the rectangle is the remainder.


The number before 7 would not have an x, and then the next number before that would have x, and the next number before that has x^2 and so on. The quotient should always be one degree lower than the dividend.


okay


Do you want to do another synthetic division problem or try to learn another concept?


try another problem


Do you want to try solving this on your own first?


You are doing it mostly right. The only mistake is that you have to bring the 4 down by itself. Then you start the series of multiplications


okay, can you show me?


ohh okay i get it


Do you know how to write the quotient and remainder?


not exactly, i think so but it's probably not right


You can try and then we can check


do i use variables or no


You use x in the quotient.


The first term of the quotient should be one degree lower than the divided. If the first term on the dividend is x^4, then the first term of the quotient will be x^3.


can you write it for me so i can see


Do you have any specific questions about the process of synthetic division?


not really


Do you want to do another synthetic division problem or learn another concept?


learn another concept


Which concept are you the most worried about for your test? We can cover that.


all of it but probably the theorems or rational functions


Ok, do you need to know how to graph rational functions for your test?


I can do an example showing graphing.


yes please, just in case


To find the vertical asymptote, we solve the bottom part of the function, in this case X-2. The vertical asymptote is at x=2.


For horizontal asymptotes, there are some special rules. I am going to write them out under the graph.


okay'


When the largest degree of both the numerator and the denominator is the same, you divide their coefficients to find the horizontal asymptote.


If the degree at the bottom of the rational function is greater than the top, the horizontal asymptote is always y=0.


In our original equation, both only has x. So we divide the coefficients, 1/1 to get a horizontal asymptote of y=1.


The next step, after figuring out the asymptotes is to find the x-intercept. To find this, we find the solution to the top of the equation. In X+3=0, X=-3. This is a point we plot on the graph.


Then we draw a graph approaching the asymptotes going through the x-intercept.


Then we draw a graph on the side opposite to it.


Do you have any questions, I know that was a lot of information


not really i think i just need to practice utt


it


Do you want to go over remainder theorem?


umm that's okay i have to go to dance and then i'll come back and start another session to finish the topics, but thank you I really appreciate it


Ok, it was great working with you. Good luck on your test.


thank you


hi StudentA


hi i need help i have a test tomorrow


on Saturday?


Precalc now pre calc


please help


you'studying, studying?


Precalculus cource


OK


the rules say I shouldn'tutor student, math class is OK, help students anyway, if I can


thank you so much


i need help on difference of quotient and verifying a inverse


wow, that's getting very close to calculus


it is?


yes. difference quotient is almost a derivative, and a derivative is most definitely calculus


let's see the problem


ok ill bring it up


I tutor all math subjects except calculus, and had to look up difference quotient


is there a calculus option on here?


there are 2, I think


but let's see if I can help you


ok


so its f(x)=-^2+5x


wait no sorry


this


do you know the formula for the difference quotient?


no


I'll put it on the board


can you guess what to do next?


wait its over that and not h?


the x's cancel and you get h


ohhhh ok


writing it this way shows that you are using x+h and x in both numerator and denominator


so, what next?


we should plug in the equation


yes, plug in x+h and plug in x on the top


go ahead


work on the board


good start


what do i do with the 5x


replace x with x+h again


let me make it smaller to give you more room


ok thanks


there


now the -fx)


-f(x)


do i expand the biononiaml


put the -f(x), first


huh where


numerator


f(x+h)-f(x), right?


now you need another set of parens


yeah, like that


and divide the whole thing by h


now expand the binomial and distribute the other terms


wait


oh, no, that's good


over h


keep going. you're doing great!


if i cancel the h on the -2h^2 will the 2 go away


oh wait its still h


so this?


you can either cancel all the h's inside the parens or the one outside. can't do both


the one outside would have been easier


wait im confused


wait, me too


where did that h come from?


i thought i had to factor out the h


like here


I see. canceling h inside the parens was from factoring, then the h outside the parens cancels with denominator


so we dont cancel from the denominator


you could have just divided every term inside parens by h while canceling the denominator


so the h is gone


almost


just the middle term


yea that one is staying


but is this right


Mr. Miller


let's talk about derivatives


i dont think derivatieves is on my test tomorrow i hope


hmm, a - sign seems to be missing


but i know inverses will be on it


huh what negative sign


ah, I see it


should have been x^2+2xh+h^2


like the answer?


which makes it -4xh and then -4x


I fixed it on the board


ohhhhhhhhh


i see it now


for derivative, you multiply the exponent 2 times the -2x to get -4x, and the derivative of 5x is 5


so the derivative of f(x) is -4x+5


looks a lot like your answer


all you really do for the derivative is let h go to 0


as it becomes a really tiny number, the answer becomes -4x+5


can we work on verifying inverses because im not good at that either


that's why I told you this is very close to calculus


let's do inverse now


ok


clear the board?


sure


uploading a problem?


yea


difference of quotient, or find, then verify inverse?


verify inverse


what's the inverse?


i dont know


can't verify the inverse if you don't know it


how do i solve for an inverse first


I can show you that


do i swap the varibles or something


are you sure it asks you to verify the inverse, but doesn't give you the inverse?


its asking me to find the inverse then verify it


like I said above


swap the x and y, then solve for y


ok


do i mutiply 6 both ways to cancel 6


yep


subtract 4 from both sides


what did i do wrong


ohhhhh


trying to get y to be all by itself


i was to solve for y


ohhhhhhhhh


i forgot


thank youuuuu


yayyyyyyyyyyyyyyyyyyyyyyyyy


so how do we verify it


you have to calculate both f(f^-1(x)) and f^-1(f(x))


make sure that both of them equal x


how we do that


which do you want to do first?


which one is commonly done first


doesn't matter


which one do you do first


then lets do that one


replace the x in (x+4)/6 with 6x-4


oh to see if they match or something


to see if it equals x


um i dont know where to start


6x-4, right?


ohhhhh


do i mutiply 6 to cancel the denomitor


just remove the parens, first


cancel


it does equal to x


now go the other way


so verifying the inverse is always equaling to x


plug in (x+4)/6 into the 6x-4 formula for the inverse


yes, always must equal x


i think i should distrubute or something


6 outside the parens is in the numerator, 6 inside is in the denominator, right?


um i think so


multiplying times 6 is the same as multiplying times 6/1


so numerator


huh?


im confused


if you write 6 as a fraction it is 6/1


oh so like make it a fraction


yeah


no


oh


it's easier than that


what can you do with 6 on the top, 6 on the bottom?


cancel


isn't that simpler?


wait thats it


so they are inverses and thats way moe simpler


verified!


perfect


indeed


you should be ready for tomorrow


Course credits


you should be able to do difference quotient and inverse problems


can we move on to domain and range of piece wise functions and drawing them too


hmmmm, OK


i dont have any practice problems on it


none at all?


let me look on google


Mr. Miller< or equal 1 & 3/7x+15/7,x>}


there's a grid


ill write it on there sorry


we start with the endpoints


part of it is missing


probably x>1 at the end


oh yea i forgot that part


first equation, what's the endpoint?


wait what endpoint


the function is defined to equal -8/7 x - 2, but only for values of x where x<=1


so, from x = - infinity all the way up to 1, but not past 1


the end is <=1


yeah, x=1 is the endpoint


not <=


what is the value of f(x) when x=1


just x=1 for the endpoint


endpoint is a single point


what is the value of f(x) when x=1?


there is no endpoint


what do you mean?


there is an endpoint at x=1


what is the value of f(x) there?


like slope


value of f(x)


plug in 1 for x


sure 1 there want any endpoint


there is an endpoint at x=1
what is the value of f(x) there?


value of f(x)
plug in 1 for x


f(x)=-8/7 x - 2, for x=1


this is all i have please point out the end point bc i dont see any endpoint


I'm telling you that because the first part of the function is defined for x<=1, there is an endpoint where x=1


but to find the whole point we need to know the y-coordinate, which is the value of f(x) when x=1


plug 1 into that equation and tell me f(x) for x=1


negative?


i dont know


just replace x with 1


like I just did on the board


ok


so the <= is a closed circle but we need th slope first right?


WE NEED THE POINT FIRST


AND WE DON'T YET KNOW Y


what point? i thought were just graphing it?


WHICH IS WHY I KEEP ASKING, OVER AND OVER


we need to graph a point on f(x)


its x-coordinate is 1


we can't graph the point until we find the y-coordinate


please just answer my question about the point)


im really lost


can you find another problem


for x<=1, isn't f(x) defined to be -8/7 x -2?


other problems will not be any easier


isn't that the definition of f(x) for any value of x that is <=1?


yes?


find -8/7 times 1 minus 2


i got -30/14


no


what is it


-3 1/7


please explain how


like I just did on the board


what other explanation is necessary?


where did you get -14/7


multiply that times 7/7


which doesn't change it because 7/7 is 1


oh


I just drew a purple dot at approximately (1, -3 1/7)


but isnt -2 the y intercept


yes


is my dot on the y-axis?


kinda of yes


my dot is at x=1


and I drew a closed circle because x<=1


yea


and I just added a small dot on the y-intercept


yea i see


y=-8/7 x -2 is a line that goes through those points


but we only draw it to the left of the big dot because that equation only applies to x<=1


oh becasue the x is from including 1 and up


1 and down


oh becasue its -8/7


I just graphed half of the function


the other half is for x>1


that will start with an open circle because of > instead of >=


and the open circle will be at some point where x=1


f(x) for x>1 is 3/7 x + 15/7


at 3/7?


we need to find that at x=1


x=1 is the endpoint again, but open circle instead of closed


how much is 3/7 times 1 plus 15/7 ?


both are wrong


which is 2 4/7, which is about 2.5


I drew and open circle at around (1,  2 4/7)


yea i see it


what is the y-intercept for this equation


yes, which is just barely above 2


but this one is only for x>1


huh


we need to find it for eerything else too?


you left out the x>1 part, remember?


first we found it for x<=1, then we found it for x>1


that covers everything


so now we have to find x>1


green line going to the right from the open circle at x=1


ok


we are done graphing


now we can find domain and range


domain


have we covered all possible real number values of x?


from -infinity to infinity?


the domain is from (-oo, 1] U (1, oo)


No


you don't need to break it up


x can be 1


there is no gap there


when do i do break it up?


when there is a gap


like x<=1 and x>2


then there is a gap between 1 and 2


ohhh so because both is on x=1 theres no need to break it up


right


range


what's the smallest value of y you see?


-3 1/7


yes


just looking at the left pointing line, can y have all possible values >=-3 1/7 ?


range is [-3 1/7, infinity]


oope


StudentA


oops


infinity)


done


do you understand it, now?


yes i do


great!


I've got to go, now.


ok bye


bye


Hello, how can I help you


I need help solving a math question


Whats the problem


A scale on a hiking map shows that 3 inches represents 1.25 miles, what number of inches on the map represent 10 actual miles


So 3in = 1.25 and ?in=10 miles


Correct?


Yes


Okay first we need to find out how many miles is in one inch


Do you know how to do that


Do we divide?


Correct!!


Which numbers though because we're given 3 different numbers


Maybe 3 and 1.25?


Exactly! So go ahead and divide 3/1.25


1.25/3 is what I meant!


Great, now we need to multiply that number by what?


Yup!


So it's 4.16


Perfect!


Is that all you needed?


Yep


Thank you !


No problem, enjoy your evening!


Hey there!


Hi ace


I need help with a math problem


Hey! What do you need help with?


Ok can you put a photo of it or type it in the chat?


Ioodie-133 has a half-life of 8 days how much is the original 40-gram sample would be left after 40 days


that the question


Hm, are you able to put a photo of it on the paper


ok


if you could flip it Idk how to do that


no worries, let me take a look


I know the method for it


Hi Leo


hi


so I was asked to solve for this using partial fractions


and im not sure if I'm doing it right


I'm checking your calculation...


Can you give me 2 minutes to solve, to see if your solution is correct?


We can start. Do you see what I boxed in blue color?


yes


This is one method of solution for partial fractions.


By assuming that x=-a, we quickly find the value of A, as I'll show on the board.


Then, we assume x = -b, and we get the value of B.


ohh ok


There are other methods, but what I'm showing works well.


ok


Anything else I can help you with?


not tat the moment no


thanks for the help:)


Hello


hi, I'm trying to do the problem on the board but it seems like no matter which way I try it i cant do it


the first one is labeled 1 with an explanation of why it didn't work the second one I started but also didn't finish because it didndt work


so what are u trying to do in the first one


are u trying to find the zeros or the vertex


in the first one I distribute the negative 1 before trying to complete the square


the vertex


ok so for complete the square ill show you how to do it and compare it with what you did


let’s find the zeros first because that is what complete the square is mainly used for, so we set it equal to zero


mainly, the negative sign is the part that causes the confusion so we can remove that by dividing both sides by -1


so now the left side becomes positive


so would this be the function in standard form then?


yes so this is the function in standard form