This homework assignment has been meticulously prepared under the strict supervision of the math god of planes, Schlomo.
A little known fact in mathematical history is that in the early 17th century, Schlomo (then just an MGIT - math god in training), had a surplus of matzo which he distributed to European philosophers for sustenance. One of those philosophers was Rene Descartes, who later became the father of the cartesian coordinate system, aka the coordinate plane. Coincidence? I don't think so!
So, as you munch on matzo this Passover, think about slopes, parabolas, intersections of systems and all things algebraic... Guten Pesach!!
pg 557-58 #5-7, 9-33 mult of 3
pg 560 1-infinity (at least #3,8,15,21,26-30)
Pretend you are having a quiz on Weds.... you're not... do as much as you can... please ask questions where you don't understand!
i have a question on #21, #24 on the first page....how do i factor if I only have the a and b values without a c value?
ReplyDeleteIs it 5-7 all or mult of 3?
ReplyDeletei have the same question for #21 on the review.
ReplyDeletePaul...
ReplyDeletei did all for 5-7 cuz m of 3 wdnt make sense!
Listen guys, I know Passover is a night for questions, but I think 5-7 ALL would make more sense than mult of 3!!
ReplyDeleteFactoring without a 'c' is FUN-NER (it's a word, look it up) and EASIER than factoring trinomials (I know what you're saying, how can ANYTHING be MORE FUN than factoring trinomials??!!)
ReplyDeleteLet's take y=x^2-4x
What's the common factor?? 'x', right?
So... y=x(x-4)
So now you have the expression in factored form. What value of 'x' makes 'x' zero? Hmmm, that's almost a trick question! When x=0, x=0... doh!! How about 'x-4'... x-4=0 when x=4 right?
So, your two solutions are x=0,4 ... yes?
Ca-peesh?
As for #21 on the review... in order to solve an equation using the ZERO PRODUCT PROPERTY, the equation MUST BE SET EQUAL TO ZERO.
ReplyDeleteSo, how can you set t^2-3t=28 equal to zero? Subtract 28 from both sides, yes? To obtain:
t^2-3t-28=0
I'll let you finish, since I don't want to steal the FUN of factoring from anyone!!
Ca-peeesh?
Actually, the previous answer works for #21 and #24 on pg 558... you weren't MISSING 'c'... it was HIDING on the right side of the equation... gotsk it?
ReplyDeletethanks mr c....!
ReplyDeleteMy questions will come a bit later..
ReplyDeleteYup... all Justin's are welcome btw... small, medium, large, or jumbo...
ReplyDeleteOOOOOOH MR.CHAMBERLAIN, YOU HAVE YOUR FIRST FOLLOWER!
ReplyDeleteFor #5, when it says "solve" does it also mean graph?
ReplyDeleteI don't know how to answer #6..
ReplyDeleteFor #7, I don't really understand the first part of the question, and the 2nd part seems too easy. Of course it's not always true that a or b=8, because 8 has other factors than 1 & itself!
ReplyDeletei can do #27 mentally but not using algebra?
ReplyDeleteWell for #6
ReplyDeleteTo factor the expression, you just chose your factoring technique (we are area modeler's for the most part) and write the expression in factored form... easy... one-step... done... duh!!
To SOLVE a quadratic equation (the same expression set equal to zero), we have a two-step procedure:
1) Factor the expression (EASY)
2) Use the ZERO PRODUCT PROPERTY to find (i.e. SOLVE for) the values of 'x' that make the equation true.
Ca-peesh?
Ohhh, so for what they have in common, you factor both, but in solving the equation, you have to use the zero product property?
ReplyDeleteFor #7, you are correct. Most of you seem to have trouble with the easiest questions... since all other real numbers have infinite factors (remember, not just integer factors... e.g. 1/2 has factors of 4&1/8 and 64&1/128, yes?) the zero product property cannot be extended to other numbers.
ReplyDeleteFor #27, see problems 3&4 on pg 556-57... then let me know if you still have a question.
ReplyDeleteNot use algebra??!!!! I'll pretend that post was anonymous!!!
Dear Ohhh, Yup.
ReplyDeleteI don't understand the last part of what you just said.. "the zero product property cannot be extended to other numbers"?
ReplyDeleteAnd for #15, I can't factor that equation, 32 doesn't have a "Good" square root.. it goes far into the decimals!
AHHH BLEHHH Sorry I just blurted out the comment above! I wasn't thinking! Please ignore the second part of that comment. ^
ReplyDeleteFor #15, I can't find 2 numbers that multiply to -128 and add to 4!
ReplyDeleteThink about it. If the zero product property worked (could be extended to) other numbers, would the math gods have named it the ZERO product property??
ReplyDeleteI don't understand how to make #27 into an equation..
ReplyDeleteAnd for ZPP, gotsk it!
For #15, first you try to "square-root" 32 and then you 128 involved? Huh?!
ReplyDeleteTo paraphrase the CapitalOne commercial "What's in YOUR box?"
(Hint: g^2 in the lower left and -32 in the upper right)
As for #27, don't you read OPQs (other people's questions)??
ReplyDeleteAs I stated above, see problems 3&4 on pg 556-57... then let me know if you still have a question.
Sorry about #15, I was multiplying -32 by 4, for some reason I thought g^2 had a coefficient of 4..
ReplyDeleteYes, I read the explanation, but I don't see how I can use #3 and #4 to make an equation out of that explanation?
Wait, for example, if the equation was
ReplyDeletex^2+5x+7, would 7 be the y-intercept?
I am answering my own question =)
ReplyDeleteYes, anonymous, it would.
=)
For #27, do you find the function for that description by finding coefficients (A & b), which in the formula -b/2a come to be negative?
ReplyDeletefor #27, before you jump into formulas, let's make a verbal model and then convert to algebra...
ReplyDeleteYou don't know the length or width (in feet)... so let's define
x is the length of the blanket
y is the width of the blanket
Two variables. Boo-hoo! Can we reduce the number of variables? Hmmmm... AH-HAH!! The width is 2 feet less than the length, so:
x is the length of the blanket
x-2 is the width of the blanket
That's better!
Since the blanket has a length and a width, I guess we'll say that it is rectangular (if it had a base and a height, it could be a parallelogram shape). So how do we set up an equation for the area of a blanket that is 24 square feet:
x(x-2)=??
Can you take it from here? lmk
x(x-2)=24!
ReplyDeleteCan u take it a little further from there???????... perhaps a SOLUTION might help??? I'm just sayin'...
ReplyDeleteI'm having trouble with the same problem. I got this far.
ReplyDelete1. Turn x(x-2) into x^2-2x=24
2 subtract 24 from both sides, leaving me with
x^2-2x-24=0
3. Factor (x+4)=0 (x-6)=0
Solve x-6=0
+6
x=6 correct,
x+4
-4
x=...-4?
That's the only part I'm having trouble with.
PS. Maybe I missed something during my lesson. Maybe I could come in for lunch tomorrow.
ReplyDeleteI was quite confused about p^2-4p=21. It doesn't fit with the rest of the problems and I couldn't figure it out
ReplyDelete(ps. sorry for being so late about it. Dentist+jazz band+ passover seder=crazy schedule!)
Dear A&P,
ReplyDeleteFunny solutions make life fun. Since quadratic functions often offer up TWO algebraic solutions (aka, x-intercepts, roots, zeroes) one of those solutions is often EXTRANEOUS (remember that word from Monday?) in a real-life problem. So, x=6 is the algebraic solution (be careful, you MUST actually go back ANSWER THE ORIGINAL QUESTION!!
p^2-4p=21 fits quite well with the others... to reiterate, if you are going to use the ZERO PRODUCT PROPERTY, you must set the equation = to ZERO. Subtracting 21 fbs, you get:
p^-4p-21=0... is that a better fit??
Ca-peesh?
I helped Paul with his problem, and your help helped me solve my problem. Thanks!
ReplyDeleteAaron C
got it
ReplyDeleteWhy are there so many posts
ReplyDeleteHi
ReplyDelete