to make the question easier


and to simple out the calculations


0.75 can be written as 3/4


and this'll make my calculation easier


can we just multiply the standard form


Sure we can do that. Do you want me to do it that way?


yes


Okay


so first multiply them as integers


can you do this for me?


o


is that right


you forgot the 4 at the end


it's there


correct


and since it was 0.76


hence we divide 4712 by 100


got it?


um


can you just solve it regular way without taking out the decimal


Ok let's do it


ok


idk how to write it


write what?


the factors like setting it up


oh so if you have 2 numbers to multiply always the number with the more digits will be on the top


in this 0.76 has 3 digits 0 7 and 6 so that'll be on top


once done the next number will be written below that on the right


in this case we have 62


and then the multiplication sign on the left


and now multiply normally treating the 0 as a number


just remember whenever you multiply by 0 the decimal will come after that number


here 2 times 0 will be 0 and the 1 is added so decimal after 1


hmm


and we have our answer


did you get it?


yea


ok then is there anything else you want to ask me?


so estimated is what?


47.12 is the estimate


oh really


i have another quetsion


Sure go ahead


Did you try solving it on your own first?


no


Try solving it on your own first


idk what im supposed to do


lemme make it easier for you


okay


you go to a store to buy candy. one candy is $1 and you decide to buy 7 candies. you asked your dad for $10. before going to the cash register you wanna make sure you have the money to buy 7 candies. how do you check?


see you have $10


and how many candies to buy?


yeah


and each candy costs $1 so 7 candies will cost?


+ tax


maybe $9


that's right and you had $10 so can you buy the candies.


we ignore the tax for now


ok good


now read the question again and you'll be able to solve it


hmm


do i multiply 62 and 76?


yes


do we estimate the same as the last problem?


yes or you can estimate a bit higher cause of the tax but if that's not the case then yeah same as exercise 1


60 x 0.80/


do i estimate it that way?


no estimate it after multiplying


ohh


we multiply those?


so it would give us 47.12


do i estimate that to 47 dollars or 80?


i mean 48?


yeah it'd be 48


ok


anything else?


there


ok in this question think about what happens when we multiply and when we divide the increase or decrease


when multiplying it increases and when we divide it decreases


and that'll be the answer


no but


they are decimals


im supposed to pick which one is the greatest


it applies universally if both numbers are same


so it doesn't matter if decimals or fractions or integers


if they're same and multiplying and dividing, multiplying will give greater result and division will give lesser result


but i just calculated to make sure and apparently 0.21 x 84.63 is a bigger number


yeah that's what I am saying


multiplying gives higher results


I'll have to end the session now Liam cause I have to be somewhere real quick. I hope I was able to help you bye


pk


Howdy !


hello


So what's going on in math class?


I need to study for my final and she put out a review


Okey dokey.


my goal is to finish the review by friday and then go through the notes


do i show you the problem


Yes, people normally post a sample problem on the whiteboard.


okay let me do that


thats one of them


Sarah !


So let me post the unit circle just as a reminder.


So that thing inside the parenthesis is asking "what angle gives me a tangent value of -2/3" ???


maybe 150 degrees?


Yeah, not sure.


We'll look at that.


Tangent is negative in the second and fourth quadrants, right?


yes


So I plugged 150 degrees and didn't get -2/3.


ok well I know it X degrees


so maybe 120 degrees


So let's calculate and see what we get.


You can also (rules permitted) use a calculator...


Also not seeing that.


Im not sure I dont think we can get that fraction


No, I don't think so either.


So inverse tangent of -2/3 = -33.69 degrees.


so what do we do


So the angle that we're looking for is 33.69 degrees (reference angle to the x axis).


The sine of that angle is .554 so the cosecant is the inverse of that which = 1.80277


what


So since we can't solve this by picking values from the unit circle (like most problems) we use the calculator


Take the tangent inverse of -2/3 and what do you get?


Hold on


I get -33.69 degrees.


let me get my other calc out


Okey dokey.


I think with this one i have it in radians


With my calc i got the same thing though !


No worries.


So in degrees, we have - 33.69 (the fourth quadrant answer) and 146.31 (the second quadrant answer).


ok when I'm looking for the tangent of something i have to resort to looking for it in degrees


where did you get 146.31


So that -33.69 angle is 33.69 degrees down from the x axis (in the 4th quadrant).


That one.


The OTHER angle that gives you a tangent of -2/3 is 146.31 (which is 33.69 degrees from the x axis in the 2nd quadrant).


Im really confused Im sorry


So let's back up to the beginning.


What do the instructions say to do?


Do they list a domain and range for  angles?


find the exact value of the expression


Okay, so let's first find what angle gives us a tangent of -2/3


which is none of them


You're not there yet.


well we tried quandrant 2 and 4 and none of them matched


The next step, once we find that angle, is to take the cosecant of that angle


So slow down a bit - what angle gives you a tangent of -2/3?


you said I believe


But im not sure why


It can be either, depending on what range they want you to look at, but let's just stay with -33.69 degrees.


Okay?


okay I guess


So what's the cosecant of -33.69 degrees?


Yup.


I got the same.


So which answer gives you a decimal result of -1.802?


It's A.


Ohhh ok I think I understand so when you can't find the angle that matches -2/3 you have to find it in degrees. so it is has to be the inverse tangent of  -2/3  then whatever you get you have to find the csc of that


Yep !


ok great I have another question


An easier one maybe?


Okay, so let's try to "pick a number off the unit circle" again, okay?


I think you have to do the same thing last time right


Okay, so let's skip this step then.


I think its a because When i found the csc inverse of that I got the same decimal as a but it was a negative


bingo !


Ok great but how come I got a positive answer and the answer choice was a negative


So cosecant is the inverse of the sine function, right?


Oh wait nevermind I got a negative


my calc is tweaking


Ok wait another question


This is my calculator - too funny !!!


So what angle gives you a cosine value of root 3 over 2?


so I need to find the inverse of that equation right


You just need to find the angle that gives you a cosine of sqrt(3) / 2


So it's 30 degrees


oh wow that was easy


There are an infinite number of angles that meet this, but there are only 2 that are between 0 and 2Pi.


Yup, easy peasy !


another one please


I have 2 of them


Mark !


So let's do some algebra on # 24 and see where that takes us.


Okay so far?


where is the +2 coming from


Subtract 1 from both sides.


Combine like terms.


Now a u substitution.


wait Im still trying to figure out the 2


Okey dokey.


because so far Im at the 1-sin^2 theta = 3-3sintheta


So add sine squared to both sides.


Then subtract 1 from both sides.


Okay ?


Oh so it will be 2+sin^2 theta - 3sintheta


Yup.


ok I got that


Now, to make things a bit easier, we do a u-substitution.


Let u = sine(theta)


Okay with that?


so we can factor right


Yep.


So we get sine(theta) = 2 or sine(theta) = 1


The first root we can throw out since sine never equals 2.


why is that


Sine oscillates between -1 and +1


Oh ok


Take your calculator and type in 2 and then inverse sine.


You'll get an error message.


so if it is greater than 1 or less then its going to be an error?


Sine and cosine vary between - 1 and + 1 so anything outside that range will give you an error message.


Like + 2


Oh okay got it


So we're left with the second root which is sine(theta) = 1


Why couldnt it be A


Oh wait youre trying to find a y where it equals 1 right


But 3Pi/2 also works.


but its a negative


Oh, sorry - that won't work since sine of 3Pi/2 = -1


It's only Pi/2


Ok I understand can we do 25


So I didn't do a u substitution here (although maybe I should have).


But you get a difference of squares.


why are we doing cos ^2 theta


Secant is the inverse of cosine right?


1/cos theta


Yup.


So plug that in and solve for cosine (theta).


Im not understanding


So let's start at the given equation.


Okay so far?


yes


Still okay?


This is where the difference of squares comes in.


So it's A.


Make sense?


Yes!


There's a lot going on here !!!


Yes thank you so much Im learning and understand but I still have questions


Okay, I gotta scoot for now.


Good luck !!!


Oh ok thank you


take care...


Hello. I need help with logarithms to prepare for pre-calc.


I can help you with them


Perfect! So I have a basic understand of logs and their relationship with exponential functions but I need some help reinforcing my understanding


Can we work through some problems?


Sure


Okay awesome. Should I pull up some practice questions?


yes, you should


okay well here's a basic one from my homework: log(10) 1= ?


how would I approach this question?


What do you think you would do


hmmm I think we can see what 1^10 would be?


that'd be 1, right?


Anything to the power of zero is one


Why would it be to the power of 0?


10 is the baseand we are trying to find what to the power of 10 will give us one


And zero gives us one


ohhh okay. that makes sense.


lets try another one


log(10) 1000= ?


What do you think we have to do here?


well from the last problem, you mentioned that the smaller number is the base. So we're trying to find what to the power of 10 will give 1000


right?


Yes


For a problem like this you can just count the zeros


okay and then what


Thats you answer


Three


So it would be 3?


Count the zeros in 1000


ohhh it would be 3


got it


okay that was helpful. Thanks! thats all i need for now


have a nice day!


Alr bye


Hi Jamie


How can I help you today?


hi


oh can you check my answers


Sure


Drop them in


Ok I did


Ok give me a sec


K


he first answer is correct good job


Oh


is the 2nd one right too?


However I see a small mistake in the first question


oh okay what is it


The value of cosx approaches 1 and the denominator approaches 0


so overall we have 1/approaching 0


and that's infinity


hence the limit doesn't exist


got it?


Oh yeah okay I got it


And the second question is absolutely correct just explain the why part


Oh yeah right


so both numerator and denominator approach 0


in the 2nd ques?


Yeah


no tthe numerator approaches 0 and denominator is 2^x=2^0 and that's 1 so denominator approaches one


Oh rught


hence it'll be approaching0/approaching 1 and that's 0/1=0


and that equals 0


yah right


exactly


anything else?


alrigth


No that’s all


thanks


alright then Jamie have a good day. Correct the first question


bye


Okay thanks


Hi, how can I help?


Hello, I’m working on practice problems to prepare for my final next week. I’m focusing on Obj. 1,2,4,5,6,9,10,11,12,14,18,19,20, 23, and 21. I’m currently on problem 6 of objective 10. I haven’t done these in a while, so I may need some help. Here's the link to the pdf: https://example.com/algebra_problems.pdf


okay, got it


Thanks!


Can you write it on the board and Ill solve that way?


do you want me to do problem 6 from obj 10?


and do the whole problem on the board?


Yes!


okay


okay, done


let me know if I should explain


Lets move to OBJECTIVE 11: Factoring Trinomials (2.4)


Ohh right ac method


yes


questions?


Nope I get it


Now #4


I'll try and solve it


hey, did you go through the solutions?


I'm stuck on #2


How did we get to the 2x+3


#2, you mean 5?


oh you mean 4


Yeah


so it is (a+b)^2=a^2+2ab+b^2 formula


Ohh I see


so this is a perfect square trinomial


anyway, I need to go. My therapist just called and scheduled a meeting now.


I am sorry


submit another request maybe


bye


Hello, I’m working on practice problems to prepare for my final next week. I’m focusing on Obj. 1,2,4,5,6,9,10,11,12,14,18,19,20, 23, and 21. I’m currently on problem 6 of objective 10. I haven’t done these in a while, so I may need some help. Here's the link to the pdf: https://example.com/math_workbook.pdf


Is that a link?


Yes!


How may I help you


I need a bit assistance in solving the problem


Could you pls share the problems picture in the board, I was told not to open any link, during the session


You can


Ok


I can see that its a factor by grouping


R u familiar with this topic?


Yes kinda


Can you writeit on the board


In these kind of problem, you have to put them in pairs first, then take the common factor


You can see on the board


Yes


hey! what's up?


hi I need help with my IXL work


i can help if u paste the questions in the chat or on the board


yes


if easier just type it here


done


oh ok


15 is what percent of 100


Let's figure out what percent 15 is of 100.

Step 1: Write the problem as a ratio: 15100\frac{15}{100}10015.

Step 2: To find the percentage, multiply this ratio by 100:
15100×100\frac{15}{100} \times 100×100

Step 3: Simplify:
15×1=1515 \times 1 = 1515×1=15

So, 15 is 15% of 100.

Answer: 15%.


ignore that is paster wrong let me type it


ok I'm going to write that


we would make a ratio of 15/100


then we multiply by 100 to get percent so...


oh I'm sorry but I got to switch class thank you for your help I got to go


15/100  * 100  = 15


Hello


hi


hi there, what are you working on?


ok domain and range


Do you know what those mean?


yes


ok want to give it a try?


go ahead


What do you think for domain? ..


I'm going to exit the session, but you can ask for another tutor.


Hi!


Hello, what can I help you with ?


May I show you on whiteboard


Yes


Name three solutions of each inequality


Okay, so what do you think it means when it says 23.82 > or equal to m


It’s greater or equal to the variable m


Yes, 23.82 is greater than or equal to the variable m


23 is the question


OH


Its ok


In sorry


So for m, it can be any number less than or equal to 82


& that would be your three solutions


Oh


Sorry if I wasted your time I just didn’t understand thank you so much


For helping


No worries at all, I am here to help :)


Thank you


Have a good night!


Goodbye


hi


sorry for hopping on so late


i was wondering if u could help me check my project for geometry


Hi Ethan! My name’s Sarah. And of course I can help you go over your project!


great let me just paste the slides into the blank box on the left


Sounds good!


theres 7 slides by the way and its about rotations, like translation, reflection and rotations


Got it!


just pasted it! i just want to know if i did it correctly


Yes! I can see all seven slides


great


Do you mind giving me some background on the requirements for your project?


this is what i need to submit


You will have a Google Slides presentation containing:
o A Cover Page including your Name, Period, and the title of this project.
o Part 1 Slides
▪ Two Translations Logos (with explanations)
▪ Two Reflections Logos (with explanations)
▪ Two Rotations Logos (with explanations)
o Part 2 Slides
▪ Personal Logo (with explanations)


Part 1:
● Search the internet for popular and successful logos.
● Make a Google Slides presentation that shows the following:
o Two logos that show a translation. Include a sentence for each logo, describing in which direction it
was translated.
o Two logos that show a reflection. Include a sentence for each logo that states what type of line the
logo is reflected across. You must also draw the line of reflection in each logo on this slide.
o Two logos that show a rotation. Include a sentence for each logo that states the angle of rotation
and where the point of rotation would be.


Awesome! Please give me a few minutes to look over the slides


ofc take your time


Ok, lets go over the slides that show reflection first!


alright


I think that the logos you chose are great! I saw that in the instructions it asked for the line of reflection to be drawn on the slide. I think the first step is to add that!


so you mean draw a line in the middle right??


in the middle of the logo?


The line of reflection is essentially a line of symmetry. It divides the logo into two mirrored halves.


okay got it perfect


Great! The target logo you chose is actually unique in this case.


This is because circles have an infinite number of lines of symmetry!


In this case, I believe it would be worth mentioning this when describing the target logo!


okay yes I agree thank you


I also saw that the instructions would like you to identify what type of line the logo is reflected across


how would i find that out


For example, with the letter “A”, the letter would be divided evenly by a vertical line


oh yes yes, I was planning on putting the line vertical for the letter A, the target logo, and the starbucks logo


It is also important to remember since the circle is unique in the fact that it has infinite lines of symmetry, it can also be divided equally by a diagonal line or a horizontal line


yes so I will put a line horizontally and vertically for the target, and starbucks logo, as well as the letter A


Exactly! The letter A and Starbucks can only be divided by a vertical line. But, the target logo can be divided by various lines! Awesome job!


Do you feel ready to move onto the slides about translation?


so only for the target logo i add two lines correct? horizontal and veritcal?


diagonal lines can also be lines of symmetry


okay yes i undersatand


Great!


Lets move onto translations then


yes


I saw that your instructions require you to describe the direction in which the logo is translated


The Audi logo looks good!


Can you walk me through your description of the Adidas stripes?


yes so basically the adidas stripes are the same shape and are spaced out the same amount for each, as well as slanted so when rotated it is constant


Can you explain the “rotation” aspect to me more?


like the adidas stripes are slanted so they keep even spacing even if turned


Since this is about the translation of the shape, rotation isn’t a major concern. To put it simply, a translation is the sliding of a shape left, right, up, down, or diagonally.


The shape’s size or rotation/orientation does not change


okay will rewrite it there


I think you did a good job explaining that the shape’s size and appearance does not change. But, I believe it could be beneficial to mention the direction the shapes are moving in


Other than that, everything looks pretty good to me!


Let me know if you have any other questions or if you feel ready to move onto the rotation slides


for the direction of the shapes moving for adidas, what should i write


Does it look like the stripes are sliding up, down, right, left, or diagonally?


diagonally


to the right


Yes it appears that way!


Nice work!


yay


Are you ready to move onto rotations?


yes


Lets begin with the Mitsubishi logo


okay


Based on the instructions, it looks like you have to identify the point of rotation, and angle of rotation


Can you identify the point of location on the logo?


its the center of the logo


Yep! Thats the central point which the logo rotates around


Do you know how to identify the angle of rotation?


no


I marked up the logo a little


should i draw that on my slide?


It’s essentially the smallest angle that makes the shape look the same


Your instructions say to just write the angle and point of rotation in a sentence. Is your instructor looking for you to identify an exact measure of the angle?


I don't know, but i think it would be good if i did write it


We can find the exact measure of the angle two different ways


The first way, is if you have access to a protractor, you can line up the center point and the angles rays to find the measure


It is also possible to find the measure by hand


oh


To find the measure of the angle by hand, we first have to find the amount of degrees in a full circle. Do you know how many degrees a circle has?


Awesome!


Now, because the Mitsubishi logo has 3 diamond shapes equally spaced out around the circle, the rotational angle for the logo is one-third of the full circle!


Thus, to find the measure of one rotational angle, we would multiply 360(the degrees of a full circle) with (1/3) to find the answer!


When you try the problem, what answer do you get for the measure of the rotational angle?


Yes, exactly! Fantastic job!


great


Alright, now the last slide we have is the google chrome logo


Can you identify the point of rotation?


the center?


Yep!


Now, if we apply what we just did to solve for the angle of rotation of the Mitsubishi logo to the chrome logo, what angle of rotation do we get for the chrome logo?


120 as well??


This logo is interesting because it also has different colors.


If the logo is rotated 120 degrees, the shapes remain the same, but the colors are in different positions


So the angle of rotation that would give us the exact same image as the logo 360 degrees


In this case, I’m not quite sure if your instructor is concerned about the colors of the logo? But it could be beneficial to mention both angles


so which angles and how would i find them


So to simplify it, 120 degree rotation gives us a chrome logo that has the same shapes as the starting point, but the colors are messed up


If we rotate the 360 degrees, then the shapes are in the correct position AND the colors are in the same position as the starting point


Does that clarify things a bit more?


yes


Great! Looks like we’ve gone through all the slides! Do you have any remaining questions for me?


no


It was so great to work with you! Wishing you good luck on your geometry project! :)


thank you so much for helping me, means a lot! have a good rest of ur night :)


No problem! Have a good night! Goodbye! :)


heey


hi


I want to know how to get the answer to this


okay


A logarithm asks 12 raised to what power equals 144? So we rewrite it like this 12ˣ = 144


does that make sense so far


why did the log sign go away


the log sign goes away because we convert the logarithm into its equivalent exponential form


oh ok


A log asks what power (c) do I put on the base (b) to get the number (a)?


Replace the log with its meaning 12^x=144


we translated it into the equivalent exponential equation


final answer x=2


how did you get x=2 from 12^x=144


oh


nvm


12 squared is 144


ok I have another problem


correct


ofc


I have it on the board


okay


Rewrite the log as an exponent


I thought 2 replaced x as the exponent already


36 becomes 6² but x is still unknown


ok


if 6 to the power of 1 is 6 why did you write it as 1


When we change the logarithm into an exponent equation, we need both sides to look the same so we can compare them. One side already has a power. The other side does not look like a power yet even though every number is actually itself raised to the first power. We write the missing power on purpose so both sides match in form. Once both sides look the same, we can compare the powers directly. That is why we write the first power even if it is normally not shown.


so basically if there is no power on both sides, the one with no power will automatically have 1 as the exponent and the answer will always be 1?


yes


ok so we get rid of both coefficients and only the exponents are left


When both sides have the same base we ignore the base and only compare the exponents. That is how we solve it


back to the beginning. when you write it as (6 squared) to the power of x equals 6, are you switching spots (going the opposite way) because 6 is square root of 36 and the 6 squared is equal to the 36 ^x


We rewrite 36 using 6 because it helps us solve the problem. We are not switching anything just changing how the number looks.


hi


Hi Michael I'm Sarah Im here to help feel free to ask any questions you may have


i will put an attachment of my homework


Ah, I see this is a problem about the formula for distance based on time


Are you familiar with the formula d=rt


kinda


its like y=mx


there is a 4th on


okay that is a great start! remember that distance=rate*time


i will put it


can I ask where 2,000 came from?


that was for d


ohhh I see! thank you for clarifying


so in the distance=rate*time formula, can you see that rate is represented by the numbers in the answer?


yes


i can tell because it goes in order


Great:) do you know what the rate of the winchester bullet is?


1924 miles per hr


Perfect!


can you identify which answers have a rate that is faster 300 mph


c and d


perfect! great work do you have any questions about that?


no but there are more problems


i will let you know if i need help


I'm here to help!


here


That is a good problem! do you know where to start?


well isnt it kinda the same as the other one


sort of!


we should start by finding the rate of the graph and the equation, that will make it much easier to comparte


okay


do you have any questions about how to do that? :)


so isnt it the graoh if im correct?\


that right!!!!!!


YAYYYYY


do you have any question about how you got that answer


no


this is another good problem! do you know where to start?


thats okay, I can help :)


how familiar are you with graphing?


ehhhh.


mid-ish i guess


thats perfectly okay, I can help!


you did say earlier that you know the y=m formula correct?


y=mx yes


oh yes, the +b will likely be in the next lesson, sorry for confusing you


do you know what the rate/slope is of the equation that we are given?


no worries, in the formula y=mx, m is the slope/rate of the line


that line


we need to move the point of that line to make it y=2.5x


okay


remember that y=mx always starts at the origin (0,0)


wait 2.5?


oksy


yeah! 2.5 is the slope!


great work!


do  you have any other questions about the graph or multiple choice?


i will be right back


are you still there?


i am back noe


now*


c is the only answer correct


C is correct!!


I would also take a look at A and E. I can help explain them if you need


okay*


Do you understand why those are also correct?


yes i will be right back


im back


great! let me know if you need help:)


howdoi do the graph beccause its saying its wrong


can you show me what you submitted for the graph?


I see! great work starting at the origin, but we need to look at the second point.


Do you recall what the slope is supposed to be?


great work!!!  it might be helpful to put that into the fraction form, do you know what that is?


errrrrr. no


no worries, we can write it as 5/2, I will write the work in the whiteboard.


okay


alright, I wrote it. do you understand that process or should I explain it further:)


do i put that on the board


no i meant the graph


I can see the graph, now we need to change the location of the second point


i got it


because we rewrote the slope as 5/2, we can use rise over run


next question


I'm sorry, but I have to go now. Please feel free to start a new session with a different tutor. You did great work today, I hope you understand this better!  :)))


Laws of exponents


ok


1. Product of Powers Rule
𝑎
𝑚
⋅
𝑎
𝑛
=
𝑎
𝑚
+
𝑛
a
m
⋅a
n
=a
m+n

Meaning: When multiplying two expressions with the same base, you add their exponents.
Example:

𝑥
3
⋅
𝑥
5
=
𝑥
3
+
5
=
𝑥
8
x
3
⋅x
5
=x
3+5
=x
8
2. Quotient of Powers Rule
𝑎
𝑚
𝑎
𝑛
=
𝑎
𝑚
−
𝑛
(
𝑎
≠
0
)
a
n
a
m

=a
m−n
(a

=0)

Meaning: When dividing two expressions with the same base, subtract the exponents.
Example:

𝑦
7
𝑦
2
=
𝑦
7
−
2
=
𝑦
5
y
2
y
7

=y
7−2
=y
5
3. Power of a Power Rule
(
𝑎
𝑚
)
𝑛
=
𝑎
𝑚
⋅
𝑛
(a
m
)
n
=a
m⋅n

Meaning: When raising a power to another power, multiply the exponents.
Example:

(
𝑥
3
)
4
=
𝑥
3
⋅
4
=
𝑥
12
(x
3
)
4
=x
3⋅4
=x
12
4. Power of a Product Rule
(
𝑎
𝑏
)
𝑛
=
𝑎
𝑛
⋅
𝑏
𝑛
(ab)
n
=a
n
⋅b
n

Meaning: A product raised to a power is equal to each factor raised to that power.
Example:

(
2
𝑥
)
3
=
2
3
⋅
𝑥
3
=
8
𝑥
3
(2x)
3
=2
3
⋅x
3
=8x
3
5. Power of a Quotient Rule
(
𝑎
𝑏
)
𝑛
=
𝑎
𝑛
𝑏
𝑛
(
𝑏
≠
0
)
(
b
a

)
n
=
b
n
a
n

(b

=0)

Meaning: A fraction raised to a power is equal to the numerator and denominator each raised to that power.
Example:

(
3
4
)
2
=
3
2
4
2
=
9
16
(
4
3

)
2
=
4
2
3
2

=
16
9

6. Zero Exponent Rule
𝑎
0
=
1
(
𝑎
≠
0
)
a
0
=1(a

=0)

Meaning: Any nonzero number raised to the power of 0 is 1.
Example:

7
0
=
1
7
0
=1
7. Negative Exponent Rule
𝑎
−
𝑛
=
1
𝑎
𝑛
(
𝑎
≠
0
)
a
−n
=
a
n
1

(a

=0)

Meaning: A negative exponent means take the reciprocal of the base raised to the positive exponent.
Example:

𝑥
−
3
=
1
𝑥
3
x
−3
=
x
3
1


The laws of exponents are rules that help simplify expressions involving powers of numbers or variables. The product of powers rule states that when multiplying two expressions with the same base, you add their exponents, such as
𝑥
3
⋅
𝑥
5
=
𝑥
8
x
3
⋅x
5
=x
8
. The quotient of powers rule says that when dividing expressions with the same base, you subtract the exponents:
𝑦
7
𝑦
2
=
𝑦
5
y
2
y
7

=y
5
. When raising a power to another power, the power of a power rule applies, which means you multiply the exponents, as in
(
𝑥
3
)
4
=
𝑥
12
(x
3
)
4
=x
12
. The power of a product rule tells us that a product raised to a power is equal to each factor raised to that power, for example,
(
2
𝑥
)
3
=
2
3
⋅
𝑥
3
=
8
𝑥
3
(2x)
3
=2
3
⋅x
3
=8x
3
, and similarly, the power of a quotient rule states that a fraction raised to a power is equal to the numerator and denominator each raised to that power, such as
(
3
4
)
2
=
9
16
(
4
3

)
2
=
16
9

. The zero exponent rule explains that any nonzero number raised to the power of zero is 1, like
7
0
=
1
7
0
=1, while the negative exponent rule indicates that a negative exponent represents the reciprocal of the base raised to the positive exponent, for example,
𝑥
−
3
=
1
𝑥
3
x
−3
=
x
3
1

. Together, these rules make working with exponents systematic and much easier.


refer to this link: https://www.mathresources.org/exponents


I had a specific question actually we could do


sure


draw it


Ok it’s up


so let me be clear its 2u^3 times 3u^3


and what's the third term


It’s 2v^3 times 3u^3v-4


first multiuply the coefficients


to get 6


then


multiply the powers


bring in u^3, then combine everything


to get 6u^3/v


stick around if you need any more help


Wait so multiply 3 3 and -4


That gave me -36


you said 3u^3v-4


only 3 is the exponent there


3 is the coefficient i mean


only 3 and 2 are the coefficients


Oh I meant 2v^3 times 3u^3 v^-4


once again same answer


2v
3
×3u
3
v
−4

Step 1: Multiply the numerical coefficients:

2
×
3
=
6
2×3=6

Step 2: Multiply powers of
𝑣
v using the law of exponents (
𝑎
𝑚
⋅
𝑎
𝑛
=
𝑎
𝑚
+
𝑛
a
m
⋅a
n
=a
m+n
)

𝑣
3
⋅
𝑣
−
4
=
𝑣
3
+
(
−
4
)
=
𝑣
−
1
=
1
𝑣
v
3
⋅v
−4
=v
3+(−4)
=v
−1
=
v
1

Step 3: Include
𝑢
3
u
3
:

6
⋅
𝑢
3
⋅
𝑣
−
1
=
6
𝑢
3
𝑣
−
1
=
6
𝑢
3
𝑣
6⋅u
3
⋅v
−1
=6u
3
v
−1
=
v
6u
3

Final Answer:

6
𝑢
3
𝑣
v
6u
3


trust me


that's the answer


Everything you typed was vertical so it’s kind of hard for me to follow along could you maybe write it down?


sure


there you go


Thanks


stay in case you have more questionss


Actually I do have one more problem to do


SURE!


I can try to post it


sure!


Nevermind it’s not uploading


put it in a google doc and send me the link to the doc


Ok


1 is x^12


number 2 is x^8


number 3 is x^12


number 4 is x^12


number 5 is x^12


so its number 2


got it?


Can you show me how you solved each one on the white board?


there you go


Thank you


yes of course!


I'll be here in case you need help!


Ok!


I think im starting to understand this


that's amazing!


Can we do some more practice problems on this?


yes


Ok


The first one is y^5/Zoe


Would I just add the exponents together?


subtract the exponents


since its division


so it'd be y^2


Oh


Ok the next one is 4^6/4^x=4^0


Should I subtract6 and0


Or would the answer automatically be 0?


it would be 6 for x


since 4^6-4^6 would be 4^0


I’m confused could you write it out on the board and explain it a little more?


Where did you get the extra 6 from?


arent you asking what x is


dont you olve for x


solve


Oh I think so because it says x=?


yes


so.x =6


But how do you know that?


because of the queotient rule


it's asking what number subtracted by 6 would be 0


Oh


What does the quotient rule say again?


watch this


Ok


Oh I can’t click on the link


copy paste it in a new tab


That what I tried to do but I can’t highlight it or anything


yes you should be able to


copy paste over it


That’s*


highlight it and copy it


and paste it


It’s nit letting me highlight it


The quotient rule for exponents states that when you divide two exponential expressions with the same base, you subtract the exponents. To apply the rule, keep the base the same and find the difference between the exponent in the numerator and the exponent in the denominator. The formula is written as: \(x^{a}/x^{b}=x^{(a-b)}\).


okay that's fine


look and read i


Not*


ok


I read it


It kind of makes sense


alright bet


ill be here in caseyou need hel


brb in 5 minutes.


have to do something


Ok


need help with anything?


Hey Michael!


Hi again.


Good meeting you


You too.


Where is the line that corresponds to two batches of bagels?


every 5 people = one batches of bagel?


so 10?


All they ask is how many people can be served with two batches. So you just look at the max x value


Yes, it's 10


Okay!


so do I type in 2 or 10?


But you don't need to get a definition of the function for this problem.


Alright


2 is the batches, 10 is the maximum size of party


so I think I should type in 10


yes


What do you think?


Let's see


Yes.


I will let you know if I aced this


OK.


is it...


so it's 8?


No, 7, right?


Oh!


alright


Thank you so much!


Happy thanksgiving


Hello


Hi Alice


How are you today?


Doing well, thanks. And you?


Good, thanks


Reading the problem...


For this question I did the diagram but I don't know how to answer the questions


Ok


We can start with part (a). Do you have a guess?


Not really


You simply multiply two numbers. I'll show you.


Give me a sec to get my tablet.


Do you see it?


yes


I can also explain using probability notation if you wish.


That'd be great thanks


I'll write below the upload.


We want the probability that the consultation comes from a friend (F) AND relults in a tattoo (T). So P(F ∩ T) = ?


I don't know if that's correct


I'm showing you the correct way on the board. Did you learn about "conditional probability" ?


I don't think so


I'll explain.


I've been absent honestly so I don't know what's going on with this whole thing


I really wanna get though at least b since I got like 6 minutes of class left


Ok thanks


P(F) = probability that consultation comes from a friend = 0.5.


P(T|B) = probability of getting a tattoo (T) *GIVEN* that the consultation came from a friend = 0.8


The vertical bar "|" means *given that*.


Ok


I'll write the general formula on the board.


Im so sorry I have 2 minutes left


OK. Did you want to end the session?


Yes sorry about that thank u so much for your time I need to get to my next class 😅 I'll take a screen shot of this and see if I can figure it out


Thanks again


Hello how is it going


What can I help you with today


hi well how are you


I'm doing good


i need help understanding the concept of implicit functions


Implicit differentiation?


yes


Alright


I can help with that


if you were to throw a problem at me, a simple one, I would be able to, using a step by step format, solve it pretty easily


Sur


Sure


I'll put one on the board right now


but I need to understand and really know what the question is asking, and what my answer means


Okay


I put one on the board


Correct


Or dy/dx = -x/y if you simplify


That's implicit differentiation


The harder questions of implicit differentiation will make you use product or quotient rules


when the word differentiation is used what does it mean in any context


in calculus


Differentiation is basically just finding the instantaneous rate of change at a point (or finding the slope of the tangent line)


Primarily to a curve


so is x^2+y^2=1 a curve


It's a circle


With center (0, 0) and radius 1


what does dy/dx represent


dy/dx is the instaneous rate of change at a point x when the point (, ) is given


So maybe at (0, 1)


dy/dx = -2(0)/2(1) = 0


So, the instaneous rate of change at x = 0 is 0


It's a horizontal tangent


But at (1, 0)


It would be a vertical tangent, which implies it is not differentiable at that point


Does that make sense?


yes did i just use product rule


i meant power rule


I mean yeah to find the derivative of x^2 you did use the power rule


Finding the derivative of y^2 involves the chain rule


why is the dy/dx being mulitplied by every y value instead of x


Meaning?


why wont i do 2x(dy/dx)


Because it's not the chain rule


The derivative of x^2 uses the power rule, so it would be 2x


The derivative of y^2 involves the chain rule, so derivative of outer function * derivative of inner function


Hence 2y * dy/dx


so if it was chain rule we would?


Chain rule for what?


you said because its not the chain rule at the beginning of your explaination


Yeah for x^2


i thought it had something to do with y being the output


Yeah so we use the chain rule to find the derivative of y^2


i usually use power rule for y^2


But that wouldn't work


that's what I did in the problem though


Because y is an implicit function to x


No you did it correctly


You didn't use the power rule for y^2


You used the chain rule


because power rule is multiply exponent times coefficient and subtract by one


Yeah


so from y^2 i went to 2y


But where did the dy/dx come from? That's not apart of the power rule


It's technically power rule + chain rule in that case


because doesn't chain rule keep the original function then chain on the deriviative


I didn't do any of that


It multiplies the derivative of the outer function with the derivative of the inner function


The derivative of y^2 is 2y


The derivative of y (inner function) is just dy/dx


So, d/dx(y^2) = 2y * dy/dx


One sec


I need to use the restroom


I'll be right back


ok


Alright I'm back now


Did that explanation make sense?


not really


Oh


What part didn't make sense?


the part where you explained why I chain rule for the terms containing y but not the ones containing x


That's because y is an explicit function of x


x is just


x


In that case, you would need to use the chain rule to differentiate y^2


Or just y in general


what do they mean by implicit and explicity


explicit


Implicit basically means y is not explictly mentioned


Like I'll give an example


You've probably been differentiating functions like y = 2x + 1 or y = 6x^5 + 4x. Those functions are explicit because they clearly mention what y is equal to


Implicit functions mean y can be differentiated by, but it is not fully stated


Like x^2 + y^2 = 1


y is mentioned, but it isn't put into the form y = ...


And sure, you could do some algaberic maniputlation to make it y = but it takes time


So that's why you do implicit differentiation for that


but if you did do that manipulation what would you get versus if you did the differntiation


I believe it would be the same derivative for the answer


But maybe it's a different form


But the only downside to doing that is that it takes time and a lot of effort


Implicit differentiation is the best method to use to approach such problems


Does that make sense?


yes


can I post a probelm


Unfortunately I have to go now


You can ask another coach for assistance though


Sorry about that


no worries have a good one


You too


Hello how is it going


What can I help you with today


Also give me like one min I need to do something real quick


Hello!


i really need some help practicing chain rule


Great! I can help with that


Do we begin with the first question?


yea let me start


im gonna try doing this on paper cause its alot of writing


Alright


Do I just check your work then?


Are you there?


yea im sorry i had to get paper


No worries


and yes


Okay cool


1a is correct :)


1b is incorrect


how so


There's an easier way to apply the chain rule


oh wait


Yes?


there


That still isn't correct but let me just double check


thats weird the answer key says its right


Nevermind you're right


I'm using the unsimplified version


ohh yea


i flipped it back


I was thinking you could just write it as (t^2+3t-1)^-1


And use the chain rule from there


yea thats what i did


Cool :)


and then i just flipped it back


to simplify


Just remember that you don't need to simplify for the AP exam :)


right


im gonna do the next one


Alright


how is that


One sec let me check


You're missing a negative


You carried over 2 instead of -2


oh yea woops


now ill do d


Sounds good


would csc^3 count as 2 functions


x^3 and csc


csc^3(x) is not equal to csc x^3


Just to clarify


csc^3(x) means (cscx)^3


yeaa


In this case it would be that


so its like csc is inside of x^3


thats what i meant


Yeah it is]


ok got it


this one is very long i think


Yeah...


i think thats good?


or wait i dont think its csc x and cot x


cause isnt x technically 3x/2


Let me check


It might be a minute one sec


I think that is correct yes


Should be csc(3x/2) * cot(3x/2) though


For that one part


-csc


yea i agree


yea its right nice


ill do e now


Cool :)


this one is rhe same thing


Yep


just sec


done


Yep that's correct


nice


how is f


Let me check


Wow that's long...


I'm just going to type my answer


cos(x^1/3) * (1/3 * x^-2/3) + (1/3 * (sin x)^-2/3) * (cos x)


looks the same


oh wait


i forgot to bring down my 1/3s


Yep thats what I noticed too


Good catch


i think i just do it in my head so quick i just overlook it


Makes sense


Next question?


yea sorry starting it now


No worries


do i use product rule here?


Yep


got it


I'll write my answer once you're done


there


This is what i got


yea got the same thing


is this also power rule


You mean product rule?


yea


yep


i think ill skip this one looks pretty easy


just alot of writing


Sounds good


ill do i


I agree with the first part


Not too sure about the other part


Need to check further


Nevermind


You're correct


let me find some new questions


ok


Not too sure what standard form form is


its this


Isn't that point-slope form


kind of but a little different


I see


Just moving over some terms


You just need to find the derivative of s(t) first using the chain rule


yea


But first find the y-coordinate when t = 2


That'll give us the point


right


so 4


is the y


Yep


So (2, 4) is the point


and now i need the slope


whihc is the first deriviative


Yep so find the derivative


so now id plug in 2 here


Yes


Yep 3/4 is the slope


So y = 4 - 3/4(x-2)


Oh is it 2-x


no sorry x-2


Still learning this new form


Oh okay


it already gives us the point


For b?


yea


(0, -2)


Just the same process as a


so product rule here


so


im getting


2 + -3


so -1?


Yep


Wait


Let me check


got it


?Wouldn't it be -2 + 3?


i dont think so


how


wait


oh yea


yup


it would be -2+-3


so -5


since the right side is 3(-1


Yeah


alright im gonna star 3


start


Sounds good


what do i do from here again


are you there?


hello


Hey Maria :)


I'm needing help on a question, I'll write it on the board


You should rewrite the left side so that the base is 3 instead of  1/3


I'm not sure how to solve it. The question asked to use the like-bases property


wait, isn't the whole expresssion x+6 the exponent?


that's all ive been able to get down to so far


yes


Yes, now you can go ahead and solve it.


im not sure how to


could u give me steps, i'll do them on the board


if the bases on the two sides are the same, you just set the exponents equal to each other


like that?


wait, why did you change the sign on the 6?


bcz the original function was +6


was it supposed to change to a negative?


Yes, but then you are using a negative exponent


so was it supposed to stay a negative or is it alright


alr, i see


You still have the wrong sign on 6


when you distribute the - sign into the parentheses it makes the 6 negative


is 9/2 correct?


no


where'd i go wrong


You need to divide both sides by 9 to get the x by itself


Sry, I dont know why divided by 2 instead


thats all i had to answer


thank you


I apreciate it,


You are very welcome


have a great rest of ur day, bye :)


Have a Happy Thanksgiving


bye


heyy


Hello!


how you doing


Not good


whyy


my homework


oh i see lol


thats fine this isnt that hard i know


so wait first thing are you allowed to use calculators?


Yes


Graphing ones


But I don’t have it on me


ChatGPT can’t solve this unfortunately


ok i think you prob arent allowed to use a graphing calculator but if you ever needed to you can use desmos


but i can help you with how to solve this


ok so first we always a x intercept and y intercept


so


so this should be your first graph


This is a bit hard to copy


you can ofc try to plug in -1 0 and 1 to get other points


Can I get the coordinates


Sorry


Not coordinates


yea so the y int bro is 6 and x int is -3/2


y intercept


is 6


and x intercept in -3/2


I’m trying to graph -3/2


just estimate it


On my paper but it’s odd


but put it on the graph and say its -3/2


Okay got it


yea


Okay second graph


this looks right


but


Like what I wrote already?


if you want you can make it more clear by showing the intercepts


that graph looks right but


the y intercept looks wrong


Shucks


mhm so y intercept should be -7.5


and x intercept is 16


it would be smt like that


Okay hold on


yea take your time


Okay I’m done with her


It


ok so next one?


Yes please


so again we just need to find the x and y intercepts


so that what it looks like


Okay done


Next one please


ok sure


youre right for this one


just one thing tho


you need to label the x and y intercepts


and that should make it perfect


Yippe


math for sure


well i hope so lol


Okay great


i know these graphs are correct


but it all depends on how your teacher decides to mark


if you want to make it better


you can pick a few points for each graph and plot those


to make it more accurate


Nah I think it’s okay he just looks at it and if it’s done then u did it


That’s all


ok great then


this is pretty accurate


Yeah


any more questions


No there is a back side to this but I literally would feel bad holding u up


So I shall figure it out on my own


i mean if you really do need help i can help you with it


i am free right now anyways


I mean u can work on whatever u want


I can show u


ok sure


Do u mind if I delete this photo?


go ahead


is there anything specific you want me to do or should i go thru all of them


Uh maybe thru all?


If that’s ao


sure lol


okay


give me a min i need to go grab smt


Yep ofc


ok back


wait i think i made a mistake for graph 2


It’s fine


that should be it


Uno


One second


yea take your time i need my voleenter hours lol


Okay I’m done!


ok nicee


is this it


Yup


One question


yea go on


Per chance do u have any pets on adopt me?


LOL i do have a dog


why do you need me to adpot


you


Shucks man


mhm


No no


I have a lovely family


oh thats good to hear i thought smt else


Do u know what I’m talking abt?


not really


lol sorry


Tisk tisk


How old are you anyway


im so confused


i am basically an unc atp i am 21


Ur just unc


YO


lool


Sorry


haha


its not that bad


Okay that’s all


Thank you for ur time


David have a great night


Enjoy ur night or day


you as well


Wherever you are


hi


Jamie


how are you?


good but i was trying to put sumthing on the board and it erased ittttttttt >:(


bummer


can you try again?


yea


ok I see a couple of ovals


yea it might not be perfect but i tried I_I


hey that looks good


it's a cylinder right?


yea i think I_I


you know there is an upload photo button


if that is easier


but I like your drawing


yea but its in my math book and it would prob be rlly bad quality lol


ok


are you trying to find the volume or surface area?


i have to find both I_I


ah ok


what dimensions do they give you?


wdym the numbers?


yes


im putting them


great


thanks


alr


nice work!


is 5cm the diameter or radius?


can u see my arrow I_I


or what looks to be an arrow


so it's probably the diameter of the circle right?


i think?


honestly i dont even know I_I


like it goes all the way across


yea it does


ok cool


so first we have to find the area of the base of the cylinder (the circle)


oki


do you know the formula for the area of a circle?


no


ok I'll write it on the board


It's a good one to put on a cheat sheet so you will remember it


ill make sure to add it to my list of formulas I_I


A is the area of the circle


= pi r squared


where r is the radius of the circle


so if 5cm is the diameter, the radius will be half of that


how much is that?


right!


oops it changed colo on me


yea same happened to me lol


but you get it right?


yea


so now we will need a calculator


do you have one?


ok put in 2.5 and then hit the squared button


oki


it usually says x with a little 2


i got 6.25


right! that's it


so now we multiply that by pi


now pi is about 3.14 but it's also in the calculator


let me know what you get


19.634 so on


exactly


good job


does the question say anything about rounding the answer


no it doesnt


hhm


then let's round to 2 decimal places


do you know how to do that?


yea i think


ok take the 2nd number after the decimal place


so 3


yes


and to figure out if we round up to 4 or just leave it as 3


we look at the next number which is 4 right?


is 4 greater than or less than 5 ?


no less than


right! so we round down


which means just leave the number as a 3


oki


so what will be your answer


you got it!


that is the area of the circle remember


oki :)


for the volume we need to multiply by something


what do you think we multiply by?


do we multiply the 19.63 and the 7?


yes! that's it


because 7 is the height


tell me what you get


ok great


but there is a little rounding error


oh i didnt round lol


well you rounded the 19.63 remember?


yea lol i forgot


we probably should have left it as 19.634.....,..


and then rounded just at the end


can you try that?


sure


just leave the 19.634... as a big long number


and multiply by 7


hhm


I got 137.445


did you do the 6.25 x pi again?


wait lemme try again


ok


yea i got 137.438


that's weird


it's close to mine but not exact


dats suspisious I_I


yeah, maybe we have different calculators


idk im using desmos


ah ok, I'm just using my phone


but we're pretty close


should i try the 3d calc instead?


no that's ok


you got 137.438 right?


well if we round it would it still be the same answer?


yes exactly


oki


to 2 decimal places what do you get?


if we go to 2 decimal places the 3 rounds to a 4


because 8 > 5


so it's 137.44


which is what I get!


let's go with that


maybe yours automatically rounds?


no mine had 137.445


NoPe nvm


I rounded down to 137.44


but we got the same in the end


yea


ready to do the surface area?


ok cool


so I'm guessing it's a closed cylinder with a top and a bottom?


yes


ok so we will have 2 circles


ok?


oki


and each has area 19.63 right?


but we have to add on the area of the sides of the cylinder


I shaded it in green


ya


ok so to find the area of that part we need to use pi again


alr


but this time we want the circumference of the circle


do you know the formula for that?


no


ok this is another one to add to your list


Oh no WhYYYYYY


circumference = pi x diameter


it makes it easier to remember for you tests


yea I know lol


so we know the diameter is 5 right?


yes


so we multiply that by pi


leave the answer in the calculator don't round yet


and the area of the sides will be 7 x 5pi


so i did 5 x pi right? i was suppose to do dat?


and now multiply that by 7


oki


oki i got 109.955


yes! exactly


we got the same this time


we add this to the 2 circles


to get the total area


so i put the whole thing in the calc?


35 pi or 35 x pi  ?


35 x pi


k


i got 149.215


great!


and what is that with 2 decimal places?


what happens to the 1 ?


yes!


good job


you're doing great


just try to write those formulas down so you'll remember them


oki


keep up the good work!


yessir


have a nice day!


u too bye


thanks


bye


Hello Chloe, how are you?


Are you there?


hi


its  quite laggy


plz wait


Okay


ill upload in a few minutes


its polynomial stuff


Okay, take your time.


canvas is verry lagyy


give me more time


its alot


Can you not take a screenshot of it and upload it?


i am


but its very very laggy


im tyring to collect alot of worksheet/ givens


Can you not screenshot 1 problem at a time?


its multiple pages


and my internets also quite laggy


yeah but can't you just screenshot 1 page


then upload it


and then when we finish it you can upload the next


oki ill try to do that


Chloe


to upload rn


Okay


Is it working?


The


one it's not a problem


no.


I


is


so


is a


for you know


Yes


I can't hear you well.


So basically the first is not.


it's not


and


she's not the one. This is a um, and this is not the.


So the first picture is


all


no um


decrease to or.


what do I take


bleeding therapist Dr. Evans is negative.


This is a


anomnia


like


I like


Sorry, could you type instead cause i can't hear you well.


But yes you are correct on 1-5


it's just um


yeah.


anyone reflected


Let's not the letter B because I'm gonna upload a new one


OK


There's, there's a new BMC.


There's a good.


Yeah, multi


Yeah, still is working to for 1. There a monomial


Liam is 6 or


or.


sick.


reading there is 10 X-rays of our 6 they publish negative.


Also, if you wanna hear me.


just uh


do the microphone at the side, so cause the transcription isn't that good.


I'm sure


but.


but


quite thick


Number 3


is quite thick


Quick


one


Mason


yes


i can hear you


uh


train on um


um


yeah.


what question are we on?


I don't know, monoia constant


degree


A


alpha


the left on the hill.


can you answer the questions on the whiteboard?


for


guys


4 Secon


Secon 2


is


value is


55 since it's positive


What do you need help with?


and I just need you to check my answer.


are you answering it on the board?


i cant see it


I


uh


I know my fallings yeah.


What did you say?


It's fine. I just my answer.


What question are you on?


Well, I'm, I'm already done. I already checked.


It's all right


It's not.


my abilities can still be tested.


So, uh, can we do this together? So the degree of the new is before


right?


for a number of zeros is 4.


The possible number of zeros is also for the left tail is.


rice


rice rice.


Am I correct


yes


Teacher, it's not rice.


OK. So, second is 3. So 3rd


degrees also and the number of possible zeros is also 3.


and since it's negative, it is all rise.


It is fall rise.


thats correct


fall, rise. OK, that's correct.


Second is


2 degrees zeros is 2 possible 062, and since it's positive, it is rise, rise.


And then the last it is positive and


just positive and


odd, so it's 5th 5 number of possible 065, the left a.


is


Professor Lee rice. I know


I.


I


right.


check


so that we can do the multiple choice yeah.


Oh, OK.


Right


trying to find the answer to right now. Give me a minute.


Yeah so


3 fix this


correct


Oh


wait, this is too. This is on the identification so.


for me


This is more for me


I think I can answer this.


OK, let's consciousness.


But I can do the graphingly because there is polynomial graphing.


here.


Uh, factors number one is fact.


Do


Sir


This is using coefficients.


It's


#3 is remainder.


Number 2 is synthetic.


division


less


rational root theorem.


5. It's uh


polynomial function.


What do you mean the theorem states that the remainder is equal to.


I remain their irran.


yes


You see that


its Remainder Theorem


or I


Let's see


Let's see, let's see


I know.


Mm.


right


It is just saying that When you divide a polynomial
𝑓(x) by x−a, the remainder of that division is f(a).


Synthetic


mean the rationalno remained there. I knew it. OK.


Let's do test 2.


Namo


I 3 multiple choice. let me upload this real quick.


You seem like you are very good at this.


Daniel Springfield


I am not very good at this actually I'm cramming this because


we have a very major exam, I think tomorrow and I'm just clutching.


I am think that for this.


I discovered that


my upper cheek is covered long.


ran out of space. No. Mm.


fine.


you know, it's clear is


Do you see the new


is, what is the good one to be.


to expression is that I know, you know.


Mm.


The device or the device or is a


um


How many sign changes are.


the


what question are you on?


maximum number of 30 maximum you manage it by 1 to 8.


6. The bleeding there.


Was the leading term of this, I have 9.


The leading time is a, let me check.


like real


quick


tore


B


A huh?


huh


Yeah,


it's like


She doesn't like. I, I already checked all of them. It's fine.


It's do the last.


bit of pain, which is grafting, and I know finding all the zeros of a polynomial function, then we can do graphing.


Oh my God


context one.


conflict squad


I


this


Uh


I think we can be done before 30 actually if I'm really, if I'm being really realistic, then you can re-drill this.


and uh can you teach me thereivatives.


some sort of you can like do a takeover because


that's here


divide the polynomial I


Mm.


one time and I'm.


I so


1 minute 6 and 76.


not.


knew my cycle.


Uh, it's not a factor.


The remainder is like the ocean's like


uh.


so it, so it's not, it's not uh


for 1.)


it's not I I think I'm a 6


OK.


and 7.


30. So there are remainders-630. And then so we remain there here.


That's it


Oh my God, we just have context one, OK.


for 1. the remainder is -30


Uh, oh my God


I'm asking like that.


let me upload it


and the quotient is Dr. Miller


OK


Let's upload this, yeah


The last part we have to do is graphing and we can do it all over again.


Like we can do like


we can do the moth test.


and then the mock tests in quite a while actually.


you know for sure.


Do it called find the actual zeros, OK, then.


Hm.


is still 18


in.


negative


which


9 + 15.


1503 is a popcorn, OK. We need 6. What about 2?


Uh


I know. What about positive though.


to.


3, negative. What? A 33 and 2. OK, found it very fast.


Can you answer the questions on the whiteboard?


OK, the, the X intercept is X + 3 X minus 3, and X minus 2. So


the bond is 30, 30 and 20 and the Y intercept method.


OK


X Y and behavior of the graph since it's a positive and it's an integer. It's fall and rise.


And then we have to find the zeros of this, so 3.


33, the power function, so it's an odd


so what does the X is just


a constant. The other one is processed over.


uh


T ET It's a tangent, but this is all, so it's a process, OK.


You found it. It's very fast, I think. I wanna grab and I wanna like have it by myself and I'll take, I take a picture.


um


Oh


I feel like I am not helping you since you already know how to do this.


if


0 is 18.


Are you sure you need my help?


uh, it's fine, but like,


it's fine


Uh, I just need some other check answers because the reason why I got all children at the first place because uh


good


um,


about


I don't know where I back you.


I've been trying to check but you have been going through it on your own and not doing it on the whiteboard.


I'm trying to grab.


nothing on the whiteboard, yeah, make it on the paper but like


the reason why I wanted you on the mics so we can. I can hear you, so I


actually saw


all right.


And just before


OK.


I need this


what


the area


we here.


Um


I


for.


and above


Oh wait, I get it now


one


It's negative where is it um


What is


So it's like an inverted W, just like, it's like a really


****** WU


Oh, I got it


Uh-huh.


that


I, I was able to do that.


minutes.


honestly, the act


ual


not the equation on.


that we can do the uh not that.


um


I.


sins.


and its.


Oh, so it does look like


thing.


I got it right. OK, let's go. OK, OK, OK. We're at


visit the official mas based on the ma.


I have time to kill cause exams actually tomorrow.


wait, before we did the mock test again. Can you teach me derivatives. I actually.


What about them


Do you have a problem on it or


Yes, I do have a problem because it's in the coverage, but it's not in the reviewer, but I've heard that.


be included in the time they made a big fuss about theirs from the other sections just because


uh


of the classes because


they were there they were able to take it uh


well a derivative gives the slope of a function at any point.


And the reason why they're elastic is I don't know how, but it just happened. And it's not an, well deliverative gives the slope of a function at any point, OK, so you can use the function that we worked with earlier. That's a, that's a good starter.


What is a derivative then? Can, can you help me define a derivative like do two questions at at least 3 questions so I can do the three questions so I can be sure when I'm going into tomorrow cause there might be there, but there's an other disk. We'll just do some work problems and then we do like half a moth test and be good.


here.


I uploaded it


It's like the slope.


a slope of a function at any point, OK.


Let's do this. So, since we already found the graph.


What do we do now


What is Leibniz and what do we do with all the prime.


so do you want to use this?


like, give me an example


The general derivative.


Yes, we want to use that.


do you know what the power rule is?


And also I'll start solving on, on the board right now so that we won't be any inconvenience for you OK?


We already kind of found the slope and the form was kind of like a bubby like that.


something like this


slowing down and going from something like this


thick letter N


So what can we


Chloe do you know what the power rule is?


I don't know what the power rule is actually.


but please light


Yes, I would like to


What is the


The power rule is if you have x^n then the deravitive is nx^n-1


so basically


The power rule is that if you have N


raise the bar and derivative is


what is at the number that you're trying to find, raise the part of


X


huh, wait.


OK.


So we have the power rule formula. So what do we do with those?


Yeah


I we.


so if you have x^3


the deravitive is 3x^2


But how do we get those kind of derivatives though.


So like


uh


so we


oh, OK, I get it, so


So if it was X, wait, I'll try to do it on my own


That's I was 6 and X-rays of our or let's try to do this.


So if it ends up being this how do we


so we move the numbers of 6.


X, raised by 5 like this.


This is what we do


like this


I wanna, I wanna remember this.


like this, so there's only do like in the that I'm doing right now, am I correct?


so


So.


how on me


like if you have


when you directly


the deravitive would be


Oh


and


Oh, OK. I, I get it now. Give me some random


what about


give me an easy multiplier number long like 3 to 5


I don't wanna make it myself and let's see


Give me a random number, he raised the bar too, so 2 minus 1 is 1, so it's the derivative of 3 x 2 is just 6 X, right?


Am I doing this correct?


The deravitive would be 6x


Like that's the formula actually, not gonna lie. Yes, OK, OK. I think we did enough. We have uh a few more word columns to do.


I just keep the derivative side on so that I can to review.


There is, in fact, uh,


a few


I would like to do on the stuff that we did earlier.


and we can do graphing and we're done.


its kinda what you do with logs


I can speed rent this in 10 minutes, so.


then Noah.


I


Give me a minute huh


problems that could have been.


the writing.


Here, I submitted it already. It's been uploaded but here there is activity


where is it?


2nd semesters being uploaded right now.


OK, it's currently uploading right now. It's above


You see it already? It's above.


Yes


Yeah, I can see that, so.


then on 1.988


divided by 2. 14 to 7


and


Can you do 1. on the board?


OK


so i can see what you are doing?


The area.


because


more


a square


and read by people on for 7, so we have 7 of the square to 7.


and we have to


this basically


2 square to 7.


or


OK, that's the first.


find the volume. Ah, it's just extra for plus X +4 plus extras for essentially.


we can do this


for


well for Xs just (x+4)^3


X.


8 X + 16.


Mhm


You can do this


Nexus for once again.


because


X


F


with Y


6, and in


6 times


degree.


Oh yeah


I


work in


for


different


different.


one


group


well, I, uh.


OK.


working


OK


I'm correct


Mm.


You can do the last part for me.


Could you work on the board?


See, I'm number 4.


84 is the path to.


dress


85 to


that uh


0, what's the.


still.


so


express


Duplicity of 3,


Oh, sorry.


Yeah


You have 2 eggs


are questions like


I did number one for but we can upload a new 2 and 3.


tier. I'm tired. I need a new


Could you work on the board cause i cant rly see what ur doing


um


right


here


Wow


Let's


voice


s


Could you work on the board? OK, I will, I will.


Or the first and last part, you don't really need to be working 2 and 3 is the one that you really need to be prioritizing on though.


have


uh


one


I


square root of 14 is 7.


and 7 and 2.


14. So the number one is 14.


yes


for the last


last


the


escape. Number 4 is 96. So if you ask me how I get 96. I just substituted the ax with the 4.


I'm gonna do the number


X + 6 X + 6 X + 6.


You're gonna have to do it manually.


Uh, I think I shouldn't do it here.


You could do this on papers because


they're more comfortable


its just expanding (x+3)^3


seats


x^2 + 12 x + 36.


We are multiplied this.


with


I know X 6 all again.


X


uh.


6 and 3.


uh


OK.


18 X square.


and.


6 and it


and then we just check.


my answer


and


time


I don't seem to know where I found it from.


for


his.


Mhm.


I.


I


Yes


are you stuck?


That's just the ecstasy X 6 + X.


So zeros of -1, so it's X minus 1 X.


OK


-1 is.


one


x^2 minus 2 x + 1.


A


3 to 3.


What do we do with the 3 then


OK, so it's just positive


Mm.


so you would do


I need more pain for her.


It can be done


Thank you


I have.


Hi! how can I help?


hello


plz unbadn me sa


mic isues


unban


mic


unfortunately I'm not sure if I can do that


its fine nv


1. polynomial function


rational root theorem


synthetic divison


remainder theorem


turning point theorem


remainder


Okay let's start at D Identify the correct term


the factor


factor ehorem


lets look at D: 4 again


facotr therem


thats in the asn key


also whats a quioent


yes thats right


answer


whats a quioent


im sorry could you repeat your question


whats a quioqent


oh okay


its basically the answer u get after you divide something


so 12/4=3 the quotient is 3


ohhh


do u have any questions in part D


how to factor


do u want to look at an equation and go through it to see how to factor


yea


okay


scroll down on the whiteboard and we can go through an equation


can u write down an equation from your work so I know what level of factoring you're working with


hello


hii


done :)


What is your question?


i put up the wrong question by accident


go ahead and give this a try.


i don't remember how to start :| do we start with adding the equations together?


You could do this most easily using substitution


Those are both in the form y=


so you can set them equal to each other.


any questions about that?


but for the equation we start of with it says y-3x=5


add 3x to both sides in that equation.  If you do that, what do you get?


ohhh oki


i understand now


Now you just have to solve the bottom equation for x.


so we add like terms


do you know how to solve equations with a variable?


not really


ok, add x to both sides.


oki


where did the 5x come from?


so what do i do with the 5 +x?


Do you have any like terms on the right side?


now you don't have any x's in the equation at all


3x and x are like terms, so you can add them.


you have three terms on the right:  3x +5 +x


the 3x and x are like terms, so you can add them.


Now subtract 5 from both sides


sorry, that's not right. I am not sure how you got x =2


You want to divide both sides by 4, so that x will be by itseld


itself


Don't use the division symbol for this.


yes, that's it.


is that the end?


That is the end!


okii


well i have to go now :)


Have a good week.


youuu too


byee


bye


Hello!


How are you!


How can I help you/


Hello sorry my computer works very slowly with this website. I will put the problem up


In advance if their is any time I am quiet for a bit. My computer most likely froze. I am still present


there*


Okay no problem!


Lets work on this problem


Mean and Standard Deviation
Mean (μ):
μ = (2 + 7 + 4 + 6 + 4 + 7) ÷ 6 = 30 ÷ 6 = 5
Standard Deviation (s):
First, find the squared deviations from the mean.


Can you do that?


Okay the stdev and mean I think I should be fine. It is the z-score I am having trouble with


Mean = 5


stdev = 2?


Sum of squared deviations = 9 + 4 + 1 + 1 + 1 + 4 = 20
For a sample standard deviation:
s = √[20 ÷ (6-1)] = √(20 ÷ 5) = √4 = 2


Correct!


Z-scores
Using the formula: z = (X - μ) / s = (X - 5) / 2


Okay


For number 2 is the z-score score -1.5?


My teacher often makes us find the z-score score in relation to the chart idk if I have to do it for this?


That's correct!


Transform to New Sample (M = 50, s = 10)


Using the transformation formula: X_new = M_new + z × s_new


Should I look for the z-score score on the z chart ?


Yes go ahead!


Okay, would I like internally on the z-chart or externally?


i am currently preparing for a math 2 Chapter 4 retake, which I failed the first time, because I do not understand the topic.


Hello, are you there?


Ben!!


Yes hi*


ohhh haha hi!


did you get my message about what I needed help with?


I saw this message.  But you'd need to tell me what you are working on exactly.


and if you have practice problems, you can put them up.


Does it have to be a specific problem or can it just be a certain concept?


I can help with a concept as well, but it's just more helpful if I see a problem and can explain it.


Okay let me find it


should i send some of the notes i have and we can make practice problems?


okay, we can start with that.


thats some of them


ok let me look a minute


okay


Which one do you want to start with?


can we please begin with ex. 1 on notes 4.6


i get confused with the imaginary number (i)


alright yes


it's confusing because it's odd.  anyways


for a) it's the square root of -25.


which you cant have anegative square root right, it'd be no solution?


so sq rt 25 times sq rt -1


there is a solution- it's an imaginary solution.


Yes, normally you learn that you can't take the square root of a negative number BUT with imaginary numbers it's possible to do it.


oh okay


do you think youre able to come up with a problem similar for me to try and solve on my own


ok


try those, okay?


hmm 4 times 2 times I?


should I show you?


im trying to figuere out what two numbers numtiply to 18 that make a perfect square but i dont know.


You would use 9 * 2, because 9 is a perfect square.


no sorry


I'll explain


ohhh]


can i please have a new problerm just like that to try again


sure.


ohh hm.  This isn't right but you are getting the idea better.


You would be able to break down 24 into a perfect square times a number.


I'll let you try a little before I tell you.


the perfect square isn't 1, it's ___


uhhh


yes


like that?


yup!


yay! thank you! I have to go for the night, nbut thank you soi much fir the help!!


Glad I could help ! have a good night.


Hi! How can I help?


Hey! So i have this assignment where i have to solve for X and like figure out some angles to find which ones are alternate interior and those types of questions give me a second to show you


Take your time! I'll help you once you're ready


Okay, would you like to go through all of them together!


yes please


Alright!


So we know A and B are parallel


And so are C and D


yea


Okay so because line C is a tranversal


cutting through A and B


Angle 2 and angle 6 are corresponding angles, and corresponding angles are the same!


making angle 6 also 40 degrees!


ohh!


oh cause corresponding angles are congruent to each other right?


Yes!


and then looking at it again now that we know what angle 6 is


Lines C and D are parallel and line B is our transversal.


angle 6 and angle 11 are alternate exterior angles, meaning they are congruent to each other as well!


ohh


Let me know if you didn't understand anything for this one!


also i don’t really understand how angle 6 and 11 are alternate exterior


Okay let's go through it again


Exterior angles are angles that are on the outside of the parallel lines


Take a look at what I'm drawing


looking at this, what angles are on the outside of the parralel lines


OHH i understand it now


great!


are you ready to move on to the next question


yes


Take a look at angle 5 and 7


What is the relationship between these angles?


We can see that they both lie on a straight line


uhh i forgot the name of it


i know what it is i just can’t remember what it’s called


That's alright


linear pair?


Yes!


You can also refer to this angle as supplementary


meaning they both add up 180 degrees


ohh


Knowing that, does anything come to mind on how you could solve for x?


If not just let me know and we'll work through it


maybe adding both up and equal it 180?


yess!!


Would you like to set up the equation and try to solve it?


yea i can solve it give me a second!


take your time!


would it be 27.5?


Yes!! Good Job!


yay!


Let's take a look at 3 now


This one involves a couple of steps! It's slightly more complicated then the other two we did


Look at angles 3 and 8, what is the relationship between them


linear?


Nice try! They are same side exterior angles


ohhh


Same side exterior angles are always supplementary!


How do you think we can solve for x in this case!


so adding both up and equaling it 180 ?


Exactly!


Go ahead and solve for x


um so i got a decimal so im not sure if its correct but it was 17.18


Yes!


Quick question for clarification? Based on what your teacher has told you does this question give 2 pairs of parallel lines or just one


i think it’s 2


okay great!


she doesn’t really explain the assignments so we are just kind of figuring it out ourselves


Thats alright! We can figure it out ourselves!


We got 17.18 for X, let's find angle 8 now


plug the value of X into this equation to get angle 8


That's the measure of angle 8


We need to find angle 9 and 10


what's the relationship between angle 8 and 9


so angle 9 would equal 96.26 since they are congruent (alternate interior)?


yes! exactly!


what about angle 10?


uhh i’m not sure on that one


Let's take a look


angle 8 and angle 10 are same side interior angles


So they're supplementary


Here's a trick my teacher taught me a while ago


Same side interior/exterior angles are always supplementary (they both start with S)


this is so much easier to remember


It is!! Now that we know they are supplementary, what do you think the measure for angle 10 is?


i’m guessing also 96.26?


i feel like i might be wrong though


Since they're supplementary, that means they add up 180


We already know angle 8 is 96.26


So angle 10 has to 180-96.26


oh wait i have to subtract 180-96.26


Yes!!


so 83.74


yess!!


let's take a look at 4 now


I want you to try solving it, and if you get stuck let me know and I'll help you


Okay!


i’m done so basically what i did was that since it was linear pair i added both up to equal it 180 getting me to 30 and after plugging it both in to the equations i got 70 for angle 2 110 for angle 5


That's correct!! Good job!!


for question 5 i kinda did a bit earlier before i asked for help


Thats great! Let me know what you got so we can check!


i got 3≈14, 4≈13, 7≈10, and 8≈9 but i’m not sure


That's correct but we have a few more!


If you look at line C as the transversal, we have 2 and 7 as alternate interior angles too! And it also mentions that in question 6


We already found 5, there's 3 more, let me know once you have them


ok!


i got 11≈14, 16≈9, and 4≈5


Yes!! now we have 8 in total!


You're doing great!


Let's look at question 6 now


They are alternate interior angles


Knowing that what do you think the relationship between the two


they would both equal to each other?


Yes!!


Try solving this question, I'll be here to help if you get stuck or don't undersand


i’m having a bit of trouble trying to solve it can you help me?


Yes of course!


i made it to x^2-x-24=0 but that’s where i got stuck on


I see okay


Now we have to factor it


but it seems that its not factorable by whole numbers


we need to use the quadratic formula


have you learned that yet?


yea i learned it last year but i remember very briefly i think if i have the formula i can solve it


Try using this formula and let me know if you get an answer!


ok!


for the positive one i got 5.4 and for the negative one i got -4.4


Yes!


this is about angles, so we can't possibly have a negative number


so we plug in 5.42 into the equations to get the answers!


oh ok!!


Let me know once you're ready to do question 7!


oh yea i’m ready!


Okay, this one is also very similar to question 6


so then i can try to do it on my own


Sure go ahead!


Let me know if you get stuck


i got 3.85 for the positive one


lets solve it together


ohh wait i forgot to plug it in


for angle 2= 42.64 angle 15=30.67 but i think it’s still wrong


when u solve for x you get 2 answers


and they're both positive


oh actually? then i did it wrong


basically when you plug it in you are supposed to get the same answer for both angles since they are congruent


oh


if you scroll down on the whiteboard, I put the steps to solving for x


ohh i understand it now


I'm not sure how your teacher would want it but since we get 2 answers maybe put both..?


Or since angles 2 and 15 appear to be less than 90 degrees maybe you'd want to put the smaller one I'm not quite sure


Is there anything else you want to go over?


no


alright! let me know if you have any questions


i’m finished with my assignment thank you so much you are the best and the sweetest tutor i’ve had thank you again🤗


No problem! Thank you! I'm glad I could help1


Hi, how can I help you


hi I have to solve word problems over probability and i'm kinda clueless


Slips of paper numbered 1 through 15 are placed in a hat. In how many ways can two numbers be drawn so that the sum of the numbers is 12? assume the random selection is without replacement


ok so for this one you want to think of what combinations of numbers can add up to twelve


remember you can't repeat the numbers


to see it visually maybe try pairing these numbers together in pairs that add to 12


what do I do after


so once you have how many possible pairs there are


that will be your answer


Yup! you got it


are there any more problems you would like help with?


yes


you're taking a 20 question quiz, 12 of them are true/false, the other 8 are multiple choice (a,b, c, d). How many different possible answers are there?


so for the true/false questions you have 2 answers each time, now everytime you have another one of these questions you multiply the number of possibilities by 2 again


similarly for the mcq portion its 4 possible answers per question meaning each time another theres another mcq the number of possibilities mulitplies by 4


would you like me to explain further?


how would that look


so if you continue to do what I did on the board for all twelve questions


how many possible answers would you get for the true/false section


Yes!


yay


now you just multiply that with a calc and you have your final answer


do you have any more problems?


a child returns a five volume set of books to a bookshelf. The child is not able to read and cant distinguish one volume from another. WHat is the probability that the books are shelved in the correct order?


alright so for this one you want to think of each book individually at first


what is the chance that book 1 is placed in the first spot


wait im sorry actually theres a better way


you want to think of how many possible outcomes there are: so the first book can be placed in any five spots, the second in any 4, third in 3 and so on


to find the total number of possible outcomes you do something similar to the last problem and multiply each books possible outcomes together


so what would the total number of possible outcomes be?


now how many of these possible solutions is correct


um 30?


not quite


how do I know


for each book to be in its correct spot thats exactly one solution for each


you can do the same thing you did to find the total possible, to find the number of favorable, mutliply the number of favorable outcomes for each book


um I lowkey don't understand


ok wait lemme do it on the board


so 5?


no remember you are multiplying not adding


so if you continue to do this, multiplying by the number of correct solutions for books 3, 4, and 5


what would you get


oh so 1?


yes!


now to get the probability


you divide the number of "correct outcome" by the number of total possible outcomes


yess


good job


thank you thank you


that's all


ok great


have a great day


you too


Hi Chloe! What do you need help with?


It's finding the percent


alright, just send me the problem


Can I upload the picture on the whiteboard?


yup, no problem!


ok then


lets work through it together


so we know there are 28 well-done burgers and 12 medium burgers


and we want to know how many of them are well done


so first lets find the total number of burgers


what is that?


right!


and how many are well done?


right


so would you agree with the statement that 28 out of the 40 burgers are well done?


Yup


and would you agree that this equals to the fraction 28/40?


Yea


ok, so if we look at the word percent, it means per one hundred (cent means 100 in Latin), so we want to find how many well done burgers there would be out of total burgers


this means we want the denominator to equal 100 so we have to turn 40 into 100


how could we do that using multiplication and division?


40 can be equal to 100?


no it cant, but we have to turn 40 into 100


so how could we do that using multiplication and division?


Im so lost


ok, so are you comfortable at the point that we reached 28/40?


yea


ok, and we need to make it an equivalent fraction that is some number out of 100


to make a percent


do you know how to make fractions equal?


Yea multiply by 2 if I remember correctly


sometimes that works, but the main rule when making equal fractions is whatever you do to the top you also do to the bottom


so lets look back at this example


if I wanted to get from 40 to 100 what I could do using multiplication and division is


I could divide by 4 and then multiply by 10


do you agree?


Yea


and remember, whatever we do to the top, we also do to the bottom!


so we also have to divide 28 by 4 and multiply by 10


28/4 = 7, 7x10 = 70


so now we can say that 28/40 = 70/100


oh so we break the denominator down if it cant be turned into 100?


yes, you have to find a way to make the denominator equal to 100


through multiplicatino and division


and whatever you do to the denominator you also have to do it to the numerator to keep the fraction equal


let me show you a simple example


do you agree that 1/2 = 2/4?


Yup


so on the bottom we are multiplying by 2, so we do the same on the top


and if you think about it we are multiplying by 2/2 we are saying that 1/2 x 2/2 = 2/4. Would you agree with that?


and do you agree that 2/2 is equal to 1?


and do you agree that multiplying anything by 1 keeps it the same?


and thats what we are doing here


whatever we do to the denominator


we do the same to the numerator


so going back to our question


do you agree that 28/40 = 70/100? or is there a part you still don't get


I see it a little better now


just to summarise


what we have done is divided by 4 and multiplied by 10 to make 40 into 100


since percent means per one hundred


and then whatever we do to the denominator we do the same to the numerator


and so 28/4 x 10 = 70


so 28/40 = 70/100


do you see that?


Yea


alright so now we are on the last step!


do yk how to turn a fraction into a percentage


ok, so what is 70/100 as a percent?


right! thats the answer


you just have to keep practicing how to make the denominator 100


and then doing the same thing on the numerator and denominator


and you've mastered it!


ok have a good rest of ur day! enjoy solving more problems


Mr. Jones too


hey Sam


1. 2. 3. let's go


hey


what help do you need ?


this


so yea


e


Sam


okay, 6 multiply 2


then divide by 3


Hi how are you?


Hi Alex


Hello


How are you?


im good how are you


Good thank you


ok so u need help with this question


do u know what apr is?


Can you help me with this problem?


Yes interest rate


yeah, the annual interest rate


Yeah


so if the yearly rate is 14%, can u try to think of how we get the monthly rate?


no worries if ur unsure, but try first


ok so 0.14 is just 14% as a decimal


ok


but it's for the year, and we need for the month. there are 12 months in a year, so it is 1/12th of the yearly rate


does that make sense


yes


ok so can u tell me what the monthly rate is now?


here i put it up on screen


ok its 0.0.0117


good


thank u


ok so do u remember the formula for interest?


no i dont


ok it's fine


so usually theres a pretty complicated formula


but i feel like they wouldn't use that formula here


what grade r u in?


Lincoln High


oh ok


oh same


what math class is this for?


like whats the name of the math class


Jackson High yet


okay nice. its my first semester, and the class is Algebra 201


Northwood College 2 years


ok


yeah hold up im just thinking about what way we would solve this since u don't have the formula


im looking online for the formula


do u have an answer key?


I think for the simple interest its =P r t= Principal x rate x time


ok yeah thats what i was thinking, that it's either simple or compound interest


ok so lmk if u have an answer key so then i can figure out which formula they used by looking at the answer


and for the compound interest formula(once a year) A=P x (1+APR/n)^ny


but otherwise we can just do simple interest first


okay


aight this is hella annoying cuz i really don't know about the class ur in but ok lets just start it


wait


this is formula i think


the number in that image u showed don't match up to the numbers you typed out


this is an example


ok lets just use this formula then


so all we have to do is just plug in the values


okay thanks


do you know what P, APR, n, Y are?


yes p=4400 apr 0.22 n=12 years =6


this is for the example


ok cool


what about for ur actual problem?


p=4200 apr=0.14 n=12  years=2


yeah good


so then when you plug those into this equation with a calculator what did you get?


let me plug them


just one min


nice


i mean i got.65


but yeah


thanks


wait but that's the PMT


oh wait yeah that's the monthly cost


nvm


ok


ok so do u think u know how to do part b?


i dont really have a idea


ok so if we pay that much monthly, and we have to pay for 2 years, how much would we pay total? do u think u can guess


Below is an example


yeah


monthly payment multiplied by 24 cuz there is 24 months in 2 years


ya


what did u ge


i got.70


think it's cuz you rounded it


i didn't round so mine is more accurate but it's fine


okay cuz i got.66 and i think you got.65


yeah i understand


thanks again


yup


so what percent of our total payment is interest


do u have an idea of how to get this?


i think we need to divide right?


yea


what do u think we have to divide?


no


okay i think switch


we need to know our interest relative to the total payment


not our total vs principal


neither


okay my bad


you're comparing total and principal


we need to compare total with interest only


how would we do that?


I don't have any idea


ok so whats our total


and whats our interest only?


yup and what is this


so now what do we divide


thats interest


interest/balance


i dont know


if that correct


divide the interest by total


4200 right


your interest 639.84


total 4839.84


okay the total of the interest and the balance


so get the rate by dividing it


yeah good job


okay thanks


ok so those were the 3 parts of this question


anything else?


i understand the mathmatical problem but i have difficulty understanding what the question is asking. but thank you so much for your help and the time


oh ok


just rethink the steps we took to solve


good job


thank you so much


ok bye


have a great night


hello


I was wondering if you could help me with polynomial long division?


ok.  do you have a problem that you are working on?


Yeah. Would you like me write it on the board?


sure


Sorry my computer is being really slow about this so I'll try to type it out.


(x^3 + 2 x^2 - 5x + 16) divided by (x-4)


Do you think you could help me with it?


are you using regular long division or synthetic division?


Long division, that is the one I struggle with.


You aren't able to write on the board, is that right?


I mean i can it just lags a lot causing me to mess up the writing.


What would be the first entry in the quotient, do you think?


I think i would have to start off by doing x^2 that way when i multiply it by x-4 it will get me x^3 - 4x^2


right.


so then what do you do next?


I would do x^3-x^3 - 4x^2 and since 4 times x^2 is 4x2 I need to do 2x2 + 4x2 since were subtracting and it is a negative number it turns it into addition


x^3-x^3 = 0 and 4x2 + 2x2 = 6x2


The I bring down the -5x


I put up top + 6x that when when i multiply I get 6x2


and 6 times 4 = 24


That's not quite right


negative?


Yes, because it is 6x times -4


Oh! Ok


so then 6x2 - 6x2 = 0


and would the negative 24 turn into a positive? since were subtracting?


yes


Turning it into 19x


Bring down the 16


Could I do 19x on top? Or do I do something else?


try it


Sorry not 19x but 19


I assume that you are also doing this on paper.


Yes


I would have a remainder of 92


I didn't get what you are doing.


I did 19x - 19x


got 0


19 times -4 got me76


16 plus 76 is 92


You mean -76, right?


Yes but it turns into a positive because we are subtracting


ok, that's right


So i end up with (x-4) (x^2 = 6x = 19) = 92?


opps ignore the =s


They are meant to be +s


Yes, you can write it either way.


Ok


I have one more problem if that is ok?


Same kind of problem?


Yes


Perhaps you should do it on paper and let me know what you get.


what is the problem?


(3x +2) (9x4 + 3x2 + 4x2 + 7x +2)


Oh, you are multiplying this time, is that right?


Oh I am sorry it is division I forgot to put that


(3x + 2) then divide it by the other number


no, you don't mean that


Surely, 3x+2 is the divisor, not the other way around


The (3x + 2) is on the outside yes


Yes, this term is called the divisor.  go ahead and give it a try.


I think you made an error writing it.


That is what the problem says


3x^3 probably, not 3x^3


not 3x^2


Oh yeah sorry I thought you wrote on the board what I wrote


Sorry


I got (3x^3 + x^2 + 2x + 1) (3x + 2)


Almost. You have a sign wrong


Do you see it?


No, I am trying to look for it


3x^3 - -6x^3... ?


yes


Oh


Any questions about that?


No, I understand it I think I just need to pay more attention to my positives and my negatives


Doesn't everybody1


Thank you so much though! I undertsand it a lot better now!


Yes, I think you do.


Have a good evening


You too


hi


Hi Alex.


How are you doing?


I'm doing good. How about you?


Great, thanks!  Would you like to upload a pic of the problem you're working on?


today all I need is for you to check my answer to 1 question


I had to find the number of lines of symmetry for the picture on the board. I think it's 2


i see a couple more.  do you want to draw the lines you found?


good.  now can you try to find a couple more?


looks good to me :-)


so there is 4


yes


ok. I was unsure because when I used AI to check it said "this particular bubble-style “x” does not have diagonal lines of symmetry. Because of its rounded, stylized form, the arms aren’t perfectly straight or identical at 45° angles, so the diagonals don’t produce mirror halves."


hmmm.  you can always print the picture, cut out the x, fold it in the 4 ways, and see if they perfectly line up on each other.


maybe AI is trying to be to extremely exact, and that is probably not expected from your teacher.


looks like you're away, so good luck.  it'll be interesting to see what your teacher says


Hello! What's up today


how do I solve this?


So you're going to want to multiply all of the numerators, and multiply all of the denominators


ok


That's how you multiply with fractions! Want to try?


Put your answer in the chat or you can write it out on the board whichever you want


sorry I am not in a place where I can have the camera on.


No worries I meant you can write the answer in here we aren't using microphone


-5 x 3 x 4 and then 12 x 7 x 9


What steps did you take for that answer?


So do I multptly it all to get a comom demnontar?


So, for multiplication with fractions we don't need a common denominator! That's only for addition and subtraction of fractions


oh ok


So for this problem, since we are multiplying fractions, we can just multiply the numerators and denominators seperately


how do we do that?


I can show on the white board


Multiply those numbers top, then bottom!


Good! But remember, the 60 is negative so -60


Because the first fraction is -5/12, the negative only goes with the 5, so when you multiply it's -5


thanks


So now we have to simplify the fraction


sorry have to go know y moms here to pick me up bye.


Sounds good! No worries, have a nice day/night.


bye


I need help with this.
The water slides have 31 temporary employees and 31 permanent employees. What percentage of the employees at the water slides are temporary?

Write your answer using a percent sign (%).


Ok so let's start by finding the total number of employees


so What would that be?


Ok so it has 31 temporary employees and 31 permanent ones


so 31+31 is?


Yes ok


so that would be the total employees


and then the question asks for the temporary employees


so we can do a fraction


so what would go on top?


if we are only looking at temporary employees


yes exactly


if we simplify the fraction


what would that be


Hmm not quite


I guess if you look at 31/62


isn't 31 just half of 62?


si


Ok so the simplified version of the fraction would therefore be 1/2


right?


So in percentage, what is 1/2


exactly


Do you have other questions


no but thank you anyway


Ok no problem


bye bye


Hi! What can I help you with?


ayuda con el 62,5% de 16


Hello


Hola


Ok, I can help you with that


Ok what is 62.5% in decimal form?


Ok and then you can multiply that by 16


Let me know once you have finished that


Ok


So 62.5% of 16 is ?


Yes!


Do you have any other questions?


yeah I also need help with this 52.5%	 of 40 =


Ok same thing


what is 52.5 in decimal form


Yes


And then multiply 0.525 by 40


which is?


so 52.5% of 40 is 21


Any other questions?


no but thank you anyway


Ok no problem!


bye bye


Have a nice day!


hello


Hi! I have a specific equation that I cannot figure out. I was wondering if you can help me with it


ok sure


I think that this is a linear function


ok


so the 720000 part is right


that is the initial revenue before the price increase


for each dollar or x they 3500 customers


ah


wait


the price is increasing too


please give me a moment I'm working it out


ok no problem


are you allowed to use a calculator for this


yes


ok a couple more moments


I believe I got it


ok so first I found 5 point


(0,720000) is the first point right


60000 people at 12 each


Is it supposed to be in point formula?


no what I did is found a couple of points and then used the list feature on my calc


oh ok


unfortunately I think that the quad regression is not what the question is looking for


the numbers are too precise


how were you able to find b


I did like (12+x)(60,000-3,500x)\


oh what nvm


I typed a number in wrong and now I have the answer


sorry for the trouble


so you know how I found the points right


not really I'm a bit confused


ok so when the price is not increased there are 60000 people each for 12


this is 720000 in revenue


oh ok got it


if the price increases by 1 there are now 56500 people each at 13 which 734500 in revenue


I just continue to subtract 3500 and multiply by the increased price


after I found 3 point I hit stat on my calc


typed in the points


then hit stat calc 5


calc


and -3500^2+18000x+720000


wait


that has been marked wrong


yeah... that's why I'm confused


well you can use that quadratic to find the max of the function which you did so I struggle to understand as well why that is not accepted


what does it say when you hit the exclamation point


wait so its showing the correct answer and you got it wrong previously?


no it doesn't tell me the correct answer


so you got what I got?


yes


why is it saying you answered that then


idk I think it's a formatting thing. I answered the equation in the text box above, the same one you got