system (12:51:47:817 PM): Mod1 has joined Babylon. system (01:40:14:120 PM): Ian has joined Babylon. system (01:40:40:366 PM): Tyler has joined Babylon. system (02:10:24:887 PM): Ian left the Main chat room. Tyler (02:10:50:647 PM): Just testing... system (02:11:00:994 PM): Ian has joined Babylon. Ian (02:11:15:747 PM): Testing... Tyler (02:11:27:752 PM): No, I'm testing! system (02:39:02:690 PM): Tyler left the Main chat room. system (02:56:35:219 PM): Ian left the Main chat room. system (03:59:48:572 PM): IaN has joined Babylon. system (04:05:16:830 PM): Tyler has joined Babylon. system (04:05:42:511 PM): IaN left the Main chat room. system (04:06:58:854 PM): Ian has joined Babylon. system (04:07:53:805 PM): Tyler left the Main chat room. Mod1 (04:08:07:321 PM): good... I am glad I didn't miss it ;-) Ian (04:08:26:296 PM): I was hoping for a flood of people, actually. Mod1 (04:10:12:375 PM): me, too... but it is early system (04:15:06:856 PM): JohannTest has joined Babylon. Ian (04:15:18:620 PM): Hi JohannTestJohannTest (04:15:18:946 PM): Just testing that the Applet is loading fine... Ian (04:15:27:471 PM): Yeah, I was doing that with Tyler. Ian (04:15:33:541 PM): To make sure you could get here from the site. JohannTest (04:15:54:983 PM): Naive of us to think that it is because of technical problems that we don't have participants yet? system (04:15:58:287 PM): tim has joined Babylon. system (04:16:04:002 PM): JohannTest left the Main chat room. Ian (04:16:34:825 PM): Hi tim. Mod1 (04:16:43:807 PM): Welcome! Ian (04:17:03:900 PM): What would you like to talk about? tim (04:18:01:915 PM): Triangles Ian (04:18:15:457 PM): Triangles in general? Or some particular ones? tim (04:19:21:592 PM): a triangle with sides 7,7 and 12. Show me how to find the area please. Ian (04:19:38:289 PM): So that's isosceles. Two sides are the same. Mod1 (04:19:39:311 PM): interesting! Ian (04:19:53:595 PM): Do you know how to find the area of a right triangle? tim (04:20:08:230 PM): yes Ian (04:20:48:371 PM): Suppose I have a right triangle with one leg equal to 2, and the hypotenuse equal to 5. What would the area be? tim (04:21:35:327 PM): 4.6 Ian (04:21:45:081 PM): Can you tell me how you found that? tim (04:22:51:195 PM): 5 squared minus 2 squared then take the square root of 21 Ian (04:23:00:337 PM): Nicely done. Ian (04:23:22:845 PM): Can you see how to divide your 7, 7, 12 triangle into two right triangles? tim (04:24:09:186 PM): yes Ian (04:24:25:234 PM): So now you can find the area of the whole triangle, right? tim (04:24:42:750 PM): I will try tim (04:28:00:565 PM): Thank you I was making it too diffucult. I was multipling the apothem by the perimeter and then by .5 Ian (04:28:31:132 PM): Ah. There's also Heron's formula. Have you heard of that? tim (04:29:09:086 PM): Yes but I am not sure what it is. Ian (04:29:26:922 PM): If you have sides a, b, and c - this is for _any_ triangle... Ian (04:29:48:654 PM): the semiperimeter is s=(a+b+c)/2... Ian (04:30:09:829 PM): and the area is sqrt[s(s-a)(s-b)(s-c)] Ian (04:30:23:574 PM): It's a very handy thing to have in your bag of tricks. Ian (04:30:33:925 PM): Try using it to get the area of your 7,7,12? system (04:31:28:577 PM): Evie has joined Babylon. Ian (04:31:37:657 PM): Hi Evie. Evie (04:31:47:874 PM): HEy Ian Ian (04:31:55:625 PM): What's on your mind today? We're talking about triangles with tim. Evie (04:32:00:726 PM): Anyone good at doing word problems in here Ian (04:32:14:379 PM): Maybe we can help _you_ become good at them. Evie (04:32:35:070 PM): okay thanks tim (04:32:35:260 PM): Could you explain by example? Evie (04:32:47:295 PM): the question is long i think i have most things figured out Evie (04:33:03:941 PM): can i type in the question Evie (04:33:25:015 PM): two people say c and r want to buy a new bike it cost 300 Ian (04:33:35:452 PM): Sure. For a 3,4,5 triangle, the semiperimeter is s=(3+4+5)/2 = 6. So the area will be... Evie (04:34:03:521 PM): R has 50 dollars in her account and is gonna save 30 dollare per week tim (04:34:08:918 PM): 18 Ian (04:34:14:267 PM): sqrt[6(6-3)(6-4)(6-5)] = sqrt[6*3*2*1] = sqrt(36) = 6. Evie (04:34:27:916 PM): c has 50 dollar in his account Evie (04:34:35:099 PM): is gonna save 25 per week Evie (04:35:07:895 PM): so i ha dto write 2 equations that represent the savings plan Evie (04:35:17:165 PM): so this is what I got Ian (04:35:52:856 PM): Keep going, Evie... Ian (04:35:57:745 PM): Tim, did the example help? Evie (04:35:58:175 PM): y= 30x+ 50 and y+25x+75 Evie (04:36:08:381 PM): does that look correct Ian (04:36:42:093 PM): It looks to me like you said they both started with 50 dollars. Did one start with 75? tim (04:36:51:499 PM): Still digesting. Thanks for everything. Evie (04:37:00:398 PM): yes one started with 50 the other had 75 Mod1 (04:37:14:943 PM): what does x represent, Evie? Evie (04:37:41:480 PM): x = how many weeks its gonna take each to save enough to get the bike Evie (04:38:08:224 PM): y = 300 dollars the cost ofthe bike Evie (04:38:49:718 PM): but thats where I am confused with what the formulas should be Ian (04:39:18:807 PM): Let's look at the equation y=30x + 50 for a second. Evie (04:39:25:426 PM): then after I get the 2 equations then I have to solve them by substitution method Ian (04:39:30:927 PM): If I say that x is 2, what is y? Evie (04:39:31:623 PM): okay listening Evie (04:40:03:467 PM): 110 Ian (04:40:16:254 PM): And if x is 3, y is...? Evie (04:40:32:049 PM): 140 Ian (04:40:46:404 PM): So what does it mean when I pick a value for x? Evie (04:41:31:328 PM): I am using the x value as the number of weeks it takes for them to save enough for a 300 dollar bike system (04:41:32:788 PM): jon has joined Babylon. Ian (04:41:43:564 PM): Hi jon. Welcome! Mod1 (04:41:49:507 PM): boy, it takes a lot of time to save for a bike! ;-) Evie (04:42:09:381 PM): Is that right or am I totally lost jon (04:42:18:354 PM): hi need help w algebra 2 Ian (04:42:25:491 PM): It's almost right, but it's a little more subtle. Evie (04:42:53:282 PM): should i put 300= 30x + y Ian (04:42:56:087 PM): Let's forget about the bike for a moment, and just assume they're saving money for something in the future, okay? Evie (04:43:02:526 PM): K Ian (04:43:39:099 PM): If I ask you how much they'll have a year from now, can you tell me? jon (04:43:43:133 PM): can anyone explain this equation to me... 5x sq. + 100 = 0 Ian (04:44:36:217 PM): Jon, can you try drawing that on the canvas, so we can see what the square root covers? Evie (04:44:40:904 PM): yes I can do that if one starts out with 50 in savings and adds 30 each week thats 30 times h0w many weeks in a year jon (04:44:45:390 PM): thanks Ian (04:45:22:669 PM): Right. So the x in this case is just the number of weeks. If we pick some number of weeks, we can figure out how much has been saved. That's what y represents. Ian (04:45:50:170 PM): Does that make sense? Evie (04:45:52:322 PM): Light bulb went off in my head Evie (04:45:57:049 PM): ding Evie (04:46:02:536 PM): okay now I get that part system (04:46:15:101 PM): Mod1 left the Main chat room. Evie (04:46:40:298 PM): so how do I write it into 2 equations that I and solve by substutuation method system (04:46:46:280 PM): jon left the Main chat room. Evie (04:46:59:680 PM): can I use the two that I have or do I need to alter them Ian (04:47:04:276 PM): Well, first let's think about what it means to solve for two equations at once. Evie (04:47:17:519 PM): set to equal right Evie (04:47:37:846 PM): no wait thats elemination Ian (04:47:50:315 PM): Substitution and elimination are just two different ways to do the same thing. Evie (04:48:20:643 PM): i have to use substituation on this one my teacher said Ian (04:48:26:134 PM): But something seems funny here. Are you getting this problem from a book or a worksheet? Evie (04:48:51:369 PM): worksheet Ian (04:49:01:777 PM): Can you tell me _exactly_ what the problem says? Evie (04:49:10:447 PM): yes Evie (04:50:06:797 PM): chris and raqual want to buy new bikes the bikes cost 300 raqulas opended a saving account with 50 and is going to save 30 a week from her job Evie (04:50:43:739 PM): chris opned a saving account with 75 is is going to save 25 a week Evie (04:51:19:041 PM): then the first questions says write two equations that represent their savings plan ..what doo your variables represent ? Ian (04:51:55:479 PM): So you did that part, and you got the equations okay, but you were having some trouble saying what the variables represented. Are you clearer on that now? Evie (04:52:06:084 PM): yes system (04:52:35:122 PM): Tyler has joined Babylon. Evie (04:52:39:587 PM): but now the next question ask to sopve the equations using substituation method explaining what the solution i get means Ian (04:53:13:402 PM): Okay, so remember when I was picking values for x, and you were giving me values for y? Evie (04:53:19:289 PM): yes system (04:53:22:891 PM): Tyler left the Main chat room. Ian (04:53:38:398 PM): Each (x,y) pair was a solution for that equation, right? Evie (04:53:45:979 PM): yes Ian (04:53:59:843 PM): You could pick any x, and get some y, and that would be a solution. Ian (04:54:11:603 PM): If you graph all those solutions, what would it look like? Evie (04:54:37:507 PM): okay so i can just plug in any number and get the answer for the first equation then do I take that and solve that equation Evie (04:54:57:335 PM): thats my next thing I have to do lol Evie (04:55:10:893 PM): but i think it will be two lines that eventually cross at a point Ian (04:55:34:706 PM): Well, here's the thing. Suppose I pick x=3, and I put that in the first equation, and I get y=whatever. If I put that same x into the other equation, will I get the same value for y? Ian (04:55:50:107 PM): Right, and what's true at that point? tim (04:56:02:400 PM): If you have a pentagon with a triangle inscribed in it and the pentagon is colored how do you find the area between, if the triangle's base is in the pentagons base and both measure 3.5? I am sorry but I do not know how to draw on this. Evie (04:56:11:916 PM): hold on let me do it Evie (04:56:39:077 PM): no you get 140 for first one and 150 for second one tim (04:57:25:534 PM): Sure system (04:57:29:151 PM): jon has joined Babylon. system (04:57:35:148 PM): jon left the Main chat room. Ian (04:58:10:071 PM): Do you see the lines below, Evie? Evie (04:58:35:902 PM): yes Ian (04:58:49:814 PM): Let's say we pick x=3, so we're 3 weeks into the savings plan. Ian (04:59:26:976 PM): We get two different values for how much C and R have saved, right? Evie (04:59:50:490 PM): yes Ian (05:00:10:386 PM): And if we pick, say, 10 weeks, we get different values again... Evie (05:00:12:854 PM): so in 5 wweks they have saved the same amount maybe Evie (05:00:24:500 PM): yes 10 wweks Ian (05:00:50:251 PM): But there's _some_ number of weeks where they'll have saved the same amount. Do you see why? Evie (05:01:42:120 PM): yes i see why but i dont get how to solve with substituation cause i thought i had to solve one equation and plug it into the second equations is that the case here Ian (05:02:05:656 PM): We'll get to substitution in a minute. First it's important to understand what substitution is actually doing. Evie (05:02:17:635 PM): i figure it out its 5 weeks Ian (05:02:26:603 PM): How did you find that? Evie (05:02:29:335 PM): yhey both have the same amnount in 5 weeks Evie (05:02:52:728 PM): i just made a chart and kept pluging in weeks and solving for y Ian (05:03:06:351 PM): Good idea! That's a nice way to find the answer. Evie (05:03:11:343 PM): and at 5 weeks the solution for both was 200 Evie (05:03:22:803 PM): thanks < grin> Ian (05:03:26:098 PM): So in a case like this, with easy numbers, that works pretty well. Evie (05:03:32:579 PM): k Ian (05:03:39:472 PM): But what if the answer turned out to be something like 5.29 weeks? Ian (05:03:45:728 PM): That wouldn't show up in your chart... Evie (05:03:56:389 PM): yeah true Evie (05:04:01:148 PM): so what would i do Ian (05:04:05:581 PM): But substitution would find it! Evie (05:04:11:778 PM): holy cow Ian (05:04:13:931 PM): That's why we have substitution. It's for the hard cases. Evie (05:04:20:756 PM): so thats why we use it Ian (05:04:25:418 PM): But you practice it with the easy cases. Ian (05:04:36:243 PM): So are you ready to learn about substitution? Evie (05:04:43:749 PM): YESSSSSSSSSS Evie (05:04:46:648 PM): WHoho tim (05:05:07:393 PM): How do I send my figure? Ian (05:05:24:205 PM): So we have two equations: (1) y = 50 + 30x, and (2) y = 75 + 25x. Ian (05:05:30:481 PM): What do you mean? Evie (05:06:00:866 PM): okay i am with you tim (05:06:15:986 PM): I drew something can you see it? Evie (05:06:41:654 PM): no tim i cant see it Ian (05:06:50:321 PM): Tim, I don't see what you drew. Sometimes if you draw too low in the canvas it doesn't show up. Using the freehand tool is easiest. Evie (05:06:53:319 PM): Ian is the teacher tim (05:07:14:880 PM): How do you send Evie (05:07:15:261 PM): ask him Evie (05:07:16:628 PM): system (05:07:39:041 PM): memyselfandi has joined Babylon. Ian (05:07:53:497 PM): Hi me. memyselfandi (05:08:01:888 PM): hello memyselfandi (05:08:11:008 PM): how is everyone today? Ian (05:08:16:314 PM): We're helping Evie with linear equations. Ian (05:08:20:091 PM): How are you doing? Evie (05:08:23:980 PM): I am trying to learn substituation I am okay Ian (05:08:27:994 PM): So, Evie, we have these two equations. Evie (05:08:39:423 PM): yes ian i am with yah Ian (05:09:02:376 PM): Let's look at the first one: y = 50 + 30x. Evie (05:09:13:424 PM): k Ian (05:09:13:511 PM): Tim, I can see what you're drawing now... Ian (05:09:50:275 PM): Now, if we knew that something was equal to x, we could just put it in for x, right? Like if we knew x was equal to 3, we could write y = 50 + 30*3. Ian (05:09:54:424 PM): So far, so good? Evie (05:10:09:445 PM): yes Ian (05:10:10:242 PM): Tim, is that supposed to be a regular pentagon, or just any pentagon? Ian (05:10:45:021 PM): Let's look at the second equation: y = 75 + 25x. Can you solve this for x, so it looks like x = [something]? tim (05:10:50:747 PM): reg Ian (05:11:05:573 PM): And the triangle goes to the center of it? memyselfandi (05:11:08:528 PM): I will see you guys later. I'm going to Dr math to try and figure out how to graph an inequaltiy since my quiz was due last night. Evie (05:11:22:367 PM): inequalities suck Ian (05:11:22:609 PM): Hey, me... Ian (05:11:25:050 PM): Wait a second. tim (05:11:28:394 PM): yes Ian (05:11:31:425 PM): Can you give me an example? memyselfandi (05:11:33:445 PM): yes Ian (05:11:43:080 PM): Okay, Tim, so that's basically one fifth of the pentagon, right? Evie (05:11:45:520 PM): ian can help you he is good teacher memyselfandi (05:11:53:207 PM): i don't want to intrude if someone else needs help tim (05:12:01:236 PM): yes Ian (05:12:02:909 PM): It might not take that much time. memyselfandi (05:12:14:138 PM): ok here goes Ian (05:12:15:053 PM): So, Tim, can you find the area of a regular pentagon? Evie (05:12:15:417 PM): inequalities dontt ake that much time memyselfandi (05:12:29:161 PM): y < 1/2 x + 2 memyselfandi (05:12:35:558 PM): this needs to be graphed Ian (05:12:42:740 PM): So Evie, you're going to solve y = 75 + 25x for x, right? tim (05:12:48:181 PM): why do we not use trig func. to find the area of the triangle? Ian (05:12:57:457 PM): So, me, could you graph the _equality_ y = 1/2x + 2? tim (05:13:08:185 PM): In this case memyselfandi (05:13:13:660 PM): no Ian (05:13:20:540 PM): You could use trig. There are often lots of different ways to solve any problem. Ian (05:13:37:570 PM): Me, have you done graphing of lines yet? memyselfandi (05:13:42:891 PM): yes memyselfandi (05:13:50:930 PM): i know how to graph points memyselfandi (05:14:07:515 PM): i'm learning about slopes now as well Ian (05:14:18:185 PM): If you can graph points, you can almost graph lines. Can you find two points on the line y = 1/2x + 2? memyselfandi (05:14:39:188 PM): see that's confusing me Ian (05:14:43:237 PM): Evie, are you still there? tim (05:15:07:175 PM): But you do not find the area of the triangle with trig functions on this one. Right? memyselfandi (05:15:13:164 PM): wait a minute, i th ink i may have it Ian (05:15:17:521 PM): Okay, Me. Suppose I say that x is equal to 2. If y is equal to 1/2x + 2, what is y? memyselfandi (05:15:50:609 PM): you would have 1/2 * 2 +2 Ian (05:15:53:636 PM): Actually, I think I would, Tim, because the angles aren't familiar ones, like 30 or 60 degrees. memyselfandi (05:15:56:488 PM): so Ian (05:16:17:279 PM): So, Me, one point would be (x=2,y=3), right? memyselfandi (05:16:17:753 PM): 1/2 * 2 + 2 = Y Ian (05:16:55:397 PM): Hi Evie, I hope I didn't lose you. We can work on your problem at the same time... memyselfandi (05:17:11:059 PM): I thought after you give x a value then solve that answer would be for y Evie (05:17:46:395 PM): i am here and ready tim (05:17:58:469 PM): I know you use them for the pentagon but the triangle is not colored. Do you still use them for it? If so could you show me?Ian (05:18:06:199 PM): Okay, Evie. So you're going to solve y = 75 + 25x for x in terms of y, right? Evie (05:18:18:019 PM): yes Evie (05:18:34:280 PM): we can use 3 Evie (05:18:39:385 PM): is that ok memyselfandi (05:19:04:286 PM): Ian- in some examples I've seen, the < has to be changed to = sign. Ian (05:19:23:035 PM): Tim, if I understand your problem correctly, you could divide the pentagon into 5 triangles, all the same; and you're looking for the area of 4 of them. Is that right, or have I missed something? Ian (05:19:41:791 PM): Evie, I'm not sure what you mean by 'use 3'. tim (05:19:50:579 PM): I think that is correct. Evie (05:19:58:352 PM): sub 3 into x Ian (05:20:20:591 PM): Me, do you see why (2,3) is one point on your line? If so, can you find a second one? Ian (05:20:59:406 PM): Evie, what I had in mind was something more like this. Suppose I know that y = 3x + 4. In that form, I can put in a value for x, and it's easy to find one for y. But I can do this: Ian (05:21:00:595 PM): Ian (05:21:07:501 PM): y = 3x + 4 Ian (05:21:11:735 PM): y-4 = 3x Ian (05:21:17:105 PM): (y-4)/3 = x Ian (05:21:47:474 PM): Now I've solved for x in terms of y, and the situation is reversed. I can put in a value for y, and get the corresponding value for x. Does this look familiar at all? Evie (05:21:47:537 PM): oh okay so i gott aget it in like slope form Ian (05:22:28:362 PM): Tim, so I think the way you're supposed to attack your problem is to find the area of a regular pentagon with side length 3.5, and then take 4/5 of it. Does that make sense? Evie (05:22:30:808 PM): but why am i isolating x i though i would be isolating y memyselfandi (05:22:34:820 PM): I plotted the 2, 3 on the line but I don't understand why you chose those two numbers. Ian (05:22:54:863 PM): Usually you isolate for y, but you'll see in a moment why you want to isolate for x instead. tim (05:23:05:549 PM): yes I will try that. Evie (05:23:07:952 PM): okay let me look at this for a second Ian (05:23:17:478 PM): I chose x=2 because I new I was going to multiply by 1/2, so I wanted to end up with an integer. Ian (05:23:41:761 PM): So the next one I'd choose would either be x=0, or x=4. Ian (05:23:50:929 PM): Me, can you pick one of those and get a second point? Evie (05:23:56:649 PM): so is it y-50/30 = x memyselfandi (05:24:13:521 PM): give me a minute Evie (05:24:40:280 PM): Ian is that right Ian (05:24:44:343 PM): Evie, when you write it that way, you need to use ()'s to make it clear that the whole numerator is being divided... Ian (05:24:51:845 PM): x = (y-50)/30 Ian (05:24:55:621 PM): Otherwise, that's perfect. Evie (05:25:06:940 PM): okay now what thanks btw Ian (05:25:23:620 PM): So now here's why we call this substitution. We have an equation, y = 75 + 25x... Evie (05:25:32:446 PM): k memyselfandi (05:25:47:960 PM): okay, what about picking 4 Ian (05:25:51:790 PM): and we know that, at the point of intersection, whatver x is, it's equal to (y-50)/30... Ian (05:25:53:709 PM): Right? memyselfandi (05:25:58:341 PM): that would me 1/2 * 4 + 2 Ian (05:26:07:693 PM): Me, if you put x=4 into y=1/2x + 2, what do you get for y? Evie (05:26:33:495 PM): y=75+25 (y-50)/30 is this correct Ian (05:26:45:207 PM): That's lovely, Evie. memyselfandi (05:26:50:245 PM): 4 Ian (05:27:00:324 PM): Now you've got an equation with just one variable, y. Can you solve that to get a value for y? memyselfandi (05:27:00:608 PM): so it would be (4, 4) Ian (05:27:21:987 PM): Me, that's right. So now you have two points: (2,3) and (4,4). Ian (05:27:26:823 PM): Can you plot those on a graph? memyselfandi (05:27:31:443 PM): I did Ian (05:27:37:830 PM): How are you coming along, Tim? tim (05:27:43:783 PM): that does not work out. Ian (05:27:50:470 PM): What do you mean, Tim? Evie (05:27:52:152 PM): should i distibute 25 to what sin ( y-50) Ian (05:28:10:856 PM): Yes, Evie, that's what I would do. Ian (05:28:37:186 PM): Me, once you have two points, since you know it's a line, you can just use a ruler to fill in the rest of the line. Have you done that? memyselfandi (05:29:07:344 PM): now i believe i read somewhere in my text that it isn't necessary to plot 3 points but it's a good idea so that you can make sure the line is straight to have the right answer. memyselfandi (05:29:30:270 PM): yes, i have done the ruler and it's a line but i'm doing one more point Ian (05:29:37:716 PM): Sure, it's always good to check your work. If you get 3 points and they're _not_ on a line, it means you have a problem. So get another point if you'd like. Evie (05:30:18:781 PM): y= 75+ 25y-1250/30 is this right Ian tim (05:30:48:745 PM): I have the answer and the way I did it was to find the pentagon with trig functions and the tri with 1.75 times three sqrt.and find that area. Then subtract that from the pentagon Ian (05:31:12:157 PM): Tim,that sounds like a good solution. Ian (05:31:29:157 PM): Evie, let me check that on my scratch pad... Evie (05:31:34:046 PM): k memyselfandi (05:31:40:461 PM): I chose to use 6 for x and got 5 for y tim (05:31:40:607 PM): But why does the other not work out memyselfandi (05:31:48:426 PM): i plotted those and the line is straight Ian (05:32:27:838 PM): Evie, again you need the ()'s: y = 75 + (25y - 1250)/30 Ian (05:32:41:411 PM): Otherwise, it looks good. Can you solve that for y? Evie (05:32:42:907 PM): okay i keep forgetting that Evie (05:33:17:469 PM): uh Ian I am a little stuck now Ian (05:33:21:374 PM): Me, okay, nicely done. So here's the thing. If you pick a value of x, like 2, and you get y=3, that's a point where y is EQUAL to 1/2x + 2, right? Ian (05:33:44:717 PM): Evie, try multiplying both sides of the equation by 30. Evie (05:33:55:517 PM): k memyselfandi (05:34:14:918 PM): okay, I think I got it Ian (05:34:41:678 PM): Me, you see where the points where y is LESS than 1/2x + 2 would be? memyselfandi (05:34:50:260 PM): I first choose a number for x memyselfandi (05:34:57:107 PM): then solve memyselfandi (05:35:09:991 PM): the answer i get when i solve is the number for y memyselfandi (05:35:28:386 PM): then I plot on graph but i have to find more than one point in order to make a straight line Evie (05:35:49:683 PM): y=25-1250 is this right ian Ian (05:36:32:144 PM): Well, that would make y negative, wouldn't it, Evie? Evie (05:36:38:616 PM): i dunno that looks messed up to me Ian (05:36:55:645 PM): Tim, what did you mean by 'the other'? memyselfandi (05:37:05:499 PM): Ian, I'm not sure i understand you correctly. Evie (05:37:20:380 PM): y= 25+ 1250 Ian (05:37:28:814 PM): Me, what did I say that you didn't understand? Evie (05:37:38:421 PM): y=1275 memyselfandi (05:38:29:933 PM): Ian> "Me, you see where the points where y is LESS than 1/2x + 2 would be? Evie (05:38:32:802 PM): Ian is that right Evie (05:38:49:115 PM): Y=1275 tim (05:38:50:617 PM): Thank you Bye memyselfandi (05:38:57:608 PM): okay, never mind Evie (05:38:57:649 PM): bye tim Ian (05:38:58:769 PM): Bye tim! memyselfandi (05:39:00:128 PM): i get it now memyselfandi (05:39:05:313 PM): Bye tim Ian (05:39:10:916 PM): Hold on a second, Evie. system (05:39:25:257 PM): tim left the Main chat room. Evie (05:39:26:692 PM): 1/2 is the slope up one over 2 Ian (05:39:59:730 PM): Me, I was pointing out that the line tells you a bunch of points where if you choose a value for x, the value of y is 1/2x + 2. One such point would be (2,3). memyselfandi (05:40:30:358 PM): I got it. Ian (05:40:38:897 PM): But now, suppose we look at a point like (2,1). In that case, 1/2x + 2 is equal to 3... but 1 is less than 3. So this point satisfies y < 1/2x + 2. Evie (05:40:39:864 PM): whooooooohoooooo you got it memyselfandi (05:40:41:157 PM): Thank you so much Ian. I can do the second one on my own now. Ian (05:40:56:622 PM): Okay, glad I could help. Evie (05:41:04:123 PM): Ian is good teacher Evie (05:41:12:933 PM): Me congrats memyselfandi (05:41:27:735 PM): yes he really is memyselfandi (05:41:28:533 PM): but memyselfandi (05:41:33:342 PM): oops, now i'm lost again memyselfandi (05:41:37:683 PM): :) Ian (05:41:46:403 PM): So, Evie, can you show me one step at a time how you proceed from y=75 + 25(y-50)/30? Evie (05:41:48:779 PM): Okay Ian did you see what my answer was Ian (05:41:54:862 PM): Me, what are you lost with? Evie (05:41:57:077 PM): I got y=1275 Ian (05:42:19:058 PM): Evie, that's the result, but you went astray somewhere. I'd like to find out where, okay? Evie (05:42:33:114 PM): is the result correct Ian (05:42:34:724 PM): From y=75 + 25(y-50)/30, what's the next step? memyselfandi (05:42:49:205 PM): The last thing you said Ian (05:42:58:851 PM): 1275 isn't correct. There's a problem somewhere. Ian (05:43:25:275 PM): Me, if you look at that line you drew... Evie (05:43:34:394 PM): Ian (05:43:54:331 PM): there are three kinds of points on the plane: the points ON that line; the points ABOVE that line; and the points BELOW that line. Right? Evie (05:44:48:636 PM): okay hey Ian I cant figure it out Ian (05:44:57:915 PM): Evie, if I multiply the equation by 30, I get 30y = 30(75) + 25(y-50), right? Evie (05:45:35:164 PM): let me look at this for a few system (05:45:40:597 PM): RoMol9 has joined Babylon. Ian (05:45:48:276 PM): Okay, Evie. Ian (05:46:00:449 PM): Hi Ro. What's on your mind today? Ian (05:46:10:696 PM): Me, does the last thing I said make sense? Evie (05:46:29:878 PM): how come i didnt multiply 30 times 25(y-50) RoMol9 (05:46:44:645 PM): Hey I'm thinking if I'll ever pass my math test Evie (05:47:14:462 PM): hey I am thinking if i dont get this Take home test 100 my dads gonna slap me Ian (05:47:21:769 PM): Evie, in 'slow motion', it looks like this: 30*[y] = 30*[75 + 25(y-50)/30]... memyselfandi (05:47:21:992 PM): I suppose. If you mean that the point On the line is the middle point (4,4) the point ABOVE the line (6,5) and the point BELOW the line (2,3) Ian (05:47:48:885 PM): 30y = 30[75] + 30[25(y-50)/30] RoMol9 (05:47:49:856 PM): Hey can anyone explain to me how to add and subtract time Ian (05:47:58:597 PM): I just distributed the multiplication on the right... RoMol9 (05:48:07:408 PM): I'm in the fifth grade Ian (05:48:08:860 PM): Sure, Ro. I can help you with that. RoMol9 (05:48:23:008 PM): ok system (05:48:35:850 PM): dog has joined Babylon. memyselfandi (05:48:40:213 PM): hey Ian, thank you for all of your help. I feel better about my quiz now. Ian (05:48:48:780 PM): Ro, suppose you want to subtract 4:00 from 6:25. Can you do that? Ian (05:49:01:319 PM): Hi dog. Ian (05:49:07:263 PM): Who's messing up the canvas? RoMol9 (05:49:23:335 PM): hold on let me work it out memyselfandi (05:49:27:575 PM): i don't know, I was wondering that too. I had just cleared it. system (05:49:31:433 PM): JohannTest has joined Babylon. Evie (05:49:42:021 PM): Ian what ever I get y = to then do I substute it back into what equation RoMol9 (05:49:51:815 PM): 2:25 memyselfandi (05:50:11:757 PM): bye all, good luck Evie and Ro RoMol9 (05:50:16:560 PM): is 2:25 the answer system (05:50:22:954 PM): memyselfandi left the Main chat room. Ian (05:50:29:049 PM): Me, what I mean is that if you pick any point, and you look at the (x,y) for that point, one of three things will be true: y will be EQUAL to 1/2x + 2; or y will be LESS than 1/2x + 2; or y will be MORE than 1/2x + 2. Evie (05:50:37:996 PM): ME is gone RoMol9 (05:50:46:463 PM): Thanks system (05:50:55:412 PM): dog left the Main chat room. Ian (05:50:55:882 PM): There's no real collaboration here, just three different kinds of problems... Ian (05:51:13:543 PM): Well, I hope Me got what he needed... Evie (05:51:21:388 PM): i dont know what i am doing Ian (05:51:22:240 PM): Evie, how are you doing? Evie (05:51:29:330 PM): aweful Evie (05:51:35:487 PM): I am about ready to give up Ian (05:51:40:863 PM): Evie, hold on! RoMol9 (05:51:43:545 PM): Hello? Ian (05:51:47:361 PM): Ro, nice job. RoMol9 (05:52:04:858 PM): is 2:25 the answer Ian (05:52:26:931 PM): Right, Mo. How about subtracting 4:10 from 7:40? Evie (05:52:34:884 PM): why cant i solve this equation i know how to solve equations Evie (05:52:44:523 PM): arggggggggggg Ian (05:52:49:100 PM): Evie, let's come back to the equation in a minute, okay? system (05:52:54:112 PM): jerzeygirl714 has joined Babylon. Evie (05:53:06:572 PM): now what Ian (05:53:23:323 PM): The point is, when you solve the equation, you end up with y=200. Evie (05:53:43:868 PM): k Ian (05:53:55:453 PM): Ro, if you go into Chat Room Algebra2, there's someone who can help you with times. Ian (05:54:02:875 PM): Hi J. RoMol9 (05:54:06:608 PM): But how do you um borrow and don't know the answer Evie (05:54:16:467 PM): what equation do i put that back into system (05:54:26:556 PM): jerzeygirl714 left the Main chat room. RoMol9 (05:54:31:911 PM): how can i go in there Ian (05:54:32:631 PM): So what that tells you is that when they've saved the same amount in the same week, that happens at $200. Ian (05:54:51:631 PM): Ro, hit the 'Chat Rooms' button near the top, and select the room. Ian (05:55:14:494 PM): So, Evie. We've found that y=200 at the point where the lines intersect. Right? Evie (05:55:25:950 PM): yesw system (05:55:39:906 PM): RoMol9 left the Main chat room. Evie (05:55:54:531 PM): so i dont hav eto sub the 200 back into anything Ian (05:55:56:449 PM): Now we canlook at either of our equations, like y=75 + 25x. Evie (05:56:02:128 PM): I thought I did Ian (05:56:04:892 PM): And we know that y is 200... Evie (05:56:11:839 PM): OHHHHHHHHHHHHHHHHHH Ian (05:56:12:727 PM): So we can substitute 200 for y: Ian (05:56:21:220 PM): to get 200=75+25x Ian (05:56:27:723 PM): And if you solve that for x, you get.... Ian (05:56:29:109 PM): What? Evie (05:56:38:425 PM): okay cool Evie (05:56:39:923 PM): Ian (05:56:51:509 PM): Is this making sense now? Evie (05:57:07:239 PM): 5 Ian (05:57:07:815 PM): What's nice is that this works for _any_ two lines. Ian (05:57:35:061 PM): Even if you have y= 36.3x + sqrt(5), y = pi*x - 900,001 or something horrible like that... Ian (05:57:43:761 PM): You'd never want to construct a table for an equation like that. Evie (05:57:51:510 PM): true Ian (05:57:53:762 PM): But substitution will take you right to the answer. Evie (05:58:05:239 PM): wow i gotta practice this alot Evie (05:58:16:162 PM): i also gotta find where igot hungup o n the solution at Evie (05:58:42:870 PM): i have a question rem when i was dividing everything by 30 then all of a sudden i multiplied it by 30 Ian (05:58:47:075 PM): Let's try a simpler one, okay? 3x + 2y = 7; and 5x - y = 3. Evie (05:58:50:579 PM): what isthe rule for that Ian (05:59:15:974 PM): It's not so much a 'rule', reallyl. If you have... Ian (06:00:02:917 PM): So the 30's canceled out. Evie (06:00:20:593 PM): okay Evie (06:00:46:657 PM): 2y=7-3x Ian (06:00:48:198 PM): The thing is, that was a hard one to do by substitution. In real life, since you'd already solved both equations for y, you would just set the expressions equal to each other: Ian (06:00:57:422 PM): 75 + 25x = 50 + 30x Ian (06:01:01:683 PM): Then you'd solve for y. Evie (06:01:18:807 PM): K Ian (06:01:18:830 PM): Right, keep going. Ian (06:01:33:977 PM): (I meant, solve for x. Oops!) Evie (06:02:24:499 PM): which one 2y= Ian (06:02:36:737 PM): Right. Solve 2y=7-3x for y. Evie (06:03:30:117 PM): i got 1/2 i let x =2 Ian (06:03:53:276 PM): When you solve for one variable in terms of another, you don't use any particular values. Evie (06:04:09:749 PM): ok Ian (06:04:37:754 PM): Let's try one without fractions... Evie (06:04:39:200 PM): so 5x-1/2=3 Evie (06:04:53:139 PM): is that right Ian (06:05:35:550 PM): Where did the 3 come from? Evie (06:06:04:348 PM): earlier i thought you said 5x-y=3 Ian (06:07:12:986 PM): I think the fractions are getting in the way. Let's try this: (1) 3x + 2y = 5 (2) y = x + 1Ian (06:07:31:912 PM): In this one, you can substitute for y in the first equation. What do you get when you do that? Evie (06:08:23:374 PM): x=1 Evie (06:08:35:164 PM): i mean x+1 Evie (06:09:20:939 PM): 3x+ 2(x+1)=5 Ian (06:09:31:877 PM): Right! Evie (06:09:40:854 PM): now what Ian (06:09:44:652 PM): So can you solve that for x? Ian (06:10:01:206 PM): Do it one step at a time, okay? Evie (06:10:30:885 PM): k Evie (06:10:58:307 PM): 3x+2x+2=5 Ian (06:11:04:620 PM): Good. Keep going. Evie (06:11:25:595 PM): 5x+2=5 Ian (06:11:32:823 PM): Nice. Evie (06:11:44:761 PM): 5x=5-2 Ian (06:11:49:660 PM): Yup. Evie (06:11:52:151 PM): 5x=3 Ian (06:11:56:144 PM): Yup. Evie (06:12:06:257 PM): x=.06 Ian (06:12:14:222 PM): Um... not quite. Ian (06:12:18:599 PM): Try writing it as a fraction. Evie (06:12:38:485 PM): 6/100 Evie (06:12:48:290 PM): 3/50 Ian (06:12:50:461 PM): What do you get when you divide 3 by 5? Evie (06:13:03:978 PM): oopos Ian (06:13:08:825 PM): :^D Evie (06:13:10:445 PM): 6/10 Evie (06:13:16:399 PM): 3/5 Ian (06:13:18:031 PM): Right. Nailed it. Ian (06:13:36:620 PM): So now you know that where those lines cross, x is 6/10, or 0.6. So what is y at that point? Evie (06:14:51:814 PM): k working on it Ian (06:14:55:515 PM): Okay. Evie (06:15:31:527 PM): y=1.6 Ian (06:15:36:193 PM): Right! Evie (06:15:40:220 PM): YESSSSSSSSS Ian (06:16:05:172 PM): So the only thing that happens from here is that the equations get more complicated, with fractions and negative numbers and stuff. Evie (06:16:13:399 PM): so if i graph that those are my points Evie (06:16:22:028 PM): argggggg Ian (06:16:23:572 PM): But the idea stays the same: solve for one variable, substitute into the other equation, solve for the second variable... Evie (06:16:30:546 PM): cool Ian (06:16:46:311 PM): Want to try one more? Evie (06:16:47:253 PM): sp you really only sub twice all together right Ian (06:16:55:488 PM): Right. Evie (06:17:01:624 PM): yeah one more then i gotta ask one more question its a fast one Ian (06:17:26:807 PM): Why don't you ask your question? Ian (06:17:32:374 PM): We need to be winding up anyway. Evie (06:17:47:780 PM): I was gonna sk you the best way to scale my axes for this Evie (06:17:58:110 PM): when i graph each situation Ian (06:18:00:396 PM): Oh, you mean to plot fractions? Evie (06:18:02:729 PM): is there a trick tothat Ian (06:18:06:849 PM): Or for your original problem? Evie (06:18:13:673 PM): yeah when i make my graph Evie (06:18:20:687 PM): the original Evie (06:18:28:388 PM): the bike Evie (06:18:31:079 PM): ?? Evie (06:18:37:842 PM): any hints for me there Ian (06:18:50:383 PM): Basically, you pick numbers that will make it easy. So you have weeks that will be like 1, 2, 3, 4, ... Evie (06:19:13:566 PM): k Ian (06:19:59:704 PM): And you'll have savings that will be in hundreds of dollars... Evie (06:21:05:845 PM): wow how come your going backwards is that because your saving and not spending Ian (06:21:07:454 PM): So those are the tick marks I'd choose. Ian (06:21:24:299 PM): What do you mean 'going backwards'? Evie (06:21:39:990 PM): sorry i a i am tired Evie (06:21:49:938 PM): ijust ignore what i ask Evie (06:21:58:304 PM): duh duh thats me Evie (06:21:59:903 PM): lol Ian (06:22:00:255 PM): Well, we need to finish up anyway. But are you understanding the whole substitution thing? Evie (06:22:18:918 PM): yeah i am gonna practice i will maybe come in again sometime soon and tellyou what i know Evie (06:22:25:124 PM): do you get paid for this Ian (06:22:28:720 PM): Okay. Ian (06:22:45:141 PM): Our math doctors are volunteers. Evie (06:22:53:295 PM): I am glad because yuou work so hard and help us so much in here Ian (06:23:01:343 PM): We have fun doing it! Evie (06:23:07:494 PM): you are great Ian (06:23:12:310 PM): Thanks. Ian (06:23:22:976 PM): We'll have another one of these next week. Evie (06:23:23:543 PM): i thanks ian I really really really appreciate i t goodnight Ian (06:23:30:104 PM): Good night! system (06:23:41:035 PM): Evie left the Main chat room. system (06:32:34:824 PM): Ian left the Main chat room. system (06:38:54:425 PM): JohannTest left the Main chat room.