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Pre-Algebra - 5.1 Homework Problems Worked Out

Added Jan 29, 2021 •

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Walk-Through for the Homework Problems Follow the steps and Check your work

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so we have a rectangle I'm not going to draw on my page right here but you need to realize that the other sides are not numbered so you have this 3 and 8 but you need to realize you have 3 and 8 also the perimeter a lot of guys messed up on the perimeter because you only added these two sides remember I give you guys the answers you guys need to show the work the perimeter equals it's up to you which formula is how to use formula for rectangle is nice and easy cuz it's double the length plus the width perimeter equals 2 and our length is 8 + 3 body guys only added m3u forgot there's the other one but if you want to go straight around length + width length + width length + width + length + width all the sides but if you see that repeating these on two numbers that are different 2 * 11 your perimeter is 22 now that is versus the area the area formula of a rectangle is the length when's the wits or base times height I'm prepping you guys for the geometry the base is always the bottom or the top the height is going straight up and down so base times height 8 * 3 which is 20 for two different numbers 7 that's a good one right here what it so they gave you three numbers but they had to give me three numbers cuz there's a difference what's the perimeter and what's the area the perimeter of a triangle is just adding up all the sides A + B + C which one's a which one's me which one to see it doesn't matter cuz all you're doing is adding I'm just going to go go on a run start I'll start right here 5 + 12 + 13 if I started down here 12 + 13 + 5 if I started right here 13 + 5 + 12 heck I could even go backwards it doesn't matter when you do cuz when you're finding perimeter you just adding the sides up you just got to imagine take one of the angles of corner and cut it just imagine unfolding it and straightening it out to one flat line so you no longer have a shape how long would that be of a line so right here 12 and 13 what is a 25 + 530 area though of a triangle 1/2 base times height but which is the base which is the height is in a triangle you got three sides and one of them is not the base or the height now this is why I said important that's why this was a trick question and I went over that using the rectangle a right angle a right angle right here so pretty much your base is always based on if you have a right triangle is connected to the right angle so the base cuz literally how flat something is 12 is how flat how high is straight-up we describe height as remember when you were young some your parents still do that treat you like a little baby they have you go by your door and they measure your height and they tell you to stand straight up a right angle means you're not leaving back you're not leaving for your standing straight up so the height is on a right triangle is one of the legs so quick thing of a triangle you have a leg and hypotenuse so the hypotenuse in a triangle hot and noose is the longest side the legs of a triangle are the two shorter sides short besides shorter sides not always the case there are exceptions I'm not going to go with exceptions right now but but what is the height the height of a triangle of triangle is the perpendicular segment perpendicular line so when it's talk and the base of it is what is it perpendicular to base segment height is there's a symbol for perpendicular it's upside down capital T base is segment height is perpendicular to Seoul look at this diagram I'm going to redo it sometimes the hypotenuse is a base but it's never your height so if you look at this here is this right here the 12 is flat perfectly straight up from that 12 is the five this side is just there for your perimeter it doesn't really affect your area so you got to think and another one I could have done it is what if you made a rectangle out of it cuz I could have made a rectangular right here and look at this what's the area of this rectangle 5 x 12in because the triangle cut it in half can you do that so 1/2 V * 12 and I'm going to rearrange it I'm going to go 1/2 12 X 5 cuz what's half of 12 6 * 5 30 now I'm going to go do number 6 even though I didn't assign it so looking at number six listen to this diagram play that right there notice that right there is your height you're not always going to have that but notice it's perpendicular so they gave us that so the the perimeter of this is 10 + 10 + 12 the perimeter is 32 so perimeter equals 32 I'm just doing Mental Math right here but the area equals 1/2 base times height in this triangle the base is the bottom part to your which is 12 and your Heights is 8 41266 * 8 create rare occasions are your perimeter and your area the same but for the most part 98% of the time they're different numbers that's why that's what this is trying to get you to understand you got to difference formulas to use and especially in triangles you need to be able to identify the base and height that's why that was hard I get it let's go look at did anyone have not don't type it in saying I'm it yourself if you want to comment let me see if anyone wanted to know oh yes 9 let's go 9 word problem find the third side of a triangle with the perimeter where the perimeter is 120 1/4 ft and the two side given two sides has a measure of 36 and 3/4 let's just draw a triangle where visual learners is a triangle we don't know how exactly how the triangle is but make a sketch this is one of the most hard things to get people is that they want to do geometry that's the whole thing schools are getting rid of the geometry class which I don't agree they're combining Algebra 1 geometry and algebra two three classes into two classes called I forgot what it's called mathay and math be your math 1 and math 2 high school math integrated math 1 integrated math 2 so 3 years of math in 2 years I do and don't agree with it so I'm not going to add on with it's too much blood for the so we know the perimeter they gave us they give us information perimeter is 100 24 and 1/4 what's the formula for perimeter perimeter here's forget using a b and c a perimeter of a triangle is 3 sides add upside one plus side to plus side 3 what these numbers are there not called exponents exponents are up top these are called what I don't know what they're called anymore there's sub numbers submarines below something just say if I got three sides and I don't want to give different variables for it this is side one side to side three they don't have any value there just to differentiate the different sides all right so to find the perimeter you add up all three sides but they gave us other bit of information and two of the sides is 36 and 3/4 which are the two sides it doesn't matter because like that other triangle when I showed you was perimeter two of them are two of them you can put any order you want so substitute in pretty much Algebra 2 when you guys get to Algebra 2 or integrated math 2 realize that this is all just substitution if you get that simple Concept in your head super easy if you don't super hard so they give us the perimeter of 124 and 1/4 that is equal to one of the sides plus the other two sides which was 36 and 3/4 there you go there's your variable equation we took a formula and then we substituted the information we knew now we have a one variable equation and all we got to do is solve for the one side unless that look at this find the third side here's a third side that's the tractor 6 3/4 - 36 3/4 I am not going to change it to an improper fraction cuz I'm just going to treat it like subtraction is 1/4 is smaller than the 3/4 so I got to borrow so I got to turn this for into a 3 and I got to bring one hole into here so one who is 4/4 4/4 with 1/4 comes V Force 5/4 - 3/4 I got to force I'm going to write it down as 2/4 first and now I just subtract the rest o I can't do this three how to track 6 I got to borrow again that becomes the one that becomes at 3:13 - 6 that is seven one can subtract 3 * 11 - 387 + 2/4 which is 87 + 1 practice practice practice that's all any of this stuff is all right and then I saw a 11 somewhere I believe thanks donde estan say had heard it's the same concept it's just like what we just did right here so 11 they gave you the area of this rectangle we have one measurement but missing the other one now here's another concept you need to understand if there's a formula write down the formula without putting any numbers in there we know that we have a narrow area area of a area of a rectangle is area equals length times width forget base times height listen length times width for now we have one of them we're missing the W they gave us the length then they also gave us the area so now what substitute in instead of the area as a it's 4:32 instead of all we could substitute 36 36 * W is just 36 w look at this we have a one-step variable equation keeping for a lot of people in the very beginning is not understanding how to set it up if you know there's a formula this right here is the first step in practicing and mastering write down the formula if you know there's a formula connected to this idea write down the formula without plugging in any numbers yet it doesn't take that long to write down for unless you know you have that take the information and substitute and then usually there's the light switch light bulb turns on and you like you find your wits I don't know why we could do what it what is 432 / let's just do long division for 32 / 36 there's one and there's we subtract 36 13th get sick 72 so are with equals 12 and that's it and this ain't this one's the same that who cares that it's the length it makes no difference so I didn't that take it out 361 equals 19 times the length 19 * 899 * 9 I'm at the square alright I've done the next one 13 - Mazda do all of them check her work so why do you guys not a lot of yesterday but some of you turn this in and if this many people are having issues with this that's how I know you faked it I'm going to give you credit for this homework but you could lie to yourself I hope you keep on cheating your way to get a higher and higher class till then sure you get to a class where how you going to cheat when the smartest person gets a lower grade than you that tells the teacher that you don't know you fake that wreath so thank you for just turning in work with no work turning work with just a bunch of answers and copying down a problem that's not showing work but again for those of you guys at tell me about these people you know I can't do anything to those people right now cuz I can't see that they're cheating I can only suspect but thank you you're doing everything for you to earn your grade you're honest enough and at some point in life you're going to realize that work you do will help you if you're going to fake it at some point it's going to come back and haunt you cuz he can't do the work yes all right so yeah cuz you guys are doing a good job keep on doing it now here's a thing for all of us. I give you the answer key that's where people copied on the answers that's where they copy dumb as I give the answer key the whole thing is like the math we all talk about a maze for some reason when we we can do a maze going backwards I don't know why it's weird psychological think we start at the end of the exit and we can work our way back to the beginning for some reason we're able to do a maze faster that way I don't why try it next time get your gold go have your parents go to a a bookstore something and buy you one of those maze books in a crossword puzzle but you time  it up instead of getting on your phone looking at stupid videos people falling I love watching people falling videos especially if they fall off their bike but until they get blood so yeah I love you or falling off their skateboard it's all fun and games till someone gets hurt I love it when they try to do a rail grind like literally on a stair rail and they just fight it can't help but laugh I have been in the circumference of a circle is the distance around a circle it can be found by using the formula circumference equals 3.14 D so here circumference the regular from is 2 pi r 2 times pi times the radius so what day did instead they went pie to our two times the radius so in a sir the radius is from the center of a circle out that's a radius now if I did the radius the other way going this way. Just cuts the circle in half so there's another formula by going hi d d stands for diameter Empire they change it to 3.14 so that's why I C equals is about an estimate 3.14 diameter that's where that came from so they're cutting it short so they went all that they didn't want to explain it and I just did find the circumference in inches of the world's largest pumpkin pie that has a diameter of 14 ft so14 so the dab they literally give you the diameter 14 and all I got to do is plug it in 3.14 times 14 that's your circumference substitution all it is is is Messi what it is 3.14 * 14 43.96 turn in a second so the question is what is this wavy thing so equal literally means equal but when you cut off numbers an estimate so why is some huge number 3.14 something I don't know these fancy calculus you have a pi button and ever gets is how many decimals which pie I assume we're here Ernest pie so pies right here and to get you a to get to a symbol on top you got to use this second by me see it look at this flashing this a square press 2nd and now it's an arrow it means the button whatever's on top of the button and blue so now noticed that I got a pie 3.141592654 now that's the pi button not noticed all they do is round off they cut off to decimals 3.141 rounded two decimals 3.1 for the fraction the closest fraction to Pi is 22/7 but notice the decimals are different the very beginning looks the same but as a fraction Pi is closed 22/7 it's still 3.14 this is the closest fraction that gets you 3.14 but 22/7 is little bit bigger than Pi so notice of change but that's why sometimes pie is 3.14 22/7 but 43.96 and because we use an estimation we cut off it's no longer equal it's about that means about two wavy lines and 7 equal sign that was 11 13 oh that was 1315 that's 1415 use a diagram of a vegetable garden here's the vegetable garden it's a rectangle 15 by 22 you want to put fencing around the garden to keep animals out how much fencing do you need so it's literally you put the fence around you know you got 15 feet of fence here this is Lexile right here you got 15 feet of fence you got 22 feet of fence but if you want to keep all the rabbits the cute little rabbits from eating all your I don't know what are those dozen strawberries cauliflower strawberries I don't know what those are fake cabbage but if you only fence this in use your Lexile logic that's why Math Connects to wet sounds the symbology we use the symbol the idea to connect the fat if you only put fence right here what's the point is you can still get in here how long is this 15-22 so double this what is this perimeter equals 2 * 22 + 1537 W 37 what is a 60 70 for your perimeter 74 feet long and then it goes this one bag of fertilizer covers 150 square feet how many bags would you need for the garden now that's the whole thing area understanding area remember area I got 22 Rose I can't do 22 Christian I just can't show it then and then you Criss-Cross it area represents how many of these little squares you have one square feet one two three four five seconds adding till you get to this the one right here at the end your final one so how do you find that your * 22 * 15 what is that 10 Carroll 110 and then 0 then you too and a to 320 we need to fill 320 Square here's a thing one bag one bag gets you 150 square feet 1 bags sales in 152 bags get you 300 square feet but we need to cover it completely cuz 20 so this is one of those things in life and in math you need to go all right man I'm 20 short but who cares you still need to buy 3 bags Even though three bags covers 450 you'll have left without that they're you it would not be complete so you need 3 bags even though it's more than you need cuz if you get too bad you don't have enough you always want to fill in so three bags that's where that came from how many bags would you need and I can't next one what is it 17 involves you counting that's what makes this one hard so you actually need to be able to count how many plays find the area so look at this this one's nice Seventeen it's four squares across 1234 so we know that's four units what's the area how many units high is it I got four up top three on the bottom so I know it's 7 the area for this is 4 * 728 you could tell every single square and you'll get 28 littlest first row the four second round for four squares in each row on each column and then I got 7 Rose 4 * 728 2725 us-62 that was 1715 1323 2325 27 19 all right getting these variables by themselves look at this so V volume Eric v stands for volume capital A stand for area height volume is the volume formula is length hair that's a different version but they went straight volume equals length times width times height this pen is done but you get it and let what's length times width that's why they can switch to down that but it says solve for the indicated variable that means age equals what so looking at this right here this is technically area times height to get anything by itself always do the inverse operation to what you want to get rid of so let's rewrite this as volume height times area we want to get the H by itself and its times a do the inverse operation to get about self what's the opposite of x a / a * / a look at this * a * a friend of there a Over as1 leave me with h over one which is just eh but what you do on one side of the equal sign you got to do to the other volume divided by area equals your height that's all thing how you get the variable by itself these are always questions are going to ask a bunch of bunch of different variables and they want one of the variables by themselves practicing your inverse operation let's look at one of bond I'm going to do 20 just for the heck of it true 2 PT equals best - t i want s by itself how do I get the S5 self whatever is connected do the inverse instead of minus tea let's add tea to both sides now the hard thing for Elida guys to understand that p and t are different terms you cannot combine them so you got to keep it separate you get to p + C equals -0 leaving you with s this these right here help you understand how to do steps 20 same concept R equals s t plus p I want the P by itself how about this I'm going to rewrite this you don't need to do this stuff you guys should go straight I'm just showing you this p plus s t i want P by itself the red how do I get rid of a plus s t i got to subtract St on both sides best team on SSD that's a zero leaving you with just pee literally reading are minus St they do not sound alike so it's our - s t you have an expression leave it at that and then 2323 how to get baseball what's self area equals 1/2 base times height area equals 1/2 base times height so let's let's get rid of things one at a time how do I get rid of 1/2 here's a way to think about it any time you have a fraction and you want to get rid of a fraction you multiply by the reciprocal area equals on the put some space here so you can see we could do things one at a time so let's * 2/1 what I do on one side I need to do to the other two over one is just too so I end up with two a 2 x 1/2 at the one goes away and left with base times height how do I get Base by itself I / the height height over height is one leaving me with just the base so 2 times the area divided by the height I guess the bass inverse operations seeing how to do things and go backwards and is that it let's check when's 2527 Merrick this might as well finish on 25 and 27 25 right and salt it was 1 to 23 odd and then 27 we're not doing no hoping in the stuff that takes too long 27 though find find the dimensions of a rectangle with the largest area is the perimeter is 40 we got a rectangle we had a rectangle that the perimeter equals 40 what's the biggest possible area if you know the perimeter is 40 so you got to look at all this think about all the different numbers you can add to get 40 so the whole thing you do length times width so we cut that here's here's the wits here's the list together 2 times the length plus width equals 40 length plus width equals 20 what are all the different rectangles you can make with the length of forget decimals we don't want that symbols and the whole thing is which one has the biggest here which one has the biggest area look at how area changes so we could go 1 + 91 * 19 so that adds up to 20 and we double that we get a perimeter 40 the area for this is 90 look at this right here we make it slightly bigger and now that shrinks this becomes too and this becomes 18th 2 * 18 the area for this is 36 it gets bigger and then we could go three and 17 notice there's all these combinations what's 3 * 17 what is that 3051 and then 4 + 60 notice what do I know I'll get there but I'm just showing this to the people who don't see the pattern and noticed that the air 4 * 1640 + 24 64 notice that if I make it more narrow and I make it wider it keeps on getting bigger there's a pattern until yes finally we get we can get what's the furthest we can go the furthest we can go is 10 and 10 a square a square always get you the most areas better than a rectangle so the area is 100 so a square room is much there's a thing Ware rooms people don't like it because everything is too even when things aren't even we get little bit more comfortable living relax a square room even though this room is bigger than a rectangular room if you look at Perimeter wise more square footage but sperm is never comfortable that's why they kind of make it slightly less than the square psychological thing don't ask me why you explain to me when you become rich famous and charged with what kind of money what if we go further notice once this gets bigger this becomes 11 it just shrinks it goes the other way instead of a rectangle longest I going to be this way longer side goes up and then it shrinks down eventually become eventually you get this when you shrink it back down you get 19 and one so when you get to ask where it goes back to rectangle with the rectangle start flipping the other way so there's your biggest rectangle all right let's go

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Pre-Algebra - 5.1 Homework Problems Worked Out

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