do you have to put a star in between the constants and xs


this symbol


to represent multiplication


I don't think so, bc they turned the equation that I entered into one with the star already


maybe x^2


I've never had to use those formats on any other question for this program.


I think that we have the correct answer its just a formatting issue


can you consult your actual math teacher before this is due?


He probably wouldn't answer my email since it's a Sunday and it's due tonight.


ok


I also asked a friend in this class and they can't figure it out either so maybe I'll just count my losses.


just wait a little bit longer


1 minute


I'm very sorry but I'm stumped hopefully worst comes to worst you can talk with your teacher about the formatting because the math itself is there


thank you so much for going through this and trying to help though!


of course have a nice night and goof luck


Howdy !


helloooo


So how's your math class going?


um


i failed my midterm and have a 56% in the class


Bummer !


I need a 70% to pass


yeah I struggle with math the most


Like everybody else. :-)


So it looks like you're doing integration by parts?


yes I am


Yeah, these can be messy.


Do you understand the basic idea?  That by "picking apart" what's in the integral that we can maybe solve it?


And by picking apart, I mean picking part of the integrand as u and the other part as dv.


yeah I believe so


So I just pasted a reminder of how this works.


Is there any particular one you wanna start on?


i want to work in order 1-11


Okay, so let's start with # 1 then.


So I write down the u and the dv first.


Then I calculate du and write that down.


Then I calculate V and write that down.


okay okay I see


You're probably wondering - how do I know what to pick as u and what to pick as dv ???


yeah I was just going to ask


The answer is - you don't really know.


But, as you work more of these problems you'll get a better feel for it.


And if you "pick wrong" you'll find yourself with a problem that is getting worse / not solvable.


So let's work this thru using the choices I made and then we'll work it again with the "wrong choices" - okay?


Alright, Sarah


So in this step, I just applied the formula from the upper right and substituted the values of u, v, and du.


Okay so far?


yes


So we can bring that 1/2 outside the integral.


does it matter if you dont bring it out or is it more of a preference thimg


More of a preference thing.


Mathematically, it works either way.


Luckily, we've already integrated e to the 2t (we did that at the beginning and maybe I glossed over it a bit?).


Make sense?


yeah but why does it matter if theyre the same or not'


like the part you circled


It just so happened (in this example) that we had already calculated that integral already.


But let me erase the red part.


So what is the integral of e to the 2t?


will all the examples have +C


The indefinite ones will (the ones without upper and lower limits on the integrand)


oh okay okay


The definite ones will result in a number of some sort.


So in the purple text, I quickly did the integral of e to the 2t.


yeah


It's really a "u substitution".


You're okay with that?


yes


Ready to go back and rework this with the "wrong choice" ?


is that like just an example


Just an example of how to do u substitutions?


Yep.


okay I was just making sure


Okey dokey.


Can I erase a bit and we redo this one?


yes ofc


Okay so far?


So by picking dv = t we make it worse because the integral of that is a t squared thingy.


The exponent on the t gets larger, and harder to handle, not smaller.


ohhhhh


So this just takes us back to where we started.


i see


So once you reach this point, you might think "hmmm, maybe I better re-select things and try again".


Okay so when I basically get to where I started, I should re-evaluate and pick a different U and DV


Yes.


Or you get a super-nasty looking integral and you want to avoid it.


I see


So just a heads up - I  have some food in the oven and the timer is going to beep here in a bit...


yeah no problem


Want to do # 2 then next?


yes please


So pi is a constant to let's multiply that out to make it a bit easier to deal with.


And we can put each term inside its own integral sign.


Okay so far?


so did you just put Pi infront of cos then sub it by the -x for the other


I just distributed out those terms (multiplied them out).


Usually, they are written in that order.


Did that make more sense?


Yes, David


So we don't need integration by parts to solve that first one.


We can just "do it and be done with it".


oh okay!!!


Not so bad, eh?


wait Im confused


which is this for


This is for that first integral (the one you don't need integration by parts).


oh ok ok i think I was just confused bc the PI moved


Yeah, sorry about that.


These things can get messy !


So I'm gonna replace that first integral with the sin(pi x) okay?


So I do have to move the pi


We did a simple u substitution like last time.


We let u = pi times x


So du = pi times dx


ok ok


so then cosUdu turns into integral sinudu


The integral of the cosine of u is just sine of u


Because the derivative of sine of u is just cosine of u.


The two process work backwards to each other (like multiplication and division).


so like


Get rid of that integral symbol


When you perform the integration of cosine, you just get plain old sine


so does the DU turn into +c


or it just goes away since the integral sign also left


The + c is something you clerically tack on to the end of an integral.


And the reason is - see purple text.


So I just wrote 3 quick y equals equations and then took the derivate of each of them.


And low and behold - they are all the same (meaning 2x) !!!


yeahhh


This, even though the original equations were a bit different.


So when you integrate, going from right to left on the page, you don't know if you started with a +3, or a +7, or a - 14 so you just write in c as a placeholder for some constant.


Hold on - be right back.


ohhh


So now back to problem # 2 ?


Then I gotta scoot...


yes please


So here, again because we want the exponent on x to get smaller and not larger, we choose u = x


Then du = dx


ok ok


And are you okay with how I get v from dv?


yes bc its the antiderivative right


Yep.


Okay so far?


where did the part with x 1/pi come from


So the first term in the integration by parts (see the thingy I posted) is  u times v


yeah


So I'm just multiplying those two terms I circled.


Then solving that last integral like we did the previous one.


Just doing algebra now.


The difficult part with these types of problems is that the algebra gets so soupy, that you lose track of how to solve the new and exciting calculus problem.


Soupy and a bit nasty but there it is !!!


I get it now


Good luck my friend !!!


thank youuuu


I must now attend to my roast.


Take care...


Bye, Michael


hello


how would i distribute k + 1 - 4(2k-9)


and hello


you use the distributive property with the parentheses.


first you multiply the 4 times 2k


-4 I mean.


Not quite.


it's -4 times -9


that's right


now you combine like terms


not quite


what is k -8k?


think of it as 1k -8k


what is 1 minus 8


-7k, yes


so -7k+37


right


Did you have another question?


no


OK, then have a good weekend.


hello!


hi! i was just needing some review for my re-take tomorow


i can add the image


alright


this was the multiple choice


I think that number one may have been misreading "concurrent" as "congruent"


which is what I thought at firt


first*


that would makes sense for me lol


I'm trying to figure out what its asking Liam


like concurrent means at the same time


thats what i was thinking too


so would it be always


I was leaning towards never


wait


oh wait ur right


I just googled it


me core


two Geometry 202% never


idk what i wsa thinking there


the sum of interior angles is always 180 is it not?


yes lol


lol I think your logic was based on exterior angles


i think that too


because technically speaking there is one shape that has exterior angles Math 101


i swear i can blame this on being out sick for 2 weeks


yes


2 weeks is valid


I had the flu


you good with number 3?


always?


right


I think its sometimes


ohhhh


I dont know if that incredibly skillful animation summed that up


ur good lol


but like you understand what I'm saying right


that's a visual for number 5


would it be never


there are actually cases


so sometimes


and by cases I think theres only one case


ohhh


I believe it is always


okay


I'm 90% sure but I think so


k


i have a diagram next


alright


hold up


lets take a gander


wait


this has me thinking


why is number 2 wrong?


thats what i thought when i looked over it


but he was just like


becuase it is wrong i cant take more points off if you correct me again


and i was like okay diva


#baddie


certified


I think its because it cant divide exactly


it can be even but odd or smthn?


idk Boston


i wish i did


whats the equation for interior angles


180(1) = triangle = 180


180(2) = square = 360


that makes sense


yes


but 180(n-2) = 1900 so n-2=10.56


so I guess its bc n has to be a whole number


i think


that makes sense ish


well anyways moving on


you're good with problem 2 i presume


yuh


angle 2 is-108 right?


ohhhhhhh


that makes sense now


you showed the work for it too


i was lost


bro


sos


just a lil lost in the sauce


ofc i was


isgt i loose my mimd


so 72*


yeah


angle 5


Chloe found angle 4


idk how


tbh


what do we know about angle 4 and 5?


they are the same?


not quite


idk


they have a special relationship


uh whut


oh linear pair


so what do we know about them?


they add up to 180?


or wait


nvm lost af


you know that <4 + <5 = 180


oh


so 180-135t


yeah


whats the t tho


idk typo lol


i cant spell


me neether


omg


i did it again


but i forgot how i found 4


doe what I circled ring a bell?


no


that do anything?


uhm


well sorta


but homegirl is lost


consider my timbers to be shivered


lol


so basicallu


we know that the pentagon is a regular pentagon


ye


so since we know one angle is 108


e know that all interior angles are equal


k


actually wait


theres an easier way to do that


how did you find it


no clue :)))


oh wait i do


remember that equation?


it on the paper


mb


so after taking a gander


how do you find angle 4?


that is a good question i have no idea


even though i did it


i looked at it and was lost in space


(n-2) * 180


how many sides does a regular octagon have?


ohhhhh


my dumb ahh


:p


k now i get it


or know whay i did


but for m<3 what do i do


so we know angle 2


and we know angle 5


and we know its a quadrilateral


so <2 + <3 + <5 + 117 = 360


so do i add - 117


like


we know what angle 2 is


and we know what angle 5 is


2 is 72 and 5 is 45


yup


so add that together


subtract that?


indeed


indubitably


<3 = 126 :D


okay big words


its ok


i get it nowwww


yippee


you're gon ace it tmr right


i have one last diagram and then i promis i am done


alright


lets take a gander


gander away :)


i think i jsut gave up on the problem


I would too


lol


so we know that the sum of interior angles is 720


you got that much


how idk tho


theres 6 sides


okay wait i see now


alr


so do i add all like terms


yeah


you can also take the (x+30) and stuff out of parenthesis


k


375 +25x


right?


i think


whered you get 25x


do i combine the x's


theyre all being added


the middle is?


huh


wait its 30


huhhhhhhh


i am lost


for the x's


what is x+x+x


wait homegirl is lost again bcs one is subtracting


x+x+x = 3x


oh-


embarasing


its ok


wait then the whole numbers go into the sum i added


*points and laughs*


lol


yes


i 405+3x=720


i think


indeed


ah ha


so 3x = ?


i got x = 105


i got that to :D


ayyyyyeeee


so you #slayed the day


i did bcs you served


legit would be lost without ur help lol


served you spaghetti to help when ur lost in the sauce


oh wait


you clocked that


:p


hi Ben


are you here?


hi


yes, my computer was loading


ive been absent these past couple of days so I need someone to teach this brand new material to me


even the first question is odd


one answer would be that each person's share would be 1/2, but that's not a number >=1, like it tells us


so we should think about the actual dollar amount, which is big


it might be f(x)=1/2


so, call the pot P. what would each person's share be?


in dollars, if P is in dollars.


just 1/2 of whatever the amount of money you recieved


which is P/2


oh, and the given interval might be for x


so should we follow what it says at the very top?


so it might be that f(1)=1


1 person gets the whole thing.


this makes sense now


if 3 people share, what is f(3)?


yeah so 1/2 like I said eralier?


yeah


so f(3)=1/3


and f(x)?


if x people share the pot, whatever x is, what share does each person get?


f(4)=1/4, f(5)=1/5, f(6)=1/6, .... f(x)= ?


yes!


for any value of x, the share per person is 1/x


we have the equation, now they ask for table and graph


and so on right?


the equation is f(x)=1/x


those would be table values


1 is 1/1=1


do they give you a table to fill in?


no/


but i kind of get the idea


like that?


so how would we graph that


I don't know how many rows to put in


plot points (1, 1), (2, 1/2), (3, 1/3), and so on


ooh ok


alright lets move on


#4, just answer what the share would be for x people  100,000  100,000,000


oh so the same thing


1/1,000 and 1/100,000,000


and 1/100,000 in the middle


those numbers are getting close to 0, right?


yes


yes, but not exactly 0


right


never quite gets to 0


but x can get as large as it wants, so you get as close to 0 as possible


#5 asks what happens to f(x) as x approaches infinity


it increases?


f(x) is 1/x


1 divided by an incredibly large number. way bigger than 1,000,000


1 with a million zeroes after it


what happens to y?


yeah


y is the same as f(x)


what happens to it as x goes to infinity?


it also goes to infinity


we already talked about 1/1,000,000 is getting awfully close to 0


as x gets bigger and bigger, doesn't f(x) just move closer and closer to 0?


ys


yes


like, divide 1 by 1 followed by a million zeroes. that would be like decimal point followed by a million zeroes, then 1.


so the answer to #5 is that f(x) --> 0


now #6-8


for these they switch x and y around


x is no longer number of people. it's the share. y is now the number of people


when x = 1/2, that's 2 people, so f(x)=2


x=1/3, that's 3 people, f(x)=3


so, again, whatever the argument x to f(x) is, we flip it upside down to get f(x), right?


so, again, f(x)=1/x


and this time, x is approaching 0, instead of approaching infinity


and can't ever get there, because we aren't allowed to do 1/0, right?


yeah


but divide 1 by an incredibly tiny number and you get an incredibly huge number


as x-->0, f(x)-->infinity


why


divide 1 by 1 point million zeroes 1, and you get 1 followed by a million zeroes


take a calculator, enter 1 divided by any tiny number, like .000000000000000000001


yes it gives me a huge number


is that all for this page


and as x gets closer and closer to 0, f(x) gets bigger and bigger


let me graph this for yu


*you


see how f(x) goes to infinity as x goes to 0, and it goes to 0 as x goes to infinity?


yes


now we're done with the page


lets do this page


does the right part of the graph look like what I drew?


the left part is the graph of 1/x for negative values of x. does that make sense to you?


kind of


x is negative. as it becomes a huge negative number, approaching negative infinity, then 1/x is negative, and approaching 0. just like the graph shows


and as x gets close to 0, 1/x becomes a huge negative number, just like the graph shows


sure


do you know the different transformations?


the upper right part of the image shows 4 of them: reflection over x-axis, stretch, translation left/right, translation up/down


which of those would give you figure 1 from the original?


reflection


yeah


so what would the equation for reflection look like if you started with f(x)=1/x?


yep


question 4 is much harder


we need a picture that matches the provided description


I'll draw you a grid. you try to graph the function


ok


there you go


start with the asymptotes


y=0, x=-3


use a different color for y=0


good


they gave you 3 points. graph those


there


I graphed the function in green


is our new function shifted up or down from the original?


(did the horizontal asymptote change?)


no?


no. both are y=0, right?


yes


how about shifting left or right?


no


oh wait yes


did the horizontal asymptote of x=0 change?


it has an asymptote at y=3


no, x=3


yeah, x=-3, instead of x=0


that's 3 units to the left


what does that do to the equation?


it shifts it left 3 units


how do you change the equation for a shift left of 3 units?


I circled it top right


x replaced by x+3


last thing to check is whether there is a stretch. to do that we check the 3 points


(-2, 1) before the shift left would have x coordinate 1, right?


what is f(1)) in the parent function?


remember, f(x)=1/x is the parent


right. and new function also has f'(1)=1. Seems like no stretch. let's check one last point. intercept (0, 1/3).


try working that one out for parent function


what value of x will you use before the shift left of 3?


I don't inderstand


the new function has point (0, 1/3)


what x-coordinate does that correspond to on the parent function before you move the whole thing 3 units to the left?


(just move that point back 3 units to the right)


so 3,1/3


yeah


again, y is the same


so, no stretch


transformed function is just 1/(x+3)


shift left is the only transformation


that's the parent


then shift 3 to the left


alright


do i move on


I can help with 1 more problem


so what are we doing for 5


what transformations do you see for 5?


i see a vretical asymptote at y=0


that's horizontal


so x-0


that would be the y-axis


is that where the vertical asymptote is?


yes


the dashed line?


ohh


i didnt see that omg im so sorry


so at like y=2


no, x=2


yeah


right


what transformation is that?


right by 2


what's the new function?


doesn't look like any other transformation


when does the numerator change


stretch


let's do 6. then I have to go


alright


any translation left/right, up/down?


no


correct


what is f(1)) for parent function?


and for transformed function?


just 2, right?


im confused, why would it be 2


point (1, 2)


but why couldn't it be any other point


used to be (1, 1)


it tells you that (1, 2) is a point on the transformed function


parent function had (1, 1)


oh so you're just comparing the points on the parent function to this one?


yeah!


we did the same before


ok


like when I asked you for the x if you shift it back 3 units to the right


here there is no shifting left/right, up/down


the only way to get f'(1)=2 is to multiply times 2


right


try it form (-1/2, -4)


*try it for


what was f(-1/2) in the parent function?


no


1/x. x=-1/2


yeah


flip upside down


so f(-1/2)=1/-1/2?


find reciprocal


of -1/2


f(-1/2)=-2. f'(-1/2)=-4


again, multiply times 2


what is the function for f' ?


start with parent function. multiply times 2


2 on top and bottom both takes you back to 1/x


2 times 1/x


wouldnt it be 2/2x


2/2 times 1/x is 2/2x=1/x


2 times 1/x is 2/1 times 1/x


multiply the tops, multiply the bottoms


oh so 2/x


#7 looks like shift left and shift down. I'm leaving now, but you should be able to figure out the details


ok bye


bye


Hello Sarah! I'm Mr. Davies, how are you today?


Hello?


I'm good. No, no, that's doesn't tell me anything. What's your status? How many you got done before you left?


Sorry that was my mom. Huh? Sorry, that was my mom. You say what?


Oh, OK


That's good, thanks for choosing Sarah, what could I help you with?


I'm about to upload it right now.


but uh


hold on


Alright


All right. All right now I'm about to go now


I,


uh


here we go


Yeah, you see.


Yeah, I see it


Yeah, I need help.


uh, with the second part of this question.


Alright one second let me take a look.


Give me just a few while I work it out Sarah.


OK


Sorry re upload the document for me, and idk if you can make it bigger


Okay Sarah, so for the first one.


Alright so as you can see, one thing you can do is put dots at each corner, and label them ABCD, that helps you keep track.


But you got to make sure ABCD corresponds so the top one's A has to be the same for the bottom


And so forth, and after you label them, write down each points, so do figure A first then figure B and write down each point.


Uh-huh


Hello


Yes Sarah


You said we should write down


the points


Yeah, write down each point for ABCD for both Figure A and B


Aren't they already up


They're plotted but in order to check you'll need a point to do the formulas on


Oh.


like


for figure A


or


Okay, that's point B, we can use that


Oh, I see what you mean


Now take point B on figure B


Uh, what


Should I write that down for you?


next to B


Yes put Figure A then B: (4,2)


All right. Uh


can, can you do that for me on the screen, they would actually have it better like.


wait, I, I never asked you, uh.


let's see, 4.


OK


Alright, what'd you get for figure B?


We'll figure


Right, that would be


OK. Well, I figured B.


point B is


Right


Alright now did your school give you a formula/formulas for rotation?


No


Ohhh, so how do you find rotations?


I feel like uh


it's cause uh here it says


what is the church for?


I'm gonna go back to it


It says one separation chase razor for figure C R D


I could tell that it's rotating.


I could tell it is. I just don't know like which which way is it clockwise 180 or car clockwise 90, you know.


That's the thing because I got a formula chart but I don't want to confuse you with something different than the way you learn it


I'll think it'd be easier for me to chart.


Alright let me see something really quick


And is the choice multiple choice or you can only choose one?


Uh, you could choose only one.


Alright so let me walk you through it


Okay so for the first one for question 1 it says to translate figure A to the left 4 units


So take Figure A's point which is (4,2) and subtract 4 to the left


Gotcha


All right, 4 to the left.


That means it'll be on


on


I believe


2, I mean, -3 and 2.


Let's talk about figure A on the first one, correct?


Yes


Yeah, well, if it score of 4 to the left, that would be beyond


Well, yeah, I think


maybe


Remember X is left and right, Y is up and down


oh no, it's 2.


Yeah, it's


-2 and 2.


I mean, that's what it is, at least from all points.


Nott all the wayy, so look


So B right is (4,2)


Our x is 4, our y is 2


So subtract 4 from 4


because you're moving to the left, so it's subtracting, anyhow you were moving to the right it would be addition


Alright so 0,2


Now compare that with point B on Figure B, does it match?


Gotcha


OK


Uh


I think it does.


Right


It doesnt


(0,2) on Figure A; (2,-6) on Figure B, doesn't match


So the first one is wrong


Alright, we can do the same for the second one, except it's down, so we subtract four from Y

(4,2)


(4,2)
  -4


I don't even think that


I'll take that a second is right either.


Nope, it's not


Oh Mrs. Smith said the ones I have it down to.


So now we have the reflects and rotates


Oh yes


So let me give you the formulas for reflect, write it down


Reflect over x-axis:

(x, -y) -> Y becomes negative

Reflect of y-axis:

(-x, y) -> X becomes negative


OK


Alright so let's try the third option


So we gotta reflect A over the x axis so apply the point (4,2) to the reflection rules


So then it would be


Over x axis, remember the formula


(x, -y)


All right. All right. So I meant say.


Oh


Yeaaa


So when we compare that to Figure B it doesn't match so that's out


Now do the same for over the y-axis


That's it, still doesn't match so now those two are out


Alright so now we only have the last 3,


Yes


So the rules for rotation I have right


OK.


the last to July.


you it


or


Rotation 90* clockwise

(y, -x)


I


they're.


all


and


Rotation 180* counterclockwise

(-x, -y)


Um


Alright, and did your teacher teach you subtract rotate add?


no


Okay, well basically to sum it up right,


First you subtract whatever point they give you from the original point you're using so in this case our point is (4,2), you would subtract the origin


Which we know is (0,0) so you don't gotta subtract anything because you'll get the same number


Yeah


So in this case we just rotate, so do (4,2) with 90* clockwise rule


(y, -x)


So


Remember to swap places with the numbers


So, like,


So 4 is X, 2 is Y


Yeaaa


uh


let's see, let's see


Right, and that doesn't match to (2, -6)


So that's out


And then the last one, 180* counterclockwise


Oh


What point did you get?


Well


this is the same point as last time, right? 42?


Yes


But, but this time we're the rotation, the, the


the counter clock rotation formula


And the rule is (-x, -y)


Sarah


So that means it would be


-4 -2.


Right, and that also doesn't match


So it's none of these


So there's no option outside of the last one


But I would question


if, if those two figures were congruent, and the exact same places.


what


were rotating be one of them.


So if they were the same size right it would probably be rotating


Oh, OK, I see.


I see


But seeing as how it got bigger, it's dialation and as you said it's not congruent


So the second part of the question


right


Yeah


So we could've easily pointed out that it's none of these, but just so you get the jist of it


I mean, it just by looking at the second question, I could tell that.


it's rotating because.


you know, it's definitely that reflecting and it's definitely not transity at all.


And their book grew it, so


I could tell it could, it could be rotating.


Let me take a look at it real quick


I


Right so we can tell this is congruent because it didn't grow in size, now we just gotta see which option it is


Can you tell me the points for A on both figure C and D?


OK


A would be


and 6 for figure C.


and I figured it would be


Okay, thank you


Okay so going through the options, if we go to the right 6, what do we get?


Um


Remember X is left and right (horizontal), Y is vertical (up and down)


Well


I went right 6 then.


point A would be on


I think


We're using figure C's A to see if it maps on to figure D, my bad for not letting it be known!


So the point we're using is (4,6)


and you add 6 to 4, since we're going right (positive)


Yes


Excuse me


Okay so it would be (10,6) correct/


Uh-huh


Alright, so that doesn't match to (-6,4)


Wait, so that means that.


So you know what, instead of me stressing you out right, we can clearly tell it's not gonna be translate and the reason why is because they're both going up


yeah


I already had that to rotate it.


And we're trying to get to (-6,4) so we can't be going up if we're tryna get negative


Yea so we can cancel those two, make it easierr


But yeah


Now reflections, do you still have the rule?


So over the x axis
(x, -y)

(4,6)


What would it be?


It would be 4-6.


So, doesn't work


Yeah


Does the second option work?


Uh, no.


Cause of the rule for that one, that one is uh


why


and X, correct?


And that would be


The rule for over the y-axis is (-x, y)


6 and 4.


When you said send it to me to text message


I was flipped


But OK


So x-axis is
(x, -y)

Y-axis is (-x, y)


The one your speaking of is rotations which is next


That one says who you see is rotating clockwise 180.


Right so we know its rotation but which one? So let me send you the rules


Clockwise 180*
(-x, -y)

Counterclockwise 90*
(-y, x)


Solve those two from (4,6)


What did you get?


Uh


-4, -6.


and


Correct


I have to go to the bathroom real quick. I'll be back.


Alrighty


You want some more food


huh


You want some more food.


I'm back


Alright broskii, so looking at the two we just did


Compare those to figure D's point A which is (-6, 4)


Which one works?


Um


let's see


I think it's the clockwise one.


Not quitee, look at them again


You said, (-4,-6), that was the clockwise


And (-6,4) was the counterclockwise


So that would mean the counterclockwise one is the one that works


Oh


You see it?


he


I'll try to look to see.


All right


I think I understand it


Uh, yeah, it says I got it right.


I wanna make sure bro! Whatever you don't understand let me know


The time for more questions.


Of course.


OK


Well


But just to make sure you get it, you sure you get it?


Uh, oops, I got kicked out. I need to get back into it. Hold on.


Uh, yes, I understand it


No problem, okay I'm gonna delete this so I can upload the formula chart so you can use


Give me one minute, let me go take a picture so I can upload it.


OK, I see I'm not a snipping and upload it.


Alrighty.


Shoot


Oh


you see it


Okay, I'm back, yes i see it


Okay, one moment let me look


Alright so let's go with part A, the ratios of ABC


Do you understand what to do for this?


Uh, I honestly don't understand this at all.


Alright so it says ABC and DEF are similar, not congruent but similar


Then it says we're trying to find the ratios of lengths of sides ABC


So for the first one AB/AC what tgey did is took the side lengths


Righrt which would be 6/10, you see that?


Side AB = 6
Side AC = 10


Yes, I see that


And they divided 6/10


Which you don't actually divide, just turn it into a fraction, 6 over 10


Let me simplify it


But they simplified so using the GCF which is two they simplied 6/10 to 3/5


Oh, I see


So you see it right


So the


the part that says AB over BC.


So AB, that's a 6.


and BC that's 12.


But if that was simplified, it would be, it's a 1/2.


correct


Sarah. that's it


And therefore, AC.


and therefore BC


is 12


uh, let me see if that can be simplified. I think it can't actually.


Yeah


hold on


Alright, so AC instead BC is 12, so.


1 divide by 2, that's 5, 12 divided by


So is it 5/6.


Yes


or


OK


You're right, good job


So about


this other part of Part A.


Alright so now for DEF and ABC, I believe it wants you to use both triangles but I may be wrong so for the last one

Blank/ EF can you tell me the options they have there


Uh


wait, EF or DE?


Just the last one, I want to heaer the options


Cause DE is the first one


So I understand what exactly they want


Um, OK. Well,


it says over EF the options are DE


DF and EF.


Okay, I get it


So lets work backwards this time, since they already give us the option for the last two


Repeat the options again


D E D F E F


Ok so for the last one, we see the answer is 5/6


Now we gotta fill in the letters so  work the three options they give you out, and then see what you get


How do you want me to work them out?


So you said the options are DE, DF and EF right


Yes


So take the side DE which is 9 over EF which is 18, and solve basically


for all 3


options^


Oh, right, I mean


Yeah, I do that, yeah.


lol


Uh, it's so quick


All right, let's see


DE


that's 9


you know


DF


that's 15


and EF that's 18. So,


if I try to see


uh


well just by looking at the first one we just wrote down.


I could tell that


the second option would be D DE over EF.


Well, wait, no, no, not that, no.


No, I'll do that's it though


No you're right


Um


Well


So the 1/2 one would be DE/EF


does that equal 1/2 or?


Oh, OK


Cause I was like thinking that, you know, 9 or 18 can be simplified to one half, you know, that, you know, so I was like, yeah.


Right, so you're right


OK


did not mean that um


So now we're left with 2


let's see


D


so DE


uh


yeah, all right


And obviously 18/18 doesn't give us 5/6


So something


something overeat after equals 5 or 6.


So


is that DF over


Yes, correct


over 18.


Yeah, DF, yeah.


So the last part


would be DF yeah.


So that means that the first one, that would be.


DE


over


EF again or?


Tell me the options for the first one


uh D E D F E F.


It would most likely be DE over DF, I doubt it'll be over EF again


Yeah


I think the same


way


oh you said DE DF, OK.


Also looking at the pattern from the 3 at the top, we see one is ab/ac and then the other two is over bc


And that will equal


So solve for DE/DF


hold up


what does DE say? DE that says died.


and DF that is 15. So now we fatigue.


I think that could be simplified to let's see.


3 or 5


Correct


OK


Mm


So what about part B now?


Okay so now read part B and let's try to work it out


Um, well, the first op says in each pair of proportions the lengths of side


s of ABC RSA ratio as the legs of the size of DEF.


This is coincidence


we would usually that expected from civil triangles.


um.


You will read out the whole, like all the options like.


it's a lot


Loll nah let me read it hold on


uh, have to be talking like.


Yeah


I was


bruising around his ribs, collarbone.


back of the.


head and his jawline


scans showed evidence of a


Okay so out of the top two which do you think is the answer?


Let's see


I think it might be mm


might be a.


I got around, did I


Right, so you're correct it's A, if you realize both the top 3 and bottom 3 give us the same answers which it's not supposed to because it's similar not congruent


so this is coincidence


You ain't get it wrong broo, you got it!!


Don't doubt yourself


Oh, OK


All right though. I will check it, I will check it real quick there. Let's see if I got this right.


All right.


Um.


No, I got it wrong.


I got Part B wrong


oo, that's interesting, did they give you the answer?


No, I get 3 more tries.


or 2 actually, I get one more try.


oh woww, my badd alright let me go back over


Alright Sarah, we were one off, it's the second one


Well, I was one off, my bad broskii! But it's the second one, go ahead and try it


Ah


yeah


All right, I like to see this there.


You're suck in your twenties


Sarah


Oh


Yeah, I, I, I, I was close. What you 30?


woahhh


I'm still a minor


Uh


wait, what?


I'm in 11th brobroo


You're a minor


Mr. Davies, what's?


I just feel like a adults like.


I had no idea. My fault, my fault, my fault.


You said you were there 11


Yea


I'm at 10th


You could. be doing this too bro,


Get you your community service hours


Oh, that's what you're doing this. I was like


and nah, bro, I.


Oh ****. But anyway, uh, it says I got, I got B right, so.


Good jobb, ightt what else you got


Alright, let's see


You don't even gotta do geo you could do 10th Grade math


right


actually


so great math


Mm, nah, I'm no tutor. Like,


I probably already forgot all of that.


But anyway, Cash like the next question.


Yea, go ahead


All right


How much time you got left


I don't even know, but just go ahead this will probably be the last one


All right.


A question, bro, you part of duo?


What you said?


Are you part of Duo


Duo?


Like, like, do, do you go to school in Orlando?


Oh noo, I'm in Texas, Dallas


Uh


you know, I'm in jazz, Los Angeles.


That's why it's so different because my geo last year we got formulas, it's weird ya'll don't have any


Yeah


Anyway, here's the last problem.


Let's see


that the same would last off.


with AB 3


Hold on.


You got this bro, attempt one


Yeah, Mr. Davies.


Damn


Start backwards this time since they give you BC/YZ


Man, I hope I don't get this right because if I do, I'll lose a point at like.


All right


BC or YZ, that is


6 over


what the, oh, OK


All right.


I simplify that.


I can simplify that.


Yeah.


So 6 divided by 6 obs one.


and then 24 divide by 6.


That's uh that's 4, right? Yes, it's 4.


So 1 of 4


Right


Uh


What are the options for the second one


this was his AC AC over sub equals 1 or 4. Let's see what AC equals.


uh


AC


equals 5. Yeah.


Uh, let's see


one of the options that says XY.


see, oh, I said, we like real quick or try to look at this.


All right


Let's try 5/12.


Uh, another type of be it. It's talking about 12 um.


let's see


5/20. Let's see.


I think it might be 5 or 20, so that means that would be AC over XZ.


You're right, good job Sarah


Now this last wood, AB


It's supposed to equal 1 for 4 again.


So we're seeing a pattern, so the last two have equaled 1/4


Yeah, all right.


Look you got it


So AB


that's 3


Oh, let's see, we got


cause that's AB


3 XYS 12. Let's do. All right, so if we do 3 divide by 3


that's going to be what the 12 divided by 3 that's gonna be.


Those are AB over XY


yep


All right


Now Part B, let's please not get this wrong and get it.


Still there


yeaa, im here im looking


Okay, it's the last one


All right, about to check


But he explained why you think you see.


Why it's not C?


What


like you said, you said a C, right?


Noo, it's D


There is no D


The last one


Yeah


The last one, there's 3. Wait, the bus trip or something.


lol


Oh, OK


Yeah, can you explain what you think is correct


and while you cross out the other options.


Go.


Alright let me start backwards, so the other two says they are not the same ratio which we know is wrong because all three equals 1/4


So those wouldn't be right, because there's a pattern which is 1/4


Uh-huh


I


was on a plane


the


last four digits in the number 5555.


That's right, call me back


And then its D over C, one because C is what was wrong the last time, but also because they are indeed corresponding sides and using SSS we can tell they are similar


He said he went to that tunnel and then to the next platform and came to the street above me.


Uh


so it's D


OK


Uh, I'm about to check the


Oh, please get this right, please get this right.


What's the


just happened


Make sure you click the right one!!


always


I see


I forgot to, yeah.


Yes, I got it right, I got it right, thank God, thank God.


Oh, thank you


All right


W, W, alright brodiee, keep it up, you got it in you, you just gotta have confidence


All right, ****. Well, that's, if that was the last word that I appreciate your help, so.


you know.


Yeah.


If if you gotta go, I understand. So, but I, I appreciate you. Thank you.


Of course, and if you come back, more than likely I'll be here to help you


Can I like save you as a tutor or.


Yea, i think at the end you can rate and save me and stuff


I will appreciate it. Thank you.


Alright brobroo, later, have a good night


Have a good night


or


wherever you are, your diet for the the times of the year, but yeah, yeah, I was like.


hi


How can I help?


I need help with my work


We can work together.


but there's a problem


Tutor Provider said my homework is innapropriate, so now I cant talk or screen share to show you my work


try part of the homework.


try posting one question at a time.


how?


maybe screen share one question


oh ok


umm


it doesn't let me


can you type or write on the board part of the question?


it doesn't let me do anything


are there any numbers that you can write ?


its word problems 😔


try copying one sentence at a time.


maybe I should just use chat gpt Jamie


ok


sorry


huh


ask for explanation.


I was js joking..


but I can if u want me too


I am here if you need help.


It says file deleted when I try it.


oop


it says file not found.  may be deleted.


maybe I could pay my teacher to give me A+ 😏


you could show your teacher what happens when you try to screenshare.


Ms. Davis definitely wont care


I wish you could share some of the question(s).


I want to help.


same


yay I did it


can u see the work


yes


i see the question.


each of the 3 choices have 25 1/2 and also $.80  or 80%.


see the 25 1/2 in each section.


which word problem(s) can be solved using the 25 1/2 x 0.80?


why did you choose that one?


bc it says 0.80


I see that.


what is 80% written as a decimal?


sorry my mom was telling me something


um


Is 0.8 and 0.80 the same number?


no, well I don't think so


they are the same number.


I don't think so


they are.


really


ok


so they are all correct?


I think they are.


I hope your right


it was wrong


ahhh


no I'm just joking


we can work on another.


oo this next problem is easy


7/20 as a decimal is obviously 0.35


I agree


this is the next one


I see the expression at the top.


there is a minus sign with Math 101.


that can help us find the right answer.


cool


is it 1 and 2


I agree with 2.


why not 1?


the loan balance could be considered a negative.


3 is definitely a plus answer.


so 1 and 2 ?


ur the teacher here not me


I am the coach working with you.


I'm just going with my gut


hopefully my gut is happy today


CONFUSING


I think we should count the minus signs.


negative signs?


when we have 2 negative numbers multiplied, is the answer positive or negative?


posotive


that would make the question at the top positive, right?


yes


are there any choices that have 2 negative numbers?


the third one, and last one


and 4th one


if there are 3 negative numbers multiplied, will the answer be positive or negative?


nvm not last one


good work


ty


those steps look good


well there's not an option that says nothing


where does the 4.9 come from?


idk


it should be 3.9


correct


we could change all of those into percentage.


why?


40% ?


Has Ben spent 50% or 75% of the gift card?


What percentage has he spent?


idrk


right about 95%


that leaves 5% still on the card.


how much is 5% in money on a gift card for $25?


how much is 10% of $25?


right


IF 10% is 2.50, what is 5%?


yes!


so $1.25 is left on Ben's gift card?


yes


the price of apples went down.


yes 😭


would the price difference be a positive or a negative answer?


negative I think


what is the price difference for 4.8 pounds if the price went down 30 cents?


idk


we would multiply 4.8 times .3.


ok


I got 1.44


not 4...


o


kk


We will need to find out how much flour is needed for each scone for all of the batches.


some of the scones are for one batch.


how much flour is needed to the blueberry scones?  there are 2 batches.


2 1/4


that is for one batch.


4 2/4


we will multiply 2 1/4 times 2


right


now the chocolate chip batches


5 1/4?


great work!


when u put 2 2/4 did u mean 4 2/4?


sorry, I wrote it wrong.


would it be 13 3/4 (or 13.75)?


that is the correct number of cups of flour.


ok


we need to see if that is 45 ounces.


bruh


I forgot about dat


is Geometry 101 fluid ounces?


not fluid ounces, that would be for water or milk.


if one cup weights 4.25 ounces, how many ounces would 13.75 weight?


we are asked for a good estimate.


66 ounces?


14 cups (estimate) times 4 ounces would be 66?


my bad 60


Chris's estimate is not good, right?


too low


oh no


I'm cooked


what happened?


my assignment is due at 8:00....


you have answered quite a few.


but I'm only at 60%


I have to get to 80%


we can get maybe 2 more.


we can try I guess


how do I do dis one


work on the parentheses first.


too late...


do you want to finish this one?


sure..


hello?


yes


wait I want to ask the chat bot thingy  aquestion


kk


wait my mom is calling me


k


back


can you see what I wrote on the board?


what would be the next step?


add the two numbers'


-2 3/4


one is positive.  one is negative.


that means subtract.


um ok


we can't do 1//4 subtract 2/4.


have you been borrowing from the whole number?


some change the 2 1/4 into a improper fraction.


1 3/4


right


that's the answer?


yes


ok


do u think we can do one last one


sure


how much is the bike and the helmet?


idk


let's check that adding.


k


I thought that 3 was a zero at first


David has saved 2/5 of that.


he needs to save 3/5 of the cost.


how much is that?


see how I moved the 5 to be under Algebra 300.70


we can do division before multiplying.


why


the numbers get large if we do the multiplying first.


are you allowed to use a calculator?


some say no.


I don't think she cares


she lets us in class


you could change 3/5 to a decimal.


and then multiply 305.70 by  the decimal.


kk


I don't just have a calculator though


that would Calculus 405.42.


ok


David needs that much more.


how many hours will he have to work to earn that much ?


um


he earns 10.19 an hour.


183.42 divided by 10.19


18 hours


i don't wanna do math


so I just guess


It is a necessary subject for school.


sadly


it is bad and boring and hard


Please sign on again for more help.


wow


you have been working almost 2 hours.


try a few minutes each day.


please lets finish this problem


i thought we did.


we did?


how many hours does David need to work?


idk


I said I guessed


so I'm probably wrong


your guess for 18 is correct.


oh


were you using chatgpt ?


but idk how much he needs to save


no chat gpt doesn't work rn for me


sadly


bc 10 x 18 Physics 102


how much does he need to save


183.42 divided by 10.19


I don't have calculator


3/5 of the cost Economics 200.42.


that's how much he needs to save.


oh ok


Statistics 310.42 divided by 10.19 is the number of hours he needs to work.


yay


I got to 80


ty


you're welcome.


we want to work with you.


wait, who is we?


we, the coaches here at Sarah.


oh


phew


We are here to help.


We will explain and give examples.


Jessica once again, but I need to go eat now


bye


kk


Howdy !


how do i distribute 8x-6(3-2x)


Let me write that on the board.


follow up question


would i leave pu the 8x and put it in thr equation that it will turn out to


Did that make sense?


thank you


this helped me with variables


Anything else?


no


Okay, have a great day then.


hi


Howdy there !


So what's going on in your math class these days?


So what does it say when you click on the hyerlink for "one-to-one" ???


Still there?


yes


So what does the hyperlink say then?


A function is one-to-one if no two different inputs into the function give the same output. In other words, a function f with domain A is called a one-to-one function if.


Yep.


I was curious to see how they phrased it.


So all these functions shown are 1 to 1.


that was wrong when I checked


Oops - I've got this backwards.


In their definition, you can't have two different x values give you the same y value.


So it's the "horizontal line test".


Try that. :-)


Did that work?


no


Bummer.


I'm not sure why they are saying that it's wrong.


I have some more problems like this


Maybe 3 is also not a one to one?


It's hard to tell if those two dots are at the same level or ont.


Yeah, let's try another one.


ok


Okay, so let's take these a bit slower.


One is NOT.


Two is.


Three might be - see the question I wrote there?


yes they are the same height


So then it's not.


Is this making sense?


yes


Cool beans - that's the important part.


Let me know what the computer says here (I'm assuming that you're typing this stuff in "live" so to say).


it was right


Got more stuff to go thru?


Okay, so do you know how to do these now?


Still there?


that was correct


I got time for a couple more...


ok


We are CRUSHING IT !!!


Posting another one, or are we all done for now?


I'm trying to post the image but it will not let me


You're not the only one - others have had the same issue.


Not sure what's going on...


Okay, so I gotta run.


Best of luck to you and sorry for getting started on the wrong foot.


Take care...


hello


Hi


i need help with understandinv


understanding what?


doing linear equations


can you show me an example?


2(4y−4)=
32


first thing you do in this case, you open brackets, can you do that?


what does that mean


x(a+b) = a*x + b*x


i still dont understand


You need to get rid of brackets () we have to ways to do that. First way we can multiply number before brackets on everything that inside of brackets. Or you can divide both sides of equation by 2, it will work either


okay so


Can you do that?


maybe


ill try


i did it


do u mean distributive property


Okay, I will show you


Yes, distributive proeprty


okay im doing it


cool, you did it


yes


Now you need to put all numbers with y coefficient in one side and numbers without y coefficient in another side


okay, can you type it in chat?


just three


and wait no\


but isnt 24 divided by -8 -3


why is it 24?


its 24 because i subtracted


you need to add


why is 8y being isolated


because you need isolate all y numbers


oh ok


cN i try the problem


y = -3


no


can u explain


do you need more explanations?


I wrote on the board


do you have questions?


Are you here?


no im fine thsnks


okay, bye


bye


Hey how's it going


how may I help you?


With that please


Alright


I have a question for you


Yes


could you understand how to do the first part


No I can


Cant


that is totally fine


we can walk through it together


Thank you


so the table, it shows the different x values and y values


in some places they filled the x-values and left the y-values are blank


and you have to fine x or y by plugging in the values in the table


Ohhhhhh


you understood?


would you be able to do the very first question?


I can try


sure


and once you are done, I could check it


Is it 27


yes


you got it


great job!!


Can u show me the second one I’m a little confused


alright


the second one gives the f(x) value, instead of the x-value


you can do a similar thing for what you did to solve the first one, except you plug in the value for f(x) instead of x


and then solve for x


Can u show me an example


you could see the whiteboard


I solved the problem


I plugged in 11 for f(x)


are you able to follow?


Yes Imma try


great


Hello Liam


Hello, how are you?


Good, what about you?


I'm doing well.


what exactly do you need help with here?


I'm just going over a review guide for my exam


sounds good


is this test on all the conics?


Yes


alright


I did circles, now I'm on parabolas


Is this correct?


Also I did this question before that's why I did it so quickly. I realized while I was doing it.


I'm not a genius lol


i see


let me check your work real quick


ok


yep looks good


Nice


it seems like you know what you are doing here so did you have any specific questions or areas where you have issues in this or with circles?


Not exactly.


I was just trying to go over it


And see if I had any issues


Is that allowed or no


What I would reccomend is to go through the guide you have and see what you are good with and if you run into any issues, come back for a session. If it's just you doing the work and me checking, you technically don't really need me for that


you get what i'm saying?


Yeah


I can give you some additional sourcee for extra practice thought if you'd like


Sure


Okay so for supplemental videos, I'would recommend and Mario Math. Mario Math is by far the best Precalc tutor on youtube in my opinion because his teaching is excellent and concise. For practice, Kuta Software makes decent worksheets you can do. You can also potentially look in the Stewart Calculus online textbook, as it has a very detailed page on Professor Smith with practice too.


Here's what I reccommend you do. Go through your study guide, additional practice, etc and note what is giving you trouble. Once you have that, come back Liam and we can work it out together.


wait so for Mario Math what do i search


wait i think i foudn a playlist


Liam


yep that's the one


wait so for the Stewart Calculus online textbook,


I like Mario Math because he is super clear, concise, and comprehensible


what am i supposed to be looking for?


i can paste the link here


ok


Oh wow


Thank you very much


no problem


Okay I foudn the resources


found*


I'm going to go over it now


perfecr


Thank you for the help


do you think the reccommendation I gave you is a good idea?


yes


alright sounds good


queue up for another session once you have that list


k


bye


hi


Hi


What would you like help in?


Um math duh


I meant what topic


lol


and please paste the question in the whiteboard


okayyy


gimme me like 1 minute


sure


The rectangle on the right is a scaled copy of the rectangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.


This?


ok, but i need the side lengths...or ideally the picure


*picture


can you paste that in the whiteboard


no


it don't work


alr, does the question give you the side lengths


small ones upper legnhth is 8


there.


perfect, thank you


now


if a rectangle is scaled uniformly(meaning that all sides are properly scaled) then the new side can be written as original side*scale factor


basically that means that i increase each side by some amount(multiply by a number)


the scale factor is nothing but the ratio between the sides of the rectangle


are you ai or something like you type so fast


yeah you can take ur time to read through it and then ask any questions


if you want me to explain again then i can do that too...a bit slower as well


Aight


would you like me to explain again?


Sure! I do not get it


ok so when we scale a rectangle, it means multiplying each side with some number


Okay i understandd now


the number we multiply is called the scale factor


the scale factor is 2?


perfect!


Alrr ty


any other questions?


Yes gimme a min


yup


The radius of a circle is 1.1 cm. Find the circumference to the nearest tenth. This?


so the circumference is defined as 2(pi)r


now would you like me to walk you through the calculations?


Yes


so first we'll do 3.14*1.1


any doubts here?


in the first calculation


No but just so you know ik what multiplication is


yea, i just wanted to go step by step


Okayy


if you want to try out the last step then you can go for that too


Nahh i got it down


Are you a real person? I thought your ai


no im a real person😂


anyways


so now that we hve 6.908


Oh sry


to round to the nearest tenth


that gives us 6.9


the units would be cm^2


any questions?


next question?


ek mint


shoot i mean 1 min sryy


im not used to english that much


what language is that though?


Hindi


ohk


Here is next prob?


oh sorry, i didnt see


all good


anyways, do we have to find the perimeter again?


Actually


What language do u speak


this is your answer


Okay


can you see the calculations on the whiteboard?


no


oh, 1 sec


you should be able to see it now


it looks smudged but it works


if you need me to re write it i can do that


nah its fine


sorry about that, im drawing with a mouse so handwriting comes out a bit tricky


its fine.


what language do you speak


idk why im so curious


Priya comfortable hai to wo Amit


um no thx im fine with english


i gtg


ok sure, i hope i helped


ya


bye, have a good day]


you too


Hello Alex!


How may I help you?


Can you help me with this problem?


None of the tutors have been able to help me.


No Problem!


Give me a moment to analyze this.


No, I just appreciate it. Thanks a lot.


What am i supposed to look at


there are like ten images


I do not see the image


Okay


Right so


Do you know what vertical angles are?


Aren't they like when vertical angles intersect.


OK


Can you hear me right


Yeah


OK, so


this question is asking for angle DGB.


Mhm.


Is this one I marked right here with Alex


Mm.


Mhm


So what you have to know is you have to know a few properties. You can go by solving for this angle first.


and then soft rags, or you can go by solving for this angle.


and then sol res


So let's do the way that makes sense.


and


um


so


vertical angles, yeah, look.


vertical angles


it means that when they are caught by a trans wrestle.


these ones are congruent.


OK


So this one, if this is 86 and it's caught by this transversal and this transversal.


This one would


They're just two lines that intersect.


yeah, yeah, and then this one would also be 86 cause it's vertical to this angle right here.


Oh, OK, OK


to 86, so they would be congruent.


OK.


right? So, do you know what supplementary angle is.


Um


hold on.


If, if not, I'll just explain it


kind of.


OK, so you see this, hold on, let me use a different color.


Do you see this uh red line that goes across like the black line, but I just marked it in red.


aren't they just the sum that adds up 180.


Yeah


straight lines have a degree 180.


So if we know that this one is 86. The first one is 86


plus, and then this one is 62, right?


62, and then


um this part of the line is done.


and then you need to find this part.


that that's X and then that should equal 180.


So this whole line is 180. We know this part right here.


you know this part, and we have to find this part, which is Alex


And if you add all of these up, it's supposed to equal 180, so


um, you're supposed to solve, you're supposed to set up this equation.


and


solvera. Do you know how to do that or?


no


Not really. See, this is all new to me.


OK, so


+ 62.


is going to be


plus X equals 180.


Mhm


and then


you're going to subtract 148 from both sides.


and you're gonna be left with 32.


Mhm.


So essentially


your answer is 32, but you have to show like the different steps that


um


that leads up to like your answer, you know.


OK. So for


for the fill in the blank


um type in for the M angle.


type in DG


F


Yeah, type in DGF.


And then BGC


No, no, no


you see where it says M angle and then you typed in DGF in the first month, right?


Yeah, yeah, yeah, yeah


For the second box next to it, type in 86.


cause it's it was congruence'86.


Oh, OK.


And then for the reason, for the reason, type in or select the one that says vertical angles are congruent.


If there is an option like that.


Oh yeah, you posted it on the bottom.


Yeah, it's the first one, vertical angles.


Uh-huh


and then


um, you're gonna, you're on DeltaMath, right?


Yeah, yeah


OK, so you're, it's gonna give you another line after you filled that out. Now this is gonna be your actual proof.


You're gonna type in


Wait, wait. It said it's um hold on. It says BGD does not have a vertical angle, but the measure that vertical angle is not yet known.


wait


can you screenshot it


Of course


Give me one sec. I am not.


No problem.


Is this like


um 10th year.


geometry, 10th year


Between 9th and 11th.


Oh, OK, OK


It doesn't really say anything on my screen.


It says, oh, yeah, it wouldn't be 80, it would be 86.


Oops, that's my bad.


It's fine, it's fine


OK, it would be 86.


Yeah, it's still doesn't like that.


Oh, it's cause you're a Bostonian.


D


It's supposed to be


Angle DGF


Oh my gosh


So type in DGF in the first box, and then the second box.


OK, it's right, it's right, it's right.


OK, OK


That was my


So


it's OK, it's OK


For the next line, you're gonna type in DGB in the first box.


I was giving you this 3 step.


Oh yeah, 3rd step, whatever.


86 was 62.


Yeah, for the first box, type in DGB.


DG


B


Yeah, DGB


DGB


yeah


and DGF.


No, no, no. Give me a sec


No, no, why, why do I keep saying that? Oopsies.


OK, 86 was 62.


minus 148.


OK, did you type in DGB in the first box.


Yeah


in the next box, type in 32.


equal 32


Oh, I see


And then for the reason,


Did you just like subtract it.


uh yeah, you basically saw solve for that angle, so.


it's so.


smarter than me, man.


And then um


for the


for the reason


Is it


give me a second here, it's vertically.


do you want me to screenshot the reasons.


I think I have them on my side.


The first one is vertical angles, linear pair, right? Is it those ones?


Linear


No, no, no


Yeah, linear


Yeah, just tell me the order that it's in on your screen.


of course.


Vertical angles, linear pair of or triple kangar angles, some of angle in a triangle, some of angles and quadra.


OK, OK. Um


face


you, you're gonna want to choose linear pair.


OK


and then that should be your answer


Oh my goodness, perfect. Oh my gosh, thanks.


Mhm


You're welcome. Are there any questions or are there any other questions?


OK.


Yeah, of course, yeah, absolutely.


Uh, yeah. I mean, as long as you can help me if you have time. I totally get it if you don't have time.


No, no, I have time, Dory


Thanks.


Let me just delete this one


Here's a different one


is your teacher like horrible in the subject or?


I mean, like, what happened, he gave me this. But like did not explain it as like, well,


and then he kind of like got frustrated at me cause I don't


I didn't really get it.


OK, OK.


it's fine.


he wasn't that good.


It's fine, it's fine


Um


so it's asking for angle B


if you do this, this would.


this would be corresponding.


OK


so


um


Corresponding


no, no, no, give me a second


Let me analyze it


OK, so


that is 1:45, this one will be 35.


Uh.


um type in BCA


Did you type it in?


Yeah


And then for the second box type 35.


Yup


and the the reason will be vertical angles.


Did you do it


Uh, what did you say? Sorry, I was typing that.


Uh, vertical angles


OK


All right, and then


Did it work


yeah


OK. Um


Hold on, let me show you the four step.


OK.


Um


OK, so


you got that out of the way


Wait, can you show me like the one without the


Oh yeah, sorry, my bad.


it's fine, it's fine


Wait, that's not the right one. Ignore that. Wait, ignore that.


Uh, not technical.


Uh


It's fine, it's fine. I, I think this should work.


That's not the right one.


Oh.


It's fine. I, I, I can work, I can work off of this.


There's not really a difference


next one would be 35.


give me a second here


triangle and isosceles.


base of


uh


OK


corresponding angles


same side interior.


addition angle subtraction postulate.


OK, for the next one, type in um


angles CAB.


I


is equal to


and


the answer or the reason is


um


uh subtraction postulate.


Try that and let me know if it works.


Angle subtraction posture is.


OK, I see it. Sorry.


yeah.


CAB 35.


angle subtraction postulate


It. I didn't work.


It didn't work


It says CAB is different of any two angles.


Um, try


wait, give me a second


No, you're good


Oh wait


I forgot


Um


you have to type in DEC.


DEC


DEC equals 35.


OK


Um, and the reason is linear pair.


That worked


OK.


So now you can say angle CAB.


For the 5th 1


Yeah, yeah, CAB equals 35.


fine


Yeah, and


And then that is


the reason is alternate interior angles.


And then


Did that work


Yeah


104 + 35. OK, we need


180 minus


41. OK


So now you're gonna want to type in


um angle B


is


equals


OK


and uh


the reason is


um


OK.


let me find it here. Some of, wait, no, no, no, no, no.


Some of angles in a triangle.


It's like the 4th 1, I believe


It's like a 4th 1 I believe


Hello?


Some of Ingles


Um


it's some of Angles in a triangle, yes.


some of Angle's in the triangles.


It's the 4th 1


I think.


OK, I see it


Yeah, yeah, yeah


It


fit


that's your answer, right? It worked


Yeah, yeah, we're good. We're


OK, OK


And then


another one


on


Just for the time being, I might have to leave after this one, so.


No, you're good. I appreciate you so much.


of course, of course


You're good


OK, so


says angle AB is congruent angle BD.


This means that this is gonna be 25.


and then it says angle A is 25. It says findingle C.


Oh, and then it says that's comprehensive.


we see


OK, so for the first one, you're gonna want to write BDA.


Um


BDA


um


give me a second here


BDA is equal to 25.


equal to 25.


and


Oh


the reason is based of an isosceles triangle.


All done.


And then step 3.


That worked right


Yeah, yes, yes.


OK, so


for step 3, you're gonna want to write A, B, D


A B D equals 130.


Mhm


and the reason, the reason is some of angles in a triangle.


OK, that works


OK, um


the next one is CBD.


CBD, OK


um


CBD equals


that was 1:30 to CBD equals 50.


and the reason is linear pair, said the second one.


OK


Yeah


Um, and then for


the last one, it's uh Angle C.


equals.


Um.


e


al s


wait a second


Angle C equals 65.


and the reason is based of an isosceles triangle.


That's correct


Yeah, thank you so much.


OK, of course


I got it.


OK, I'm gonna have to go for today. Yeah, unfortunately.


OK, thank you so much.


the time being, of course, you're welcome. Just make sure to leave a review based on how I did.


the rest of your night


Oh, I will. Thank you.


of course.


Hello. Hi, Alex


How are you


good how are you


Oh, it's so good, thank you.


Um, so you can turn on your mic if you want. Also, you can listen to me by turning the speaker on.


Uh, otherwise, you can just type in the chat box. That is also fine.


How can I help you today?


I have a test coming up


OK


and there is something that I just cant figure out


Um, OK, so just tell me what topic is it or just uh give me some questions on that topic, and we can work on them together.


let me fins the problem real quick


Yes.


it is where two end of a rhombus or rectangle are in an angle and it is in an equation and it has exponents and I just don't understand it


Um


2 ends of a rhombus or rectangle are in an angle


Uh, can you draw that on this white board if possible.


it looked something like that


So


two ends of thrombus we


are in an angle and


it is an equation


mm, I'm sorry, I'm not able to understand what exactly you want to ask.


Um, do you have, have the exact question statement?


Alex


Do you have the exact question statement?


give me a sec


OK


(7x+^2-18)   (6x^2-7)


I, yeah, I got the equation.


those are at the ends of the rhombus


So, OK, so basically


uh wait, I'll, I'll just redraw this.


oka


So you have a rhombus like


this, let's say, and you know the


two angles


So this angle is


x^2 minus 18, I guess. And the other angle is


66 square minus 7.


Uh, is this the question and um


I think you need to find the value of eggs from this.


the equations are diagnole from each other


Value of X


uh equation


diagonal from each other.


Um, OK, so


if this is 7X2 minus 18, then you are saying that this angle is 6 x^2 minus 7.


Is this what you're trying to say?


yes


OK


Then the problem is really simple. So, uh, do you need to find the value of eggs here.


I mean X


OK. So, do you know this property of rhombus or any parallelogram that opposite angles are equal


what do you mean?


armor cap


So there, there are certain properties for parallelogram, let's say.


this is a parallelogram. So we know that this side is equal to this side, the length of these sides are equal, similarly, the length of these two sides are equal. We know this thing. You know that if this angle is, let's say, X, then the measure of this angle will also be X


and if this angle is by, then the measure of


this angle will also be by


Uh, so this is a property, right, that the uh


opposite angles are equal, right?


yes they are


Yeah. They're called opposite angles, right? Because like X and Y, they are called ads and angles


so, uh, these are like opposite angles.


So the same I was telling you here. So, OK, is this a rhombus?


yes


OK. So these angles should be equal, so I'll just equate these 27 x^2 minus 18 equals 6 x^2 minus 7.


Now we just need to solve this equation. How should we solve this equation?


do the exponets first


Um, OK. So, basically, I need to


take all the variables on one side and the constant on another side, right?


Of the equal to sign.


this is 7


so yeah


so if I subtract 6 X square from both sides.


What will I get? It will be 7X2 minus 18 minus 6X squares equals these post cancel out and I get -7 here.


after this


What is 7X2 minus 6X2.


Yeah, it's


minus 18 equals -7. Now I need to like kind of isolate x^2. So I need, I don't need this, so I'll add 18 both sides.


These will cancel out to become x^2 equals minus 7 + 13, but is 18 minus 7.


No, wait, 1897.


17 minus 8 is 9, 18 minus 7 is what?


my bad 11


Oh, OK, no problem.


So, yeah.


So 2 equals 11. Now I'll take root on both sides, so I'll get X equals sqrt(11).


It can also be minus root 11.


Yeah


This should be your answer


Is this clear


okay, yeah thanks


OK, no problem. Uh, do you have any other questions? So basically, the concept we use here was like quite simple. So in any rombus or let's say any parallelogram opposite angles are equal.


You just need to keep this property in mind.


That is all I guess


Um, yeah, is, is there any other question I can help you with?


no. thank you though


OK


Have a good day. Thank you


you too bye


Bye


okay do i say what it is on the chat because i cant draw it on the board


sure! go ahead


okay Unit 5 Test Part 2-TGA - Solving Linear Equations


Just to clarify, the equation I'm seeing is "3.7p = 21.3"?


sorry i didnt finish writing


All good! I'll help you once you're finished writing it!


im done now


Alright! Let's take a look at it!


What do u think is your first step when you look at an equation like this


multiplication?


Nice try but let's take a closer look


What are we trying to isolate here?


i dont know?


That's alright, but looking at your work I can see that you're trying to solve for p


ohh


take a look at the left side of the equation, 3.7p


okay


What operation is happening between 3.7 and p? Are they being multiplied, divided, added, or something else?


multiply


Exactly! And to solve linear equation, we need to undo these operations. What do u think will undo multiplication?


divide?


Yes!! That's exactly right!


Would you like to give this question another attempt, and I can help you further if you need?


yes that was one question on the lesson but theres another one do i draw it out on the board or paste it ?


Anything works! You can draw it out on the board or paste it in the chat and I can draw it on the board!


ohh okay


(the following equation was solved incorrectly by a student. identify describe the error in the error in the equation above.) it says


I see, once you show me the equation and the process of the student I can help you out!


do i screen share how do i do that


To screenshare, you can click the button on the very left in the functions for the whiteboard


If that's difficult, you can always draw the question as well!


okay!


ok i think im done now


Alright! Looking at the equation, what do you think the first step should be to solve for x


3/4 x = 1/2


To clarify, is that a negative 3/4 in the equation?


its a minus


alright got it


so looking at this, the student added 3/4


What would your first step be


if ur not sure, just let me know and we can figure it out together!


ohh okay would the first step be multiplication?


Nice try, lets take a closer look


Just how we did for the last equation, we need to determine the operation between -3/4 and x


What do u think that is


If ur not sure just let me know and we can work through it!


Hello, what can I help you with today??


how to draw a 85 degree vertical angel with a protractor


Okay, I don't think I can show you on here because we don't have a protractor but I can explain it to you?


ok


Okay, so first


You would start by drawing a straight horizontal line, & you can use a ruler if you would like


yea


You would then place the protractor on the baseline


& make sure the 0° line on the protractor lines up with the baseline


you would then find the 85° on the curved scale


After, you will start from 0° on the protractor on the same side as your baseline & Move along the inside or outside scale until you reach 85°


Make a small mark at 85°


& Use your ruler to draw a straight line from the vertex up to the mark


You now have an 85° angle!


I found this picture online that I think really helps imagine the steps I explained :)


However, instead of making a mark at the 40 degree mark in the picture, you would do the 85 degree


It says that the vertical angle needs to be in the shape of an x


Oh okay!


For me they taught me to drag the line all the way down.


For example, we can use the picture I uploaded


Something like that similar to that


Do you think that's helpful?


Great!


So yes, once you draw your line, you would just drag the opposite just how i did in step 4 of the picture I provided :)


Is there anything else I can help you with?


no thank you


Okay, I hope this session was helpful in getting a better understanding!


Hi Alex. How are you doing?


Ben, im good


oki im done


OK, what does the Pythagorean theorem say?


wdym?


It says "Pythagorean theorem" so I think that's what you're learning. What is it?


well it says its a fundamental principle that relates the length of the sides of a right triangle.


Yes ... and what is the relationship?


the square length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.


It's actually quoted in Wizard of Oz


Yes that's it. x² + y² = z² if x and y are the sides and z is the hypotenuse


What is the one side measure?


yea i think


You think? I mean, did you write 75?


oh yea i did


So can you solve it now?


75² + x² = 156²


oki i can try


Use a calculator


alr


That 156² - 75²


So that is x²


What is x?


so i would find the square root of 18711?


Sure.


oki


You know the length can't be 18711 because it doesn't fit in a triangle with sides 156 and 75


yea


so the sqrt of 18711 ..78


Right.


So that is the length of the base


This is one of those formulas you want to learn and remember for your whole life.


Just like area = πr²


oki i have 1 more


OK


It's OK it doesn't have to be perfect.


yea ik just trying to be a little quick I_I


So solve this the same way


so would it be 35^2 + x^2 = 38^2  ?


yes


oki so i got x^2 = 219


and x = 14.79


Actually 14.80 with rounding


Good, you have the idea now.


oki


So if they give you the sides and ask for they hypotenuse, you just sum the squares of the sides and take the root


And recognize that 3-4-5 is one, as well as 5,12,13


alr


well thank you for the help :)


You're welcome.


Have a good day! :-)


u too bye :)


Bye


hi


Hello Liam, how are you today?


good


How may we help you today?


I need help with a promble


Can you please tell or show us the problem.


yes


so it says new command 2 start at 6/ move 1/6 to the right in I don't know the answer to 6/


I am not sure that I understand.


Is this on a number line?


so they trying to say like if we move the 1/6 to the right what will the answer the for 6/


Do they mean move 1/6 to the right of 6?


I think so


Let me put a number line on the board.


So if we start at 6 and move to the right, the number get larger.


does that explanation make sense?


So our number line is marked off in sixth's.


Can you draw a circle around the mark that is one place to the right of 6?


Hello Liam, are we still connected? It has been ten minutes since your last response.


I will need to end this session in a couple of minutes unless I see a response in chat or on the board.


I hope that you have a good day.


Hi, Sarah. What do you need help with?


haii im doing scientific notations


i idk anything about it


In scientific notation, you express a number as a*10^b, where a is at least 1 and less than 10.


Let's do a problem similar to what you have.


oki


so how do i get the decimal?


What do you mean?


like how did u get 2.3 from 2,300


Imagine moving the decimal point until there is only one digit to the left of it.


so would 45,000 be 4.5?


Yup


times 1000


1 zero for every hop you make.


so 3 zeros


No, four zeros, because 4.5 x 10,000 = 45,000


ohh oki


4.5 x 1,000 = 4,500


Good job!


Correct!


That's correct!


oki i have harder ones


Do you remember the order of operations?


yea


like PEMDAS ?


parentheses, exponents, multiplication, division, addition, and subtraction


Now, apply that to the numbers.


oki


Do you still need help?


wait gimme a sec to solve


so 10^6


is 1000000


Yes


so 1000000


is dat right?


is 10000


You're right.


so 48000


Yup.


oki imma put another one


k


would it be 125000?


Correct!


oki :)


Need any more help?


sure but do u know how to do the pythagorean theorem?


oki i have a few of those


oki


The sum of the squares of the legs (the two sides that are at right angles to each other) is the square of the hypotenuse (the longest side).


so like this


If you need more help, you can reconnect.


hi


Hi Sam. I only have a few minutes, but maybe I can help.


I see you have mastered the whiteboard.


yes


i need help with a math qestion


ima take a screen shot


What is the question


Okay.


Can you make it bigger please


ok


like that


yup


do you neeed a bigger screen shot


It's fine, but I can't see the names on the equations. Which one is Sarah's, and which one is Ben's?


okay so the one that has 46 in the middle is Emily the one that has a qestion mark is Jack


Okay, I figured it out. And I see you already got the first question answered correctly.


The last item wants to know what number is the next 10 after 25, and what do you have to add to that to get it?


you have to add 10 to get to the next ten right


No. think about what the tens are. So if you start with 10, what's the next 10? And the next 10?


10 20 30 40 like that right


Exactly. So, what's the next 10 after 25?


That's not in your list of tens.


They aren't asking you to add 10-25. They're asking if you counted by tens, what would be the next ten that you got to after you passed 25.


So go back to your list of 10, 20...


still dont get it


10...20...30     So 25 gets in between 20 and 30, so the next ten after 25 is?


Don't get discouraged. This is a goofy question.


right


Now they want to know what would you add to 25 to get to 30?


i added 5


And you can see what Emily did with that.


Precisely.


And that is what goes into that?


question mark....


https://example.come 5 in the equation


They are trying to show you that you can break numbers apart to make the addition easier.


Apparently it's not making it any easier for you, and I think it's a little bit misleading.


i dont really know math like that sorry


No problem. I am right there with you, Sam.


I hope that helped. I'm sorry, but I have to go now.


ok


I'm betting you could have just added it up, and all would have been well.


hello, i would like help on my geometry homework please


hello


so


we know that these 2 tris are congruent right?


yes


ok, so if all the angles are the same, we can assume that these two are congruent because of SSS


but it shows angles tho?


wdym shows angles


ur close tho


like 30 degress and the 50 ?


yes that is correct


sorry typo, its not SSS


AAS


do u understand?


Liam that one


yes yes


nice one


any more help with more of geomtry questions?


yes give me a sec


ok


this one I think is SAS


lemme see


not quite


we can see the a side and an angle are the same


wdym?


For the SAS postulate, the side you use must be the included side (the side between the two known angles).


aha


so from that, the answer would be AAS instead of SAS


these questions are tricky so dont fret


Noah got it thanks


yep np


anything else?


yes sorry


For this problem, look at the sides. You have three pairs of sides that are either marked as equal or are a shared side. Can you identify the three pairs of congruent sides?


WSV and XYW?


Nice! That is correct.


You have the right answer, but do you know why?


not really?


Ok, let me clarify.


We know that the two sides are congruent.


yup


From that, we can use the reflexive property.


Because WZ is a shared side


okay


Hence, we can determine that the triangles of the shared side are both the same length.


And since we have 3 equal sides, we can say that they are both congruent because of SSS


ohhhh got it got it


Nice, you have the answer, but do you know the reasoning?


yes because it shows the first angle then the side so in the R it will clearly be another angle since there isn't a side to it


That is correct, but can you explain why the other angle is congruent?


because both of them both have the same angles and sides


Do you remember when two lines intersect, their angles opposite to each other are congruent?


That's why, but nice you got it correct


ohhhh okay thank you


ye


nice, u have the correct answer


thats because of the reflexive property, where the two triangles share the same side


oh yeah!


Any other problems?


this one please


You are doing very well, that is right


Since you have two congruent size and an angle, we can say that is is bc of SAS


yes since they already gave us them right?


Yes, correct


this one I'm kinda struggling with


Remember when two lines intersect, their opposite angles are the same, so...


I think it'll be SAS


yes, correct


Oh! Nice!!


Anything else?


yes give me a sec


ASA?..


This one is straight forward, that is correct


oh okay


2 angles and a side are given


now this one I don't know at all


Hmm, this problem is tricky.


I know!!


What is it? and why?


A?


Correct, nice


ohh thanks


one more question sorry


ofc, Im happy to help


thanks!


this one I think it'll be AAS


Leo see


ofc


So we see that two angles are given


and due to the reflexive property, we have a congruent side


do you know whats the diff btw ASA and AAS?


they have same amount of sides and angles, but they are diff


ye ASA give the Angle first then side then angle


unline AAS it give two angles then side


Correct, it is AAS


notice how the side isn't between the two angles


ohh yes!


nice job


i gtg, u did good


Thank you for your help today!


have a nice day


np u too


thanks


hello


eveing


I want to practice for a math test I have tomorrow


its based on these topics


give me a minute


give me a few minutes, I have to get water


simplifying and expressing in the form A+Bi
simplifying radicals and multiplying radicals
Prove that if a and B< or > 0, then Root a x root b =- root ab
multiplying and dividing complex numbers
Absolute value and their conjugates
Finding values of x and y to make each equation true.
calculating the distance of a complex number from its origin on a graph
determining real numbers for x and y for which the given statement is true.
Finding discriminant and how many roots and the type of roots it has
solving with any method of complex numbers
solving quadratic problems with the square root property
Writing a quadratic equation for a given solution set
finding the other root and value of c or b if one root is given
determining the value of k to see whether the graoh will have its indicated number of real zeros
checking if the solution set for the quadratic set is correct
determining the value for k so that the given conditions are satisfied.
Sketching vertex, AOS, 2 other points, zeros, and type.
Finding an equation through 2 points.
Algebraic word problems


hello?


Mr. David


which one you want to start wiht


I have one question to go


then I want you to find me some problems


check what i did


nope


is that correct?


I have another problem as well


eeyp


one root is 5


find the other root and p


This I dont know how to do


you mean this?


yes but its 2px^2


not just 2x^2


Then you substitute x=5 into here


huh?


why 5?


for x


one root is 5, yea?


yes


Mr. David


I'm done


ok


can you help and look around for some algebra 2 problems based on the ones I wrote here?


like quadratic word problems, finding x and y, checking the roots and type and whatnot


maybe give me another one?


I kind of dont have any


I can provide examples though


look, if you don't have any imma get going now


Can you help me better understand this problem


sure! for the record, are you allowed to use a calculator?


No


ok so, to start, we're gonna want to turn this into an improper fraction. 1 as a fraction with a denominator of 4 is 4/4. So what is 4/4 +3/4?


what is it as an improper fraction?


Idk


well since both fractions have the same denominator, just do 3+4. What's 3+4?


so the numerators combined are 7, and we just leave the denominator as 4. So it's -7/4, because there's also a negative in front of the number.


The answer will be a positive


Now, something nice we can do with this exponent on the outside of the parenthesis is we can apply it to the numerator and denominator seperately.


yes it will


Okay


so now I don't really know how you would compute this without a calculator 😭 but you would simplify both 7^12 and 4^12 and then divide the two numbers you get


so 7x7x7x7x7x7x7x7x7x7x7x7 over 4x4x4x4x4x4x4x4x4x4x4x4


No i do have a calculator on my iPad but i don’t really like using because i have to study for a quiz


You dont have to, but multiplying 7 and 4 twelve times each on paper without a calculator is kind of tiring


Hello, How are you doing today?


HHi


What can I help you with?


Oh


He


Hello


Hi


OK, now


OK, can you, can,


yes


Yeah.


what do you need help with?


OK. I need


need help with um uh not having any I will um put it on the board.


OK


What?


Um


so, um, yeah, this is what I need help with


um


27.5 divided by 0.55.


ok I can help you with this


OK, thank you


an easy way is to remove the decimal by multiplying


OK.


Um, I I you for.


Mm


Hey! What can I help you with


Hello, I am having difficulty with proving two triangles congruent using a two column proof. I have some practice problems in a book I would like to solve.


Okay! Can you take a picture and paste them in board?


I'll draw it because I dont know how to take a photo


Sure


The given is that DE is parallel to FG, and angle E is congruent to angle G


Alright! Let me take a look


From what I can see, these triangles are congruent because of AAS


could you explain that to me?


or draw it out?


Sure! The triangles share segment DF so they have an equal side


And because of alternate interior angle thereom, they share an angle as well


Oh, I think I understand it now


Great! Is there any other problem you need help with?


I would like to try another


the given is MS is congruent to RQ, and that they are also parallel.


Here, the alternate interior angle thereom also applies


This means that angle M=R, and S=Q


Do you get how to look for alternate interior angles?


I think it's if they are plainly shown as on the interior of the angle, and alternate from eachother. am I correct?


Yes! In this instance, you can also use the vertical angle theorem to show AAS


Do you understand this problem now?


Yes


Do you have any other problems you would like to look over?


Would it be possible for me to also show that point P is bisecting MR and SQ, to make MP congruent to PR and QS congruent to PQ? If so, could I say that because the sides are congruent and that MS and QR are parallel, I can use SSS to state that the triangles are congruent?


Unless it is given that point P bisects MR and SQ, you cannot do that


I would think that there is a way to show that P is a midpoint, but I don't think that it's possible here. I have one last one I would like to do


sure!


Yes, there is a way to prove bisection, but you're right that it's not possible in this one


The given is that AB is congruent to CB, angle A is congruent to angle C and that DB bisects angle ABC


The book says that I have to prove AD congruent to CD, but I would like to see if I can prove the triangles congruent


These triangles are congruent because of ASA


since DB bisects angle ABC, that means angle ABD = DBC


I see


Thank you for the help!


Alright! Have a good one


hi how are you


Hi, I'm doing good! What would you like help with today?


i am doing integrals and i forgot how to do one when theres a denominator


Okay, no problem! Do you have a specific example you would like to discuss?


theres this one


Okay, your antiderivative for the first term is correct! It is indeed (5x^3)/3.


So, for the second part, it's best to rewrite it where x has a single exponent. What do you get when you do this?


Yes, that is correct! Now, what is the antiderivative of x^(2/3)?


Yes, that is correct! The antiderivative is (3/5)(x^(5/3)). Good job!


Now, add back in the constant. What is the antiderivative of the entire second term?


So does the 2 not matter?


oh is that the constant


It does - that's white I'm referring to when I say the constant.


*what


sorry


So, what's the antiderivative of the second term?


Yes, that's correct! It is (3/10)(x^(5/3)). Now, there's one small thing I want to point out: there shouldn't be a negative sign on the sum of the two terms.


oh yes youre right i thought the 27 was negative for some reaon


Alright, no problem. Now, evaluate the antiderivative by plugging in the two bounds. What do you get?


So, your first, second, and last terms are correct. Try plugging 8 into 5/3 * x^3 again. What do you get?


Yes, that updated value is correct. Now, what does the expression evaluate to?


oh oops so 32014.96


Yes, that is correct! Nice job.


hm it doesnt say to round


but it keeps saying its wrong


Maybe try plugging in the value with the two decimal places. That would be either 32014.96 or 32014.97 based on how you round.


no its still wrong


I've plugged the definite integral into my graphing calculator and it gave 32014.966. There might be an issue with the question's answer.


okayyy


thank you for your help!


happy holidays


No problem! Feel free to come back if you need help with anything else!


Happy holidays and have a great day!


thankss bye


you too


Hey, can you hear me now?


It says that your mic is off for me


Can you turn it on and see if it works?


Hey, can you hear me


Yeah, yeah


Oh, thank you. Um, this is Sarah's's parents. I just signed up for her so that, uh,


since she has issues with um


algebra 1


Mhm. OK.


So I need her


she says her knowledge, she wants to deepen her knowledge, but she's kind of nervous. She doesn't like the algebra, so.


I go through this with that.


she can get help from here.


OK. Sounds good. Um


Uh.


I'm ready to help to


So you can continue speaking with her, Shes here.


Yeah, OK, sounds good.


Mm.


Mhm.


Oh yeah, yeah, expensive.


OK.


Hey man


Alex


Hi


uh


Good evening


Uh, so what do you need help on withoutwara one.


Uh, I'm still working at.


I


Compound inequalities.


compound inequalities, OK.


OK


Um, do you have a worksheet or an assignment that you want me to look at that you can send over?


Uh, no, I don't have a worksheet or a, an assignment, but I don't really understand it much.


OK. So


let's see


OK, compound inequalities. Let me find some.


practice problems we can look at together.


All right. Also, I'm sending you a link right now.


OK, copy and paste that link for me. Will you?


this.


Do you see the link


Yeah


perfect


OK, so let's work on number one.


All right


Does this look familiar? Is this like what your lemming stool as well?


Hold on a second, please. She needs helping.


OK, sounds good


the


OK


Con.


Yeah, I see it.


OK do you see it


Yes


OK. All right. Let's work through the first one together, right? I'm gonna write it out on the whiteboard.


So it's edge of one less than.


2 x + 3.


plus the 9


You see my wife, can you see my right here?


Yeah


OK. So


when you have to compound inequalities like this, with this less than or equal the size. What you can do, you can split them up.


into two smaller inequalities.


like this.


but because


but by splitting it up into two smaller inequalities, you need to include the word and.


Do you know what the word and means


OK


And now we would just solve both the these, these two sides. So we would get


negative uh


4, I'll do the left side first, so it's -4, less than 2 at.


So, and that gets us to add to straighter than -2, right?


Yeah.


And now we got


2 at less than 6.


for the right side, right, which is -3.


And then X is less than 3.


OK.


Now that we've solved both of these um inequalities, the two sides, right?


Now, what I like to do, that it, um.


I draw up both inequalities. So this is the ads greater than -2 draft, right?


Let's just say this is -2.


Mhm


I have an open circle, which is not a, and then I shade everything from here on out, right?


And then for the second side, I would go.


less than 3


say 3 is about there


Open circle again, shade.


And because this word says and I would be looking for points where they both are. So like I would try to find where they both intersect. In this case, they intersect at these two points, right?


So both of these this region is common in both the inequalities, right?


You see that


OK. Does that make sense?


Can you reread it again cause it's a bit confusing.


OK, yeah, yeah, sure


Um


OK, we're just, I'm just gonna write the, the final two inequalities, just I think you got it from there, right?


Yeah


OK, so add straight to the -2, and


Mm


and that's less than 3.


OK. So, let me draw this one out first.


So 2 is about here.


I'll just say it's there


Open circle


you know the difference between open and closed circles, right?


OK


Yeah. Open circles for just less than and graded in in flow circles for less than or equal to in


or graded in equal to.


OK. And I'm gonna draw the second one.


below the first inequality, and I'll and I'll say what.


and this is what, this is what the solution regions like for the two separate inequalities, OK?


Does that make sense


It is.


Mm.


for this one, because it says the word and I'm looking for the intersection between these two inequalities. So that means what part of both of these inequalities is shaded.


Like what part, what numbers are in both of these, and I see that this whole region


in between 2 and 3.


Yeah


It's common for both these inequalities, right? So the my hands.


Do you want me to say the numbers in between those?


Uh, no, no, no. I, this


the, the numbers are just from 2 to 3. So you don't really need to say it. All you need to say is that the answer to this inequality is this that intersection.


OK


Um.


Mhm


Um


Mm


OK.


OK. Let's do


the second one on there.


OK. I'm gonna, I'm gonna ask that you do the second one and I'll just watch you do it. Uh, so 4.


less than


X + 1


less than 10


All right.


Work on that one and then come back to me if you, if you need help.


This is what I got, uh.


I


this


quite crucial


Mm.


see.


Is it correct


I feel like I made a little bit of mistake.


Hello


I'm sorry, I was on mute this whole time. That's my fault. Um, I'd say it was a really, um, you're slightly off.


but it's OK cause it's your first attempt, and we're gonna, we're gonna see where we messed up. All right, man?


Mhm


OK. So when you split up the two inequalities, you got 4 less than X + 1, right?


Yeah


And X + 1 less than 10.


right


Then, when you saw for the 4 less than X + 1, you should have got an X is greater than 3, cause you're supposed to subtract one.


on both sides


Uh,


so tract instead of act.


Well.


because you wanna, you wanna isolate the ets.


Yeah.


OK, OK


And then for the right side, you have to subtract one again on both sides.


You you


So if it's a positive, you


try


you, you, you do the opposite.


Yeah, you do the opposite operation because you wanna isolate the ets. You want to isolate the variable.


OK


All right, let's do


one more on the


But, yeah, I'd say, I'd say other than that, I think you're, I think we're almost getting it. OK, let's do this one.


OK, let's do that one


I


Oh, that one looks


OK, so I know that I have to add to both sides of the equation, but


what do I do after that for the 4?


You divide by 4.


OK.


You always do the opposite operation.


So if you're multiplying by 4, you would divide by 4, and then vice versa.


OK then


I, I can't


OK. Um, can you just tell me your, can you just tell me your answer?


I got uh negative 2 less than or if


00 my


1.5 and 1.5.


OK, yeah, perfect


Uh, yeah, um, I mean,


it seems to me that you understand it really well. I mean, uh, you did it, I mean, it was just like one minor hair up, but.


yeah, I think overall, I think you did really well in this lesson there, and yeah, I don't think you should really be nervous on algebra one.


Well


and just keep it up and you're doing great. You did great at this session, so.


give yourself a pat on the back, you do really well.


That's not, I kinda understand that part. Sometimes they get it mixed up, but the ones with the um negative in diffractions, they confuse me cause like


Oh it's like this


It's like that


You know that


something, yeah, the ones with the fraction, yeah, the ones with the fractures.


OK, so, so if you have a fracture, what you would do is multiply.


Right


It's the same thing with division. If you're dividing by.


No compound inequalities.


you want


with the um fractions.


OK, let's do one of those then.


OK, um, I don't really need that much. I'll just.


OK, that that's a, this is a compound in equality.


OK


00, I'll work this out. So, split it up.


Mhm


Then we multiply by 4 on both sides, just when you have a fraction for an et, you can just multiply. So like whatever's on the denominator, you would just do multiply, but if it was like, say if it was negative 2 at over 3, right?


Mm


I would multiply by 3 halves. Multply always by the reciprocal.


Does that make sense? Because you wanna isolate the ets.


Yeah


generally erase that.


OK, that should be fine


And then let's do it here.


So now we have 12


less than or equal to negative events, right?


But you don't like negative signs with that sis.


Yeah.


So what you would do is you will multiply by -1.


on both sides


and then you


then you flip the inequality sign. So before, uh, wait, sorry.


before it was 12 less than equals the negatives. Now it's


greater than twin sets.


Does that make sense


OK


No. I'm confused on that part.


Power of.


OK, so what about when you multiply by negative, you slip the inequality side.


doesn't make sense


Yeah, what part about it doesn't make sense?


I just


uh


I think when you, um


multiply by the negative 1.


Whatever comes, what you said after that, it was just


blurring my mind.


I'm gonna write this out differently.


Wait, can we just look at one in equality for just I just wanna look at one equality first before we move on to Alex.


Sure


So