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pooja195
 one year ago
@mathmate
pooja195
 one year ago
@mathmate

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mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We'll start with 6.8! Graphing linear ineq. in 2 variables!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Are you familiar with plotting one linear equation, such as y=2x+3?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2In the slopeintercept form, y=ax+b, b is the yintercept. Ok, good! Can you plot (draw) for me y=x+3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You know that with a slope of 1, the line is at 45 deg. with the xaxis.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433470740581:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Beautiful! I expect much less in details, but that's nice!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The line divides the xy plane into two "halfplanes". Each half plane represents the solution to the inequality of the form y\(\ge\)x+3 or y\(\le\)x+3.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Can you shade for me the half plane representing y\(\ge\)x+3 ?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433471092615:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Very good! How do you decide which one to shade?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1its all solutions greater than y right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The book tells you to test a point, and see if the point is in the good region. If yes, you shade the region containing the point. If not, you shade the other region.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For example, we can use (0,0) as a test point. (0,0) is below the line. We check if 0\(\ge\)0+3 is true. Since it is not true, (0,0) is not in the region, so it must be the "other" region, the one above the line.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1The teacher taught it a diffrent way :/

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1But similar to that so its ok ..

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433471382597:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Can you tell me what he taught?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1he said if its greater than to shade up (postivie) If its less than shade down idk something like that >_<

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yes, this is the better that I was going to show you!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Say if the inequality is y>x+3 check "y>", that means go towards the +(or plus) yaxis, so the upper half.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If it was y<2x+3, then the "y<" tells you to take the halfplane towards the negative yaxis.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433471680888:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Here are three examples, use your teacher's method to shade the correct halfplane. I forgot to write \(\le\) or \(\ge\) for the first two cases.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433471920376:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The first (topleft) and the third (on the right) are correct. The second asks for y>x/32, so the "y>" tells us to go for the + yaxis, so the region is above the line. Is that ok so far?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433472096086:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You're pretty good at it!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now if we have an inequality x+y\(\le\) 10 Can you draw the line, and the region represented by the inequality?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2When we have the general form of the equation, we can find the yintercept by setting x=0, and solve for y. Similarly for the xintercept (zero), we set y=0 and solve for x.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2x+y=5 would give an xintercept of 5 and yintercept of 5.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433472344866:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's the kind of response that is sufficient.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Both +x and +y are on the negative side, so the region is to the left, and downwards.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It may look difficult because it is given in the general form. You can convert the general form to the pointslope form with which you are familiar, or use the intercepts I showed above.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For x+y<=10 which is in general form, you can convert to y<=x+10, would that be easier?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2One easy one to remember is x+y = K has both intercepts equal to K.dw:1433472650720:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So are we good with 6.8?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We'll do Chapter 7 then.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2System of linear equations and inequalities. ===========================

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2A system of linear systems is simply a set of lines. With a system of two equations, there are two lines.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433473022450:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433473082856:dw represents the system of equations y=x+3 and x+y=8

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2so far so good, you know where the lines are coming from (how they were drawn)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The intersection point (5.5, 5.5) represents the solution of the system, x=5.5, y=5.5. Right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2* (2.5,5.5) dw:1433473201267:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now If we want to solve for the system of inequalities, y\(\le\)x+3 x+y\(\le\)8

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The boundaries of the required region are shown by the lines on the graph. Can you indicate the region (by "hatching" the region with parallel lines)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433473435556:dw The region which is hatched by both region is our solution set, as shown above.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, your turn to do something!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Graph and show the solution set (region) of the following system of inequalities: y>x+3 y<x+1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Notice that ">" is represented by a dotted line, since the solution does not include the line.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Also notice that y>x+3 is the same as x+y>3 (use the two intercepts)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433473675355:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1its messy this is why i didnt want to do graphs ;;

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It's beautiful! However, it doesn't bother me if you don't use colours, and have no graduations.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now, remember that the > and < signs exclude the lines from the solution, so must be drawn with dotted lines!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433474097592:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Can you show me how to have the fancy colours (but some other time!)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now we need to hatch the region representing the solution. Use hatching (scribble some parallel lines).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2* the solution of the system of inequalities.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433474286903:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2k, whenever you're ready, I'm waiting for you to draw/hatch the region of the solution set!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2yes, show by shading/hatching the solution set of the system of inequalities.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2similar to the example I did above.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433474544295:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1woah it screwed it up

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The solution set is which colour?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2No, I can understand, as long as you specify the colour.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1y>−x+3=pink y<x+1= mint

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2For both of them to be true, the region is blue (intersection of pink and mint). So the blue region is the solution set. Is that ok?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Here's another system of inequalities, but don't draw the graduations to safe yourself time! x\(\le\)4 y\(\ge\)2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433474989120:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433475046485:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1It keeps messing it up! >:(

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's ok, I can see that they are correct. So the solution set is......

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2the intersection of the two regions!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We have two inequalities to be satisfied, so the region must satisfy BOTH regions. I will hatch it below.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433475274853:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2:( not promising, he's crying!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We only have one more topic to do.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2When we have a system of 2 linear equations, the system is represented by two straight lines, like this.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433475491469:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Do you know what I am about to say? If yes, tell me!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1one line = many solutions two lines = one solution parell lines = no solution am i right?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1two lines interscting...

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You know the topic, but your list is not very precise. We are working with 2 lines. The intersection (or lack of it) can be described in three cases:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Can you rename the three cases?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.21. nonparallel : _______ solutions 2. parallel and _________ : __________ solutions 3. parallel and __________ : __________ solutions.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Now its more complicated _

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433475774511:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Case 1 = one solution case 2 = no solution case 3 = infinte soltuions

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Exactly! 1. interscting, one solution eg. 2x+3y=4, 4x2y=0 2. parallel and noncoincident: no solution eg. x+y=10, y=x+7 3. parallel and coincident: infinite solutions. 2x+2y=4, y=x+2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I'll leave it to you to try some exercise on 7.5

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2No, I'll give you two exercises now.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Describe the no. of solutions of the following system: x+y=6 2x+2y=12

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1you know me so well xD

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2can you elaborate please?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.12(x+y=6) 2x2y=12 2x+2y=12 0=0 Infinte solutions.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Very well. now, how many solutions does the following system have: 2x+y=3 y=2x6

pooja195
 one year ago
Best ResponseYou've already chosen the best response.12x2x6+6=3+6 0x=9 0=9 no solution

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We're done for 6.8 and 7, how's that?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2gimme a minute to find the page!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Ok, in chapter 8, we're doing exponents!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2First we need to know the laws of exponents, how to multiply, divide, raise powers, and take roots.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Then an application would be to convert numbers to and from scientific notations.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Finally, there will be a few problems related to decay and growth, e.g. number of rabbits after a certain time, etc.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2P. 440 gives some vocabularies.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433538712158:dw can you name A and B?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now calculate: (answer in exponential form)dw:1433538857123:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent! Can you now write the question AND answer in exponential form?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2don't bother with LaTex. We both understand regular text.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I gtg, but answer is 7^2 \(\times\)7^3 = 7^5

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I'd like it in exponential form! so in general 7^2*7^3 = 7*(2+3) =7^5

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2or in general x^a * x^b = x^(a+b) this is one of the laws of exponents! sorry gtg

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2So, what is \(x^3y^2 \times xy^3\). Express answer in exponential form.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good, how about \(\large \frac{x^2y^3}{xy}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2good! Now express x^3y^2\(\div\)(x^4y^4) in positive exponents.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good, I think you mean 1/(xy^2)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Power of a power property: example: (a^2)^3 = a^(2*3) = a^6

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Hint: Product of powers: (a^x b^y)^z = a^(xz)*b^(yz)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2\(\large (a^x b^y)^z = a^{xz}*b^{yz}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Wow, you're good! Am I too slow?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2please let me know whenever this happens!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Now simplify ((3)^3)^3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's a calculator answer! I need the answer in exponential form, if possible!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2(3)^9 is almost good!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I mean it's good, but not simplified enough!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1o.O i used the calc im allowed to use on the finals .. this is what i got what more simplifed can it be? o.O

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2you can simplify it as (3)^9=(1)^9*3^9 = 3^9

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's alright. I am demanding!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2We have two circles of radii r and 2r. Find the ratio of the area of the big circle to the small circle.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1i havent learned this

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Have you learned A=pi r^2 ?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1We havent done much with that i know that stuff from last year though (formula) idk that nor have we learned it THIS year

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, I'll solve this: A1/A2 = pi (2r)^2 /(pi r^2) =(2r)^2/r^2 =4r^2/r^2 =4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify (5)^4 * (5)^4

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1in exponetional form?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Yep! Pretend you have no calculator!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Perfect, you got rid of the negative signs because the final power is even! Very good!!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Simplify (5y^2)^3 * (y^3)^2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Excellent, did you calculate 125=5^3 in your head?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1400 ;; how many more of these?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Just to see if you are used to using your head. My conclusion is that you are! lol

mathmate
 one year ago
Best ResponseYou've already chosen the best response.225*16 is the same as counting how much money you have when you have 16 quarters.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2What is (1/2)n^3 when n=2?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good, still too slow?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Recall: x^0=1, and x^1=x

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Rewrite 3x^(2)/(y^3z^(1)) with positive exponents!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433557420958:dw What is 'a' on the graph (the yintercept)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge\frac{3z}{x^2y^3}\] We did not learning graphing exponetionall functions

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Good for the positive exponents, actually, very good! Are you sure about not having done graphics for exponential functions?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2what about things like solve 4^x=4096

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Calculator or in your head?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433558060131:dw

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1we havent learned this

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You see that when a<0, the graph flips about the yaxis.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ik, but just a quick overview, please bear with me!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Have you done graphing calculator?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.28.3 is for using the graphing calculator!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Does everybody in school have one? Like the Ti83 or ti83+

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Do you know how to graph on the calculator?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1no becuse we have never had to

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2That's good! I am not for it either. It doesn't do much.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2It's much easier to teach students how to use the graphics calculator than graphing with pencil and paper.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Guess your teacher does neither! :(

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1we graph with paper n pencil ;;

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2But...you just said you didn't graph exponential functions?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Not this im talking about the slope stuff lel this we ahve never done

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, so you graphed straight lines! Still it's very good that the teacher asked you to graph on pencil and paper.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2ok, "the average weight w (in pounds) of an Atlantic cod can be modelled by w=1.21(1.42)t where t is the age of the fish(in years).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Find the ratio of the weight of a 5year old cod to the weight of a 2yearold cod.
