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welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 2 . make this into a 7 . negative times negative is positive . so you have 7 . | are you supposed to flip the negative sign when you make the reciprocal ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus... | how would you figure out x - y = -1 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do . | why do you have to flip the number 3/4 to 4/3 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do . | when you do the recipricol of negitive 3/4ths why is it still negitive ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do . | how does -3/4 simplify multiply by its reciprocal cancel out ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | why those equations are called linear ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | turn this into a 4 . make this into a 2 . make this into a 7 . | what 's a `` reciprocal '' ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 7 . negative times negative is positive . so you have 7 . | is the x intercept equal to the y intercept times the negative inverse of the slope ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 7 . negative times negative is positive . so you have 7 . | i thought when you do a reciprocal you take the negative sign off ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus... | when solving for the equation `` y= -1/3x `` and you are solving for y how would you plot that on a graph ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do . | why did n't you simplify the 3 and 39 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so we get x is equal to minus 40/39 . and i like to leave my fractions improper because it 's easier to deal with them . but you could also view that -- that 's minus -- if you wanted to write it as a mixed number , that 's minus 1 and 1/39 . | why do you switch fractions ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | turn this into a 4 . make this into a 2 . make this into a 7 . | what is the binomial that must be subtracted from 2a^2-5b^2 to get the monomial 3a^2 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so rewriting it , if i had 5x equals 20 , we could do two things and they 're essentially the same thing . we could say we just divide both sides of this equation by 5 , in which case , the left hand side , those two 5 's will cancel out , we 'll get x . and the right hand side , 20 divided by 5 is 4 , and we would hav... | do you always divide both sides of the equation by the same number ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and i like to leave my fractions improper because it 's easier to deal with them . but you could also view that -- that 's minus -- if you wanted to write it as a mixed number , that 's minus 1 and 1/39 . i tend to keep it like this . | could you also simplify 3/39 to 1/13 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | for algebraic equations if the letter used to represent the factor or multiple , then why do teachers freak when you use 'the wrong letter ' ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | what is ure secret of teaching ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so this is just saying 5 times x , so instead of a question mark , we 're writing an x . so 5 times x is equal to 20 . now , most of you all could do that in your head . | if x= 1 1/20 , then how does 5 x=20 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | if you do that on the left hand side , we have to do it on the right hand side as well . minus 6/5 . the left hand side , the minus 6/5 and the minus 5/6 cancel out . | because 1/20=5/100 or 0.05 x 5=.25+5= 5.25 right ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | this becomes 4 . 7 times negative 3 is minus 21/20 . and assuming i have n't made any careless mistakes , that should be right . | what is the weight to the nearest pound of a person who is 64 inches tall and has a body mass index of 21.45 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m... | if we are going to be using a dot for multiplication for now on instead of an x then why they do n't just teach us multiplication as a dot from the begining of first grade ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | if you said 5x equals 20 , instead of dividing by 5 , we could multiply by 1/5 . and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 'r... | how do u know when to split the # in half ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do . | wait , is n't the reciprocal of -3/4 +4/3 , not -4/3 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and the right hand side , we have , well , we can divide both the 6 and the 8 by 2 , so this 6 becomes negative 3 . this becomes 4 . 7 times negative 3 is minus 21/20 . | if x is 4 and 4*5=20 , can you use variable in division ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so the coefficient , all that is , all that fancy word means , is the number that 's being multiplied by x . so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times... | say when you are doing the reciprocal of -3/4 should n't the negative sign be removed and it be 4/3 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and the reason we do the notation a little bit -- we write the 5 next to the x , because when you write a number right next to a variable , you assume that you 're multiplying them . so this is just saying 5 times x , so instead of a question mark , we 're writing an x . so 5 times x is equal to 20 . | if 3x -1=11 , what is the value of x^2+x ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . | a student pushes a box 5.0 m across the floor using a constant force of 20.0 n .how much work does the student do on the box ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m... | why is the dot only used sometimes and other times not ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | actually , let 's do one of those right now . so let 's say i had negative 3/4 times x equals 10/13 . now , this is a harder problem . | why did n't you try to find the greatest common denominator of -4/3*10/13 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 2 . make this into a 7 . negative times negative is positive . so you have 7 . | why does n't the 1 or 7 become negative when you simplify does n't the sign carry over ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so if we multiply the left hand side by negative 4/3 , we also have to do the same thing to the right hand side , minus 4/3 . the left hand side , the minus 4/3 and the 3/4 , they cancel out . you could work it out on your own to see that they do . | why does the 4 0ver 3 become a neg number ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | turn this into a 4 . make this into a 2 . make this into a 7 . | what is the solution when there are two variables , for example : 2 ( x-2 ) < 2/3 x p.s.- is there a video for those type of equations ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 7 . negative times negative is positive . so you have 7 . | how do you divide a positive fraction with a negative fraction ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so the coefficient , all that is , all that fancy word means , is the number that 's being multiplied by x . so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times... | if the number is fraction with a negative ie ; -3/4 , should n't the reciprocal be 4/-3 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so 5 times x is equal to 20 . now , most of you all could do that in your head . you could say , well , what number times 5 is equal to 20 ? | could someone explain what a recprocle is ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | why is is linear , not just a regular equation ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus... | why can the 4 become a 1 and the 40 become a 10 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | how would you do a linear equation with fractions , decimals , negatives , positives , and percentages all in the same problem ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer . | what are systems of equation ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | did anyone else notice the mager change in font size ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer . | how do you write an algebraic equation when you are trying to find two numbers ; when you know their difference ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | let 's check to make sure that 's right . the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . | what is the purpose of algebra and where in life will it be beneficial ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer . | how to write an equation in standard form ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | and if you look at that , you can realize that multiplying by 1/5 is the same thing as dividing by 5 , if you know the difference between dividing and multiplying fractions . and then that gets the same thing , 1/5 times 5 is 1 , so you 're just left with an x equals 4 . i tend to focus a little bit more on this becaus... | why did you need to divide by 1 over 5 to get 4 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | how do i apply systems of linear equations ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | you could work it out on your own to see that they do . they equal 1 , so we 're just left with x is equal to 10 times minus 4 is minus 40 , 13 times 3 , well , that 's equal to 39 . so we get x is equal to minus 40/39 . | why not reduce the 3 to 1 and the 39 to 13 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer . | is x = -2 considered a linear equation ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | how did human lifeform begin ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so you have 7 . 2 times 4 is 8 . and that 's what we said we would get . | my problem is -8 = y/-8 ( that 's y over -8 ) my problem is..i understand why y= - 64 but why does the book say it equals 64 ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | let 's check to make sure that 's right . the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . | is algebra important in high school ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m... | how can a dot mean times ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | how old is john now ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | when solving literal equations would i just replace the numbers with variables ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . | where can find test problems for level 1 equations ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | how do you check equations when the variable is in a fraction ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 7 . negative times negative is positive . so you have 7 . | my question is..when you do the recipricol of the first fraction , and the bottom denomenator is a negative , then why is it when you make it into a recipricol , the numerator becomes a negative ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | are linear equations always straight ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | well , we do the same thing . we multiply both sides by the coefficient on x . so the coefficient , all that is , all that fancy word means , is the number that 's being multiplied by x . | is it important to divide both sides by the no given on the numerator or we can just shift the numerator to the r.h.s ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular multiplication sign gets confused with the... | why does multiplying/dividing both sides of the equation with a ' # ' lead to solve a variable value ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | make this into a 7 . negative times negative is positive . so you have 7 . | why do you only use negative numbers when giving examples ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | the cool thing about algebra is you can always get your answer and put it back into the original equation to make sure you are right . so the original equation was minus 3/4 times x , and here we 'll substitute the x back into the equation . wherever we saw x , we 'll now put our answer . | what is the astigmatism of 8x-5xb if the linear equation of the equation is less than the mean of the solution ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | welcome to level one linear equations . so let 's start doing some problems . | so what does the repicle mean ? |
welcome to level one linear equations . so let 's start doing some problems . so let 's say i had the equation 5 -- a big fat 5 , 5x equals 20 . so at first this might look a little unfamiliar for you , but if i were to rephrase this , i think you 'll realize this is a pretty easy problem . this is the same thing as sa... | so what 's the reciprocal of minus 3/4 . well , it 's minus 4/3 times , and dot is another way to use times , and you 're probably wondering why in algebra , there are all these other conventions for doing times as opposed to just the traditional multiplication sign . and the main reason is , i think , just a regular m... | i don '' t get how a dot can be times ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so this is the focus right over here . so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus . so that is the -- let me make it as close as possible . | 0sal says the centre of curvature is twice the focus can anyone please prove it ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses . so that 's a parabolic mirror . i 've drawn its principal axis right over here . | does that mean that if you stood in front of a parabolic mirror in a fun house at the focus , you would see no image of yourself at all ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and so now the image is bigger than the original . so the image is real . and it is bigger . | when the object is in front of the mirror you get a real image , now why i see the reflexion in the mirror ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and the reason why i want to do there is because there the parabolic mirror is essentially flat and essentially vertical . so you can imagine that the incident ray is going to be the same thing as the reflected ray . so you could draw a ray that comes in like that . | if an incident ray were to go through the center of curvature , would it 's reflected ray go directly back along the same path it 's incident ray took ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus . | what exactly is the center of curvature ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | these lines are the hardest thing to do . so parallel incident ray , parallel to the principal axis . this is the principal axis right here . | however , what if you drew the ray downwards , towards the very center of the parabolic mirror and have it reflect on the principal axis ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus . | what is the centre of curvature ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | let me do another example like that where i do something big way out here just to make it clear . so once again , we go parallel , reflect through the focus . and then , we can go through the focus . | why do all the reflected rays of the rays parallel to the simmetry line go through the focus ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and i 'll just do it for this one right over here . it will reflect through the focus . and then , if you have something that goes through the focus , an incident ray that goes through a focus , it will reflect parallel . | i mean , how do rays reflect in a paraboloid surface ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | but they look like they 're diverging from some point behind the mirror . they 'll look like they 're diverging from some point behind the mirror . so in this case , we are forming a virtual image . and the virtual image will actually look something like this . and so it 'll be larger than the original virtual image . ... | `` 5 '' can the virtual image be smaller or equal to the object ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so here , i 'll do a slightly different ray . i 'll do a ray that intersects the parabolic mirror right over there . and the reason why i want to do there is because there the parabolic mirror is essentially flat and essentially vertical . | for the fourth ray diagram sal could use another rule or we can say a property of parabolic mirrors that is a ray passing through the centre of curvature pass through the centre of curvature itself ... ..so instead of drawing a ray from the pole ( that is on the point on the principal axis that intersects the parabolic... |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so this point will correspond to this point over here . i think that makes it clearer , that this image , the image of this object when it 's reflected by this parabolic mirror will look just like that . so it will actually form a real image . | what will be the characteristic of the image formed if the object is placed at infinity , from the mirror ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so you could imagine coming from the same direction as the focal point would be reflected parallel , in a parallel direction to the principal axis . now , these two light rays are not converging . but they look like they 're diverging from some point behind the mirror . | does the information remain constant for the two ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | they 'll look like they 're diverging from some point behind the mirror . so in this case , we are forming a virtual image . and the virtual image will actually look something like this . | in the case where the object is placed at the focus , the rays go parallel forming no image , but if we have a converging lens , as in the case of our eyes , what will be the effect ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | it goes through another ray . it goes through the focus . and then , it reflects . | is there any difference between the focus and the principal focus of a mirror ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and so now the image is bigger than the original . so the image is real . and it is bigger . | can the real image be slanted ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses . so that 's a parabolic mirror . i 've drawn its principal axis right over here . | what is the difference between a concave and parabolic mirror ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . | i understand how images can appear in different sizes and in different orientations but do parabolic mirrors also distort the image ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so it will actually form a real image . it 'll form a real image that is smaller than this original image . it 's not so clear , the way i did it over here . | that is to say , does the reflected image appear to have different proportions rather than just being scaled ( up or down ) or flipped ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and so now the image is bigger than the original . so the image is real . and it is bigger . | so a real image is formed if the light rays intersect ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus . | is center of curvature the same thing as the radius of curvature ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | you might want to pause the video and try it on paper because really nothing beats practice . so let 's stick our object between the center of curvature and the focus and the focal point . so if we put our object there , we could have a light ray that goes parallel to the principal axis . | can anyone tell me briefly about centre of curvature , focus or focal point and principle axis ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and it 's not , it does n't look like it 's diverging from some point in the mirror . so it wo n't even form a virtual image . so here , there will actually be no image when the object is actually at the focal point . | is it possible to see the magnified virtual image ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so let 's stick our object between the center of curvature and the focus and the focal point . so if we put our object there , we could have a light ray that goes parallel to the principal axis . and then , it will reflect out through the focus . | why is the object put on the top of the principal axis ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so here the image , just so we can keep track of things . here , the image is real and smaller than the actual object when the actual object is beyond the center of curvature . and actually , let me make it a little bit clearer by drawing . | why is an image smaller when the object is much behind the center of curvature ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | which will be a pretty useful tool when we tackle other types of reflective or refractive devices like lenses . so that 's a parabolic mirror . i 've drawn its principal axis right over here . | just a quick question , is the center of curvature always twice the focus in a parabolic mirror ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | let me do another example like that where i do something big way out here just to make it clear . so once again , we go parallel , reflect through the focus . and then , we can go through the focus . | is there any way to geometrically prove that the rays from an object at the focus will emerge parallel to each other after reflection ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and the convention is to use an upward pointing arrow . this is n't a light ray . it 's used to show an object . | does the light ray that had hitted a body carry the information about the body that it has hitted ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and then , a ray that goes through the focus will be reflected out parallel . it would be reflected out parallel . and at least for the light that comes from that tip , they will re-converge at that tip . | so do the photons of light carry information about the part from which they are reflected ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so in this case , we are forming a virtual image . and the virtual image will actually look something like this . and so it 'll be larger than the original virtual image . so it 's kind of a magnifying . | why , when the arrow was drawn at the focal point , there could n't have been a ray drawn like it was drawn ( the second ray ) ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so let me just draw the focus right over there . and this is the center of curvature . it 's twice the distance from this point as the focus . | what is the center of curvature ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and so now the image is bigger than the original . so the image is real . and it is bigger . | can someone please explain the differences between a real and a virtual image ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . | are convex and concave mirrors parabolic mirrors ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | and anything that , any light that goes parallel will then look to come out in a direction that would go through the focal point . so it would go through the focal point . it would come out in that direction . | what would we exactly see if the object were at the focal point ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . | so , will the screen remain dark ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | these lines are the hardest thing to do . so parallel incident ray , parallel to the principal axis . this is the principal axis right here . principal axis -- that 's what this line is right over here . | how do you determine the image location of an off axis parabolic reflector , when you are viewing it at 90 degrees relative to the parent parabola 's central axis ? |
let 's draw a bunch of parabolic mirrors . and what i want to do in this video is , do a bunch of examples of objects in front of parabolic mirrors . and think about what the images of those objects will be based on how far those objects are . and besides just giving us a better understanding of parabolic mirrors , thi... | so it will actually form a real image . it 'll form a real image that is smaller than this original image . it 's not so clear , the way i did it over here . | when the image is in front of the focal length , the image that is projected , is it larger or roughly the same size as the object we have ? |
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