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we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | on the left-hand side , you 're just left with 3x , and on the right-hand side , you are just left with 9 . now we want to solve for x , so we have 3 times x . let 's divide it by 3 , because 3 times x divided by 3 is just going to be x . | how would i solve |x-6|=5 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | how would you deal with these problems if there was another number outside the absolute value signs ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . | how does the absolute value play a role in this equation ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | if the absolute value is equal to zero why is the absolute value of |w| = -5 not -5,5 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is 3x minus 9 -- is equal to 0 . | what if my question is 2 ( 3x-9 ) -5 = 28 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . | why is there no graph at the end ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . | what if the absolute value equation had two different equation between absolute bar ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if you had , say , a 1 here , you could say , oh well , then this thing could be a 1 or a negative 1 . but here , if you have a 0 , this thing can only be 0 . so solving this equation is fairly straightforward . | so , when we have |a|+|b|+|c|=0 , we can know that a=b=c=0 , right ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | wait , so the number that comes out of the absolute value signs is always assumed to be positive , but the answer to the eqaution can be negative , right ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . | how do you write an absolute value equation ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | on the left-hand side , you 're just left with 3x , and on the right-hand side , you are just left with 9 . now we want to solve for x , so we have 3 times x . let 's divide it by 3 , because 3 times x divided by 3 is just going to be x . | why is 13|x-6| = 5 not the same as |13x - 78| = 5 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . | can an absolute value equation be linear ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | so , the absolute value of zero is zero ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | that would mean zero is zero numbers away from zero..can you even say zero has an absolute value ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | on the left-hand side , you 're just left with 3x , and on the right-hand side , you are just left with 9 . now we want to solve for x , so we have 3 times x . let 's divide it by 3 , because 3 times x divided by 3 is just going to be x . but if we divide the left side by 3 , we have to divide the right side by 3 . | if x is needed for further calculations , why should i consider x = -3 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . | was n't sal supposed to graph the solution on a number line ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | on the left-hand side , you 're just left with 3x , and on the right-hand side , you are just left with 9 . now we want to solve for x , so we have 3 times x . let 's divide it by 3 , because 3 times x divided by 3 is just going to be x . | what is the complete set of values of x satisfying the equation |2^x -1|+|2^x +1 | =2 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | what 's the absolute value of `` i '' ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . | what happened to the `` and graph the solution on a number line '' part of the question ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . | is the vertical lines nececary ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | on the left-hand side , you 're just left with 3x , and on the right-hand side , you are just left with 9 . now we want to solve for x , so we have 3 times x . let 's divide it by 3 , because 3 times x divided by 3 is just going to be x . | how to solve |x+3|+|x-2| = 5 ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | how would one graph an absolute value function ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | and so this whole thing is going to be a parabola . we are graphing a quadratic equation . now a parabola you might remember can intersect the x-axis multiple times . | what are some real life examples of a parabola ( or a quadratic equation ) ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | so we know that our parabola is going to intersect the x-axis at x equals negative two right over there , and x is equal to six . these are our x-intercepts . so given this , how do we figure out the vertex ? | how do you find the vertex when you have an even number of spaces in between x intercepts ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | but x minus six could be equal to zero . so if x minus six is equal to zero , then that would make this equation true . or if x plus two is equal to zero , that would also make this equation true . so the x values that satisfy either of these would make y equal zero and those would be places where our curve is intersec... | why would i want to put the equation to equal 0 ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | so we know that our parabola is going to intersect the x-axis at x equals negative two right over there , and x is equal to six . these are our x-intercepts . so given this , how do we figure out the vertex ? | so when you 're figuring out the x-values for the intercepts , why does n't the 1/2 matter ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | we are graphing a quadratic equation . now a parabola you might remember can intersect the x-axis multiple times . so let 's see if we can find out where this intersects the x-axis . | can parabola intersect y-axis two time ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | so the x values that satisfy either of these would make y equal zero and those would be places where our curve is intersecting the x-axis . so what x value makes x minus six equal zero ? well you could add six to both sides , you 're probably able to do that in your head , and you get x is equal to six . | 0 in the video , why does mr. khan place positive 2 in the x place , if the x value was -2 ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . | is the software that sal uses free ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | these are our x-intercepts . so given this , how do we figure out the vertex ? well the key idea here is to recognize that your axis of symmetry for your parabola is going to sit right between your two x-intercepts . | to find the vertex , ca n't you just do -b/2a ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | and so just like that , i could draw an axis of symmetry for my parabola . so my vertex is going to sit on that axis of symmetry . and so how do i know what the y value is ? | as 1/2 is also the function 's scalar , is there another way of determining the vertex other than substituting back in the axis of symmetry ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | let me do that . so i 'm just trying to find the midpoint between the point , let 's use a new color . so i 'm trying to find the midpoint between the point negative two comma zero and six comma zero . | what software does sal use ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . | why is y 0 ? |
we 're asked to graph the equation y is equal to one-half times x minus six times x plus two . so like always , pause this video and take out some graph paper or even try to do it on a regular piece of paper and see if you can graph this equation . all right now , let 's work through this together . there 's many diff... | if x is equal to negative two , then this right over here is going to be equal to zero , and y would be equal to zero . so we know that our parabola is going to intersect the x-axis at x equals negative two right over there , and x is equal to six . these are our x-intercepts . | how do you know the parabola will intercept the x axis at y = 0 ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so then we can solve for q . if q squared , i 'll write it as a decimal , 0.09 , that means that q is going to be the square root of 0.09 , which is equal to 0.3 . just like that , we were able to figure out the allele frequency of the recessive allele . | how does the square root of 0.09 = 0.3 ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | if q squared , i 'll write it as a decimal , 0.09 , that means that q is going to be the square root of 0.09 , which is equal to 0.3 . just like that , we were able to figure out the allele frequency of the recessive allele . and i could write that as a percentage , 0.3 or 30 percent , if you were looking at the genes ... | so are genetic diseases like cloud blindness or hemophilia can be fixed ... .. ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | based on that , we can figure out what percentage code for the dominant variant . the rest of the genes must code for the dominant one , because we 're assuming there 's only two of them . p plus q equals 100 percent , or p plus q is equal to one . | can you knock out the genes with those mutations in a person and replace with other genes ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | i would encourage you to pause this video and based on what we saw of the hardy-weinberg equation , can we figure these things out , given this information ? well let 's revisit the hardy-weinberg equation . we 've worked it out in a previous video , but i 'll rewrite it right now . | but here , it seems like hardy weinberg is being used to calculate the actual genotype frequency ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | i would encourage you to pause this video and based on what we saw of the hardy-weinberg equation , can we figure these things out , given this information ? well let 's revisit the hardy-weinberg equation . we 've worked it out in a previous video , but i 'll rewrite it right now . | in these videos we have taken the theoretical case of an eye colour gene which has only two variants and thus the hardy-weinberg equation applies with such ease as in multiplication of binomials and such but in the real world we have numerous different genes with numerous different allele possibilities so how does the ... |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | i would encourage you to pause this video and based on what we saw of the hardy-weinberg equation , can we figure these things out , given this information ? well let 's revisit the hardy-weinberg equation . we 've worked it out in a previous video , but i 'll rewrite it right now . | is hardy-weinberg fact , or just an estimation ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so what is p squared ? p squared is going to be 70 percent squared , or 0.7 squared . so this right over here is 0.7 squared , which is 0.49 . so one way to think about it is , based on this , and once again , it 's a simple equation , but these really neat ideas are starting to pop out of it based on just this informa... | wait why is 9 % ( 0.09 ) squared calculated with squaring ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | and i could write that as a percentage , 0.3 or 30 percent , if you were looking at the genes in the population , 30 percent express our code for the recessive allele , or the recessive variant . based on that , we can figure out what percentage code for the dominant variant . the rest of the genes must code for the do... | how do you find the percentage if the homozygous dominant is the only one given ... ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so then we can solve for q . if q squared , i 'll write it as a decimal , 0.09 , that means that q is going to be the square root of 0.09 , which is equal to 0.3 . just like that , we were able to figure out the allele frequency of the recessive allele . | my question is why did you square root the q2 , and not the p2 ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | now let 's say that in a population , it 's a large population , one that meets all the hardy-weinberg equilibrium assumptions , let 's say that you were to observe that nine percent of this population has blue eyes . so now we 're talking about the phenotype . you can actually observe that they have blue eyes . based ... | so the 9 % of blue eyes comes from observing a phenotype ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 're going to have brown eyes , the only way to have blue eyes is to have a lower case , is to be homozygous for the recessive allel... | is n't it possible that no alleles are inherited ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | well the only way to have blue eyes is if your genotype is homozygous recessive . because if you have a capital b in here then you 're going to have brown eyes . so we can say that nine percent also has this genotype . | why is there a 9 % chance you 'll get ( b ) dominant brown eyes ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | we 've worked it out in a previous video , but i 'll rewrite it right now . it says , the allele frequency for the dominant allele frequency squared , plus two times the dominant allele frequency times the recessive allele frequency , plus the recessive allele frequency squared , is equal to one . and we saw that this ... | so in this case the probability of getting the dominant allele from mom and recessive allele from dad would be 21 % , right ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | i would encourage you to pause this video and based on what we saw of the hardy-weinberg equation , can we figure these things out , given this information ? well let 's revisit the hardy-weinberg equation . we 've worked it out in a previous video , but i 'll rewrite it right now . | when sal initially find q^2 , why does n't he simply plug .09 into the hardy-weinberg equation ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | the rest of the genes must code for the dominant one , because we 're assuming there 's only two of them . p plus q equals 100 percent , or p plus q is equal to one . so this must be 70 percent . | why we use letter `` p '' and `` q '' instead of using `` b '' and `` b '' ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | p squared is going to be 70 percent squared , or 0.7 squared . so this right over here is 0.7 squared , which is 0.49 . so one way to think about it is , based on this , and once again , it 's a simple equation , but these really neat ideas are starting to pop out of it based on just this information . | hey i understand the algebra and the equation but i 'm confused as 0.49 + 0.42 + 0.3 = 1.21 ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | we 've worked it out in a previous video , but i 'll rewrite it right now . it says , the allele frequency for the dominant allele frequency squared , plus two times the dominant allele frequency times the recessive allele frequency , plus the recessive allele frequency squared , is equal to one . and we saw that this ... | can blue eyes be a dominant allele and brown eyes be recessive allele ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so then we can solve for q . if q squared , i 'll write it as a decimal , 0.09 , that means that q is going to be the square root of 0.09 , which is equal to 0.3 . just like that , we were able to figure out the allele frequency of the recessive allele . | how come you do n't have to square the 9 % ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | the rest of the genes must code for the dominant one , because we 're assuming there 's only two of them . p plus q equals 100 percent , or p plus q is equal to one . so this must be 70 percent . | but why did you calculate the square root of q^2 but square p^2 ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so if either one of your alleles is this capital b , you 're going to have brown eyes , the only way to have blue eyes is to have a lower case , is to be homozygous for the recessive allele . now let 's say that in a population , it 's a large population , one that meets all the hardy-weinberg equilibrium assumptions ,... | what is the percentage in the population of heterozygous individuals ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | we 've worked it out in a previous video , but i 'll rewrite it right now . it says , the allele frequency for the dominant allele frequency squared , plus two times the dominant allele frequency times the recessive allele frequency , plus the recessive allele frequency squared , is equal to one . and we saw that this ... | how would you deal a more complex situation such as blood type where a and b are co-dominant and o is recessive to both of these ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so now we 're talking about the phenotype . you can actually observe that they have blue eyes . based on this , can we figure out p , which is the frequency of the dominant allele . | so how would you start the problem if you have 1 in 5000 people with blue eyes , for example ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so let 's see , that 's going to be two times 0.21 , so this right over here is going to be 0.42 . or another way to think about it is , 42 percent of this population is going to have the genotype upper case b and lower case b . and you see they all add up . | we konw that the alle frequency of the b is 70 % and that of the b is 30 % in the video , so , my question is what are the genotype of the parents ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | because if you have a capital b in here then you 're going to have brown eyes . so we can say that nine percent also has this genotype . or you can say that the frequency in the population of this genotype is nine percent . but we 've already seen , that 's exactly what this term right over here is . | i mean , in last video , we konw that the genotype of the parents are bb and bb respectively , so the all frequency are 25 and 75 % respectively , but you can not use70 % and 30 % proportion to deduce the genotype of the parents , can we ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | and we saw that this just comes from the idea that p plus q is going to be equal to one . there is a 100 percent chance , if you were to randomly pick a gene , that it 's one of these two variants . now when we say nine percent has blue eyes , what does that mean ? | and how to determine the gene order ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | : let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . | and how to determine the mapping units ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so now we 're talking about the phenotype . you can actually observe that they have blue eyes . based on this , can we figure out p , which is the frequency of the dominant allele . | is having blue eyes a mutation ? |
: let 's stick with this idea , the simplification , that there 's a gene for eye color , and it only comes with two variants . it has the dominant variant , which codes for brown eye color , and it has the recessive variant , which codes for blue eye color . so if either one of your alleles is this capital b , you 'r... | so what is p squared ? p squared is going to be 70 percent squared , or 0.7 squared . so this right over here is 0.7 squared , which is 0.49 . | why is n't it .o9 squared for q2 ? |
i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . we saw in the last video it 's interesting to find the vectors that only get scaled up or down by the transformation . so we 're interested in the vectors where... | so if i rewrite v this way , at least on this part of the expression -- and let me swap sides -- so then i 'll get lambda times -- instead of v i 'll write the identity matrix , the n by n identity matrix times v minus a times v is equal to the 0 vector . now i have one matrix times v minus another matrix times v. matr... | 2 - do eigenvalues ( and eigenvecotors ) only exist for a a matrix where the determinant is 0 ? |
i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . we saw in the last video it 's interesting to find the vectors that only get scaled up or down by the transformation . so we 're interested in the vectors where... | so given that , let 's see if we can play around with this equation a little bit and see if we can at least come up with eigenvalues maybe in this video . so we subtract av from both sides , we get the 0 vector is equal to lambda v minus a times v. now , we can rewrite v as -- v is just the same thing as the identity m... | why did sal only consider multiplying the identity matrix with v on the lamda side but not the v with a 4 ? |
i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . we saw in the last video it 's interesting to find the vectors that only get scaled up or down by the transformation . so we 're interested in the vectors where... | so if i rewrite v this way , at least on this part of the expression -- and let me swap sides -- so then i 'll get lambda times -- instead of v i 'll write the identity matrix , the n by n identity matrix times v minus a times v is equal to the 0 vector . now i have one matrix times v minus another matrix times v. matr... | just have a silly question : are addition and subtraction between a matrix and a scalar undefined ? |
i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . we saw in the last video it 's interesting to find the vectors that only get scaled up or down by the transformation . so we 're interested in the vectors where... | we already said the 0 vector is always going to be a member of the null space , and it would make this true . but we 're assuming v is non-zero . we 're only interested in non-zero eigenvectors . | can we assume that at least one or all of the eigenvalues are zero ? |
i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . we saw in the last video it 's interesting to find the vectors that only get scaled up or down by the transformation . so we 're interested in the vectors where... | so if we have some matrix here whose null space does not only contain the 0 vector , then it has linearly dependent columns . and i just wrote that there to kind of show you what we do know and the fact that this one does n't have a trivial null space tells us that we 're dealing with linearly dependent columns . so la... | i 'm making a wild guess but is a linearly independent column one where the values do n't depend on other values in the column ? |
i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . we saw in the last video it 's interesting to find the vectors that only get scaled up or down by the transformation . so we 're interested in the vectors where... | i 've got a transformation , m that 's a mapping from rn to rn , and it can be represented by the matrix a . so the transformation of x is equal to a times x . | what does the transformation from rn to r mean ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | half of 2 is 1 . 1 squared is 1 . we did n't add a 1 to the left-hand side of the equation , we added a 1 times minus 25 . | why did you put -1 for x and solve y ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | if it was centered at 0 , could x equals 0 ? well , sure x could equal 0 . if x is 0 , then y squared over 25 equals 1. y squared equals 25. y would be plus or minus 5 . | when sal finds if the hyperbola opens up and down or sideways , he says x could be zero , but could n't y be zero as well ( or y become +2 ) , it would be x = -3 , 1 ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so we 're always going to be a little bit above the asymptote . this is the asymptote . but we 're always a little bit above it . | did sal define what an asymptote was in an earlier video ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | they have different coefficients . and one is positive and one is negative . so that lets us know that we 're dealing with a hyperbola . | why is it a hyperbolic equation if one coefficient is negative and the other is positive ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | i do this to figure out what the asymptotes would have been if we were centered at 0 . because it 's a lot easier to deal with these equations than to deal with these . so we could solve -- we multiply both sides by 100 . | what are identity , contradiction and conditional equations ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so for every 2 we go over to the right , we go down 5 . so , 1 , 2 . 1 , 2 , 3 4 , 5 . | what do i do when there is no y^2 ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so these are the slopes of the two asymptotes . and one is positive 5/2 . so , positive 5/2 means if we go over 2 , so 1 , 2 , in x , we go up 5 . | can a shortcut be just that when the y^2 value is positive , the graph is vertical and when the x^2 value is positive , the graph is vertical ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so that lets us know , since we 're inside here , this tells us that this is kind of a vertical asymptote , and another way to guess it is , if you see that y squared term is positive . or the other way to think about it is , when you take the positive square root , when you take the positive square root , you 're alwa... | the positive number under the square is what makes it above the asymptote , but what would make it below the asymptote when we take the negative value of the square root ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | and i did n't add a 4 to the left-hand side of the equation . i actually added a 4 times 4 , right ? because you have this 4 multiplying it out front . | how did you simplify the hyperbola 's equations in ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | it 's equal to 109 . and now that we have the x 's and the y 's on the same side of the equation , we know what type of -- we know the general direction we 're going to go in . because they 're on the same side . | how do you know if an equation represents a circle ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so that lets us know that we 're dealing with a hyperbola . so let 's complete the square and get it into the standard form . so , the easiest way to complete the square is if you have a 1 coefficient on the y squared and the x squared terms . | when you are converting to standard form , does it usually happen that the two coefficients are swapped and divided by ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | and then if i add 25 over 4x squared to both sides , i get y squared is equal to 25 over 4x squared plus 25 . and so , y is equal to the plus or minus square root of 25 over 4x squared plus 25 . and like always , the asymptotes , the hyperbola will never equal the asymptotes or intersect the asymptotes , but it 's what... | what happened to the square root of 25 when sal was working on the asymptotes of the hyperbola ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . | what are parametric and polar representations ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so for every 2 we go over to the right , we go down 5 . so , 1 , 2 . 1 , 2 , 3 4 , 5 . | at about the 1.15 mark , how come the 25x^2 is negative , does n't it stay the same and the 50 becomes positive ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | but we 're always a little bit above it . and obviously as this number gets larger , this starts to matter a lot less , so the graph is going to look something like this . it 's going to come down and then go off , and never quite touch the asymptote , but approach it . | from around 5 and on should n't sal have obtained the y-intercept of the hyperbola in order to graph it properly ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | half of 2 is 1 . 1 squared is 1 . we did n't add a 1 to the left-hand side of the equation , we added a 1 times minus 25 . | how do you know that ( -1 , y1 ) and ( -1 , y2 ) are the vertex points ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | let 's set . if x is equal to negative 1 , x is equal to negative 1 , then what does this expression become ? i do n't want to lose it , so i 'll write it right there . | any x value that makes the expression cancel out , has a corresponding y value that together constitute the vertex ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . | what is the general algorithm to find out what conic section it is ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | we have it in standard form and , yes , indeed , we do have a hyperbola . now , let 's graph this hyperbola . so the first thing we know is where the center of this hyperbola is . | what exactly is a hyperbola ? |
let 's do another conic section identification problem . so , i have 4y squared minus 50x is equal to 25x squared plus 16y plus 109 . so , the first thing i like to do is to group all of the x and y terms onto one side of the equation and leave all the constants on the other side . so let 's do that . so , on the left-... | so , on the left-hand side i 'll put the 4y squared . 4yy squared . and , actually , i 'm also going to group all the x and y terms in this step . | is the linear term always the one who gets cut in half and then squared , , ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | who is the guy standing near mussolini ( on his left ) with all of the medals ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | he says , no this is italy 's chance for glory , this is italy 's chance to build its empire . so , in 1915 he 's ousted from the socialist party and he decides to start his own group called the fasci d'azione rivoluzionaria and i talk about that in the video on fascism , but it was often referred to as the milan fasci... | how does fascism effect us nowadays ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | how did mussolini and the fascists `` get away '' with violence ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | every picture you see of him he has these really stern looks , he has this impression of a really strong figure . not only did he become prime minister , but he 's able to get dictatorial powers . the legislator actually gives him dictatorial powers for a year . ( writing ) dictata- , dictatorial powers for one year , ... | why did the king let mussolini have dictatorial powers ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | when did mussolini begin his rise to power ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | was mussolini just as bad really as hitler ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this fasci di combattimento had now morphed into a real national party , it 's now ... and they renamed themselves the nationalist or the national fascist party . ( writing ) fascist party . obviously it was n't called that in italian . | were n't mussolini 's and his fascist party 's beliefs and ways almost the exact same of hitler 's and the nazis ' belief ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | why are mussolini and other leaders in europe so scared of communism/socialism ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | every picture you see of him he has these really stern looks , he has this impression of a really strong figure . not only did he become prime minister , but he 's able to get dictatorial powers . the legislator actually gives him dictatorial powers for a year . ( writing ) dictata- , dictatorial powers for one year , ... | what exactly is `` dictatorial powers '' ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | what was italy 's government before mussolini ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | this essentially causes the current government to be ... the prime minister to be ousted and the king appoints mussolini as prime minister . ( writing ) so , mussolini , mussolini is now the prime minister . so this is a super rapid ascend , really based on peoples ' unhappiness with the left-leaning government , peopl... | when and how did mussolini start his political career ? |
narrator : benito musssolini 's rise to power in the early 1920s in italy is a fairly rapid , and from historical perspective , fairly surprising one . to give some context , as late as 1915 , ( writing ) 1915 , he had recently been ousted from the italian socialist party based on his decent over whether italy should e... | he gets elected to the chamber of deputes . ( writing ) chamber of deputes along with several other fascists , but they 're still a fairly small party . although they 've already now they 're gaining steam , they 're becoming mainstream , but even though they 're becoming more mainstream they still have n't given up th... | are there still any countries under fasicism today ? |
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