pooja195
  • pooja195
@mathmate
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
pooja195
  • pooja195
@mathmate
pooja195
  • pooja195
Chapter 9 ;-;
mathmate
  • mathmate
Chapter 9 ======

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

mathmate
  • mathmate
|dw:1433627905280:dw| Find x (hypotenuse) shown in the above drawing.
pooja195
  • pooja195
a^2 + b^2 = c^2?
mathmate
  • mathmate
Yep, now evaluate x numerically, please.
pooja195
  • pooja195
12^2+5^2=c^ 144+25=169 13^2
mathmate
  • mathmate
So x=13 (is the final answer).
mathmate
  • mathmate
which two consecutive integers does sqrt(200) fall between?
pooja195
  • pooja195
idk this ;-;
mathmate
  • mathmate
10^2=100 11^2=121 12^2=144 13^2=169 14^2=196 15^2=225 16^2=256 ... which two consecutive integers does sqrt(200) fall between?
pooja195
  • pooja195
no .-.
pooja195
  • pooja195
*none
mathmate
  • mathmate
"between" is the keyword. We know that 14^2=196, and 15^2=225 or sqrt(196)=14, sqrt(225)=15, so sqrt(200) falls between which integer numbers?
pooja195
  • pooja195
Decimals? .-.
pooja195
  • pooja195
wait no
mathmate
  • mathmate
no, we are looking for two integer numbers! lol
pooja195
  • pooja195
This si confusing T_T lets skip this
mathmate
  • mathmate
the answer is 14 and 15. In fact sqrt(200)=14.1421356237309.... (never ends). So we know that sqrt(200) falls between 14 and 15! You were probably thinking that it's more complicated than this!
pooja195
  • pooja195
-_-
mathmate
  • mathmate
The hint is 14^2=196, so too small, 15^2=225, so too big. Therefore sqrt(200) must fall between 14 and 15. Is that ok?
pooja195
  • pooja195
yes
mathmate
  • mathmate
Solve the equation 27-3y^2=0
pooja195
  • pooja195
Would you like the work or is it ok to put in the answer?
mathmate
  • mathmate
put in the work, but LaTeX is not required.
pooja195
  • pooja195
first find a GCF 27-3y^2=0 -3 is the gcf then square root answer: −3(y+3)(y−3) set values to 0 y=3 or y=−3
pooja195
  • pooja195
/.\
mathmate
  • mathmate
Very good, shows that you're comfortable with factoring. It will help in the later sections. You can also solve by isolating y, -3y^2=-27 y^2=9 y=\(\pm 3\)
mathmate
  • mathmate
Ready for the next one?
mathmate
  • mathmate
an engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking. The model for the egg's height, h (in feet), at time t seconds since release, is h = -16t^2 + 32. Calculate the time at whic the egg is at a height of 10 feet above ground. Give answer to 2 decimal places.
pooja195
  • pooja195
10=-16t^2+32 subtract 32 from both sides then divide by 16 1.375= t^2 idk where to go after this
mathmate
  • mathmate
Take out your ti-83 to finish!
mathmate
  • mathmate
"give answer to 2 decimal places" is a hint you might need your ti-83!
mathmate
  • mathmate
sqrt(1.375)=?
pooja195
  • pooja195
1.172604
mathmate
  • mathmate
exactly! (1.17 for 2 decimal places).
mathmate
  • mathmate
Any questions before we move to simplifying radicals?
pooja195
  • pooja195
no
mathmate
  • mathmate
Simplifying radicals basically is to pull things out of the square-root sign, whenever possible. For example, sqrt(4)=2 is rather straight-forward.
mathmate
  • mathmate
But sqrt(18) is less obvious, since we write sqrt(18)=sqrt(3^2 *2)=3sqrt(2)
mathmate
  • mathmate
So I'll let your try sqrt(48) while I take a meal break!
pooja195
  • pooja195
48 6 8 3 2 42 \[2\sqrt{12}\]
mathmate
  • mathmate
almost, just one step further sqrt(48)=sqrt(4*12)=sqrt(16*3)=sqrt(4^2 * 3)=4sqrt(3)
mathmate
  • mathmate
Simplify (1) sqrt(98) [98=2*7*7]
mathmate
  • mathmate
So every factor that appears twice inside the radical you take one outside. So sqrt(98)=sqrt(2*7*7)=7sqrt(2)
pooja195
  • pooja195
Dance club.
pooja195
  • pooja195
Dance club is the method my teacher taught me because teens like to think like that
mathmate
  • mathmate
Oh! Can you show me that?
pooja195
  • pooja195
Ok its been a while but eh :P 56 8 7 4 2 2 2 2 and 2 are a couble so they leave the dance club 2 squrt 2 idk if its right
mathmate
  • mathmate
Yes, I get the part for the leaving dance club part (ingeneous!) Then we have to keep 2*7 in the club, so we get 2sqrt(14)
pooja195
  • pooja195
lel :3
pooja195
  • pooja195
Are we done with this section ?
mathmate
  • mathmate
I usually like to see you do at least one perfect answer, like (2) sqrt(60) [60=2*2 * 3 * 5] then there is rationalize the denominator.
pooja195
  • pooja195
T_T
pooja195
  • pooja195
ok
mathmate
  • mathmate
(2) sqrt(60) [60=2*2 * 3 * 5]
pooja195
  • pooja195
im confused whats the question? .-.
mathmate
  • mathmate
simplify sqrt(60)
pooja195
  • pooja195
60 10 6 5 2 3 2 2 sqrt 15
pooja195
  • pooja195
T_T say im right!
pooja195
  • pooja195
Princess demands it!
mathmate
  • mathmate
Yes, you're right, I don't think you have problem with that.
mathmate
  • mathmate
Now we move onto rationalizing the denominator.
mathmate
  • mathmate
Mathematicians traditionally do not like to see square roots in the denominator, because that would make the common denominator very messy.
pooja195
  • pooja195
Just multiply by the root
pooja195
  • pooja195
*in the denominator
mathmate
  • mathmate
Do you want me to explain, or jump to pretest?
pooja195
  • pooja195
Pretest
mathmate
  • mathmate
Rationalize 9sqrt(1/3)
pooja195
  • pooja195
9 squrt 3
pooja195
  • pooja195
^LOL
mathmate
  • mathmate
Sure?
mathmate
  • mathmate
The question was \(9\sqrt{\frac{1}{3}}\)
pooja195
  • pooja195
:/
pooja195
  • pooja195
this is diffrent .-.
mathmate
  • mathmate
Example: \(sqrt(\frac{2}{5}) = \frac{\sqrt2}{\sqrt5}=\frac{\sqrt2\times \sqrt5}{\sqrt5^2}=\frac{\sqrt{10}}{5}\)
mathmate
  • mathmate
just a recap, we were working on simplify 9sqrt(1/3). I sent this previous example to help.
pooja195
  • pooja195
sqrt 3/ 3
mathmate
  • mathmate
9 sqrt(1/3) = 9(sqrt(1)/sqrt(3)) = 9(sqrt(1)*sqrt(3)/(sqrt(3)^2)=9sqrt(3)/3=3sqrt(3)
mathmate
  • mathmate
or \(9\sqrt{1/3}=3\frac{\sqrt3 \times \sqrt3}{\sqrt3}=3\sqrt3\)
pooja195
  • pooja195
IM IRGHT??
pooja195
  • pooja195
*RIGHT?
mathmate
  • mathmate
no, you had the 3 as denominator, and not multiplied.
pooja195
  • pooja195
>:(
pooja195
  • pooja195
9
pooja195
  • pooja195
.-.
mathmate
  • mathmate
not 9, it's \(3\sqrt3\) :)
pooja195
  • pooja195
>:(
mathmate
  • mathmate
ok, try this one: Simplify \(\Large \sqrt{\frac{25}{3}}\)
pooja195
  • pooja195
\[\huge~\frac{ 5\sqrt{3} }{ 3 }\]
pooja195
  • pooja195
Am i right?
pooja195
  • pooja195
>:(
mathmate
  • mathmate
Excellent! It's correct!
pooja195
  • pooja195
:O YAY!!! :D
mathmate
  • mathmate
Yep! any questions before we move on?
pooja195
  • pooja195
Nope
mathmate
  • mathmate
Graphing parabolas (quadratic functions)
pooja195
  • pooja195
No we ahvent learned this
mathmate
  • mathmate
We need to be able to find the vertex of a parabola.
pooja195
  • pooja195
,-,
mathmate
  • mathmate
no?
pooja195
  • pooja195
^no
mathmate
  • mathmate
ok, next case!
pooja195
  • pooja195
kk
mathmate
  • mathmate
Do you know the shape of a quadratic function? (concave up, concave down)
mathmate
  • mathmate
When the leading coefficient is positive, it's concave up.
pooja195
  • pooja195
We havent learned this
mathmate
  • mathmate
|dw:1433641575278:dw| Here coef. of x^2=1 (positive), so it is drawn concave up.
mathmate
  • mathmate
sure?
pooja195
  • pooja195
yea im sure .-.
mathmate
  • mathmate
ok, next case!
mathmate
  • mathmate
Solving quadratic equations by graphing, guess not learned!
pooja195
  • pooja195
^exactly
mathmate
  • mathmate
Using a graphics calculator?
pooja195
  • pooja195
nopee
mathmate
  • mathmate
Quadratic formula, no?
mathmate
  • mathmate
Si!
pooja195
  • pooja195
:3
pooja195
  • pooja195
lets avoid that ;)
pooja195
  • pooja195
Next case!
mathmate
  • mathmate
because you already know it, or because you don't?
pooja195
  • pooja195
because i know it :P
pooja195
  • pooja195
but i get the feeling yr gonna end up giving a problem anyways :P
mathmate
  • mathmate
Right! I believe you, but I am sure you can solve this in a flash!
mathmate
  • mathmate
You know me toooooooo well!
mathmate
  • mathmate
Use the quadratic formula to solve the equation 2x^2+x-10=0
mathmate
  • mathmate
show work!
mathmate
  • mathmate
El cheapo, no LaTeX
pooja195
  • pooja195
i cant do it without latex
mathmate
  • mathmate
ok then!
pooja195
  • pooja195
a=2 b=1 c=-1 \[\huge~x=\frac{ -(1) \pm \sqrt{(1)^2-4(2)(-1)} }{ 2(2) } \] \[\huge~x=\frac{ 1 \pm \sqrt{(9} }{ 4 } \]
pooja195
  • pooja195
Right so far?
pooja195
  • pooja195
\[\huge~x=\frac{ -1 \pm \sqrt{9\times 1} }{ 4 } \]
pooja195
  • pooja195
i meant -1 on the top sorry!
mathmate
  • mathmate
But you have -1 on top! Can you simplify further?
pooja195
  • pooja195
\[\huge~x=\frac{-1 \pm 3\sqrt{1} }{ 4 }\]
pooja195
  • pooja195
Set up two of the equations + and - and then i get x=0.5 x=−1
mathmate
  • mathmate
sorry, the question was: 2x^2+x-10=0 Can you make some adjustments? such as : \(\huge~x=\frac{-1 \pm 3\sqrt{1-4(2)(-10)} }{ 4 } = ...\)
pooja195
  • pooja195
OMG NO T_T
pooja195
  • pooja195
cant i just link u to a one ive done today T_T
mathmate
  • mathmate
ok, I believe you, I have seen you work before!
pooja195
  • pooja195
Thank you! :D
mathmate
  • mathmate
ok, discriminants!
mathmate
  • mathmate
Please tell me how many roots does this equation have: -x^2+2x-1=0
pooja195
  • pooja195
2^2−4(−1)(1)=8 2 roots
mathmate
  • mathmate
Excellent! how about this one? \(2x^2-2x+3=0\)
pooja195
  • pooja195
(−2)^2−4(2)(3)=−20 no solution OR 2 imaginary roots
mathmate
  • mathmate
Excellent! now this one, you can almost answer without looking: \(x^2+2x+1=0\)
pooja195
  • pooja195
2 equal solutions :P
mathmate
  • mathmate
The answer (I mean guess) is correct. Please justify your response!
pooja195
  • pooja195
-.-
pooja195
  • pooja195
2^2−4(1)(1)=0
mathmate
  • mathmate
Excellent. I would also guess the same answer, because there are only three possible cases! lol Your books calls it "one solution", but I like yours better, "two equal solutions", or better still, two "coincident roots". So use any appropriate one of your choice.
pooja195
  • pooja195
kk
mathmate
  • mathmate
Graphing quadratic inequalities?
pooja195
  • pooja195
no
mathmate
  • mathmate
|dw:1433643467187:dw|
pooja195
  • pooja195
we havent learned it
mathmate
  • mathmate
still no?
mathmate
  • mathmate
ok, next case!
mathmate
  • mathmate
...more like next chapter!
pooja195
  • pooja195
lol :)
mathmate
  • mathmate
Chapter 10 Polynomials and factoring ========================
mathmate
  • mathmate
x^2 is a monomial (x+2) is a binomial (x^2+3x-1) is a trinomial. Is x a polynomial?
pooja195
  • pooja195
no
mathmate
  • mathmate
"ERROR", the computer game says!
pooja195
  • pooja195
O_o
mathmate
  • mathmate
A polynomial includes all degrees, including x (first degree, one term only).
mathmate
  • mathmate
What is the degree of the polynomial 4.
pooja195
  • pooja195
linear/
mathmate
  • mathmate
linear is like 2x, 5x, which are abbreviations of \(2x^1, 5x^1\)
pooja195
  • pooja195
in that case i havent learned this ..-..
mathmate
  • mathmate
\(4=4x^0\), so the degree is zero! (see p.569), perhaps the teacher went through it fast.
pooja195
  • pooja195
hmm ok
mathmate
  • mathmate
Do you know how to add, subtract, multiply and divide polynomials?
pooja195
  • pooja195
maybe >:) maybe not
mathmate
  • mathmate
We'll see!
pooja195
  • pooja195
of course
mathmate
  • mathmate
add: \((x^2-7)-(x+2)=?\)
mathmate
  • mathmate
*subtract
pooja195
  • pooja195
\[x^2-7-x-2\] \[x^2-x-9\]
mathmate
  • mathmate
Excellent! now|dw:1433644413460:dw| Find the perimeter and area of the swimming pool shown.
pooja195
  • pooja195
.-.not this
pooja195
  • pooja195
;-;
mathmate
  • mathmate
You find it hard, or too easy?
pooja195
  • pooja195
4x+3+4x+3+x-2+x-2 8x^2+2x+2
pooja195
  • pooja195
Next case!
mathmate
  • mathmate
sorry, not quite yet!
pooja195
  • pooja195
T_T
mathmate
  • mathmate
add like terms perimeter =4x+3+4x+3+x-2+x-2 =4x+4x+x+x +3+3-2-2 =10x+2
mathmate
  • mathmate
|dw:1433644752391:dw|
pooja195
  • pooja195
is that a question?
mathmate
  • mathmate
The first post was the corrected calculation for the perimeter. The second post is to calculate the area using FOIL, to be completed by you!
pooja195
  • pooja195
4x^2−5x−6
mathmate
  • mathmate
Excellent! For a rectangle: perimeter = 2 times the sum of two adjacent sides. Area = product of two adjacent sides.
pooja195
  • pooja195
ok
mathmate
  • mathmate
Have you done division? (called long division, or synthetic division).
pooja195
  • pooja195
no
mathmate
  • mathmate
Like Divide \(20x^2+17x+3\) by 5x+3.
pooja195
  • pooja195
no
mathmate
  • mathmate
ok, but can you do it using chapter 11?
pooja195
  • pooja195
omg no i hate that chapter >::( no no no ;(
mathmate
  • mathmate
\(\Large \frac{20x^2+17x+3}{5x+3}\)
mathmate
  • mathmate
But you were good at it, if I remember right!
pooja195
  • pooja195
I dont like that stuff T_T princess says skip
mathmate
  • mathmate
Teacher says "you pay now, or you pay later!" xD
pooja195
  • pooja195
T_T
pooja195
  • pooja195
skip
mathmate
  • mathmate
ok, for now!
pooja195
  • pooja195
>:) princess wins!
mathmate
  • mathmate
as always!
mathmate
  • mathmate
Now back to multiplication! \((m^2+2m-9)(m-4)= \ ?\)
pooja195
  • pooja195
\[\huge~m^3−2m^2−17m+36 \]
mathmate
  • mathmate
Excellent! You're as good as a calculator!
pooja195
  • pooja195
:)
mathmate
  • mathmate
Good so far?
pooja195
  • pooja195
yes next case!
mathmate
  • mathmate
10.3 special products of polynomials ========================
mathmate
  • mathmate
@pooja195
mathmate
  • mathmate
@pooja195
pooja195
  • pooja195
+_=
mathmate
  • mathmate
gimme a minute to find the page
mathmate
  • mathmate
ok, special products of polynomials. First, if you can, commit to memory the following: Factoring difference of two squares (a+b)(a-b)=a^2-b^2 Example: x^2-y^2=(x+y)(x-y)
mathmate
  • mathmate
But life is not always simple like that. the problem may come up as: 4p^2-9q^2
pooja195
  • pooja195
2p+3)(2p-3)
mathmate
  • mathmate
You will have to _try_ to factorize each term into a perfect square before proceeding, 4p^2-9q^2 = (2p)^2-(3q)^2 (remember the law of exponents?
mathmate
  • mathmate
Yes, pretty close, you only lost your q..lol
pooja195
  • pooja195
oops
mathmate
  • mathmate
(2p+3q)(2p-3q)
mathmate
  • mathmate
Expand (a+2b)(a-2b)
pooja195
  • pooja195
a^2−4b^2
mathmate
  • mathmate
Excellent! You get the idea, and I'm sure you can do it backwards.
mathmate
  • mathmate
like factor (16a^2-4b^2 ).
pooja195
  • pooja195
(4a+2b)(4a-2b)
mathmate
  • mathmate
Very good! Now we move on to the perfect squares. Commit to memory the following patterns: (a+b)^2 = a^2 + 2ab + b^2 (a-b)^2 = a^2 - 2ab + b^2
mathmate
  • mathmate
Example: (backwards of FOIL) 9x^2-24x+16 = (3x)^2 - 2 (3x)(4) + (4^2) = (3x-4)^2
mathmate
  • mathmate
Note that perfect squares have three terms, and both the square terms are ALWAYS positive. The middle term may be positive or negative, depending on the pattern.
mathmate
  • mathmate
I'll give you a couple of problems, but I have to go after that, perhaps for 50 minutes. factor 1. 9x^2+30x+25 2. 4x^2-12x+9
pooja195
  • pooja195
:D ok!
mathmate
  • mathmate
gtg, but hope you have the answers by the time I'm back!
pooja195
  • pooja195
ok :)
pooja195
  • pooja195
\(\huge\color{blue}{1.~~ (3x+5)(3x+5)}\) \(\huge\color{blue}{2.~~(2x−3)(2x−3) }\)
mathmate
  • mathmate
@pooja195 Yes, excellent. I would have written them as squres, so that it is easier to read. \( \huge\color{blue}{1.~~ (3x+5)^2}\) \(\huge\color{blue}{2.~~(2x−3)^2 }\)
mathmate
  • mathmate
* squares
mathmate
  • mathmate
No you don't have to do foil to get the answer, but it's a good idea to do FOIL to _check_ the answer.
mathmate
  • mathmate
If there are no questions on 11.3, then next case. 11.4 ZERO PRODUCT PROPERTY Let a and b be real number. If ab=0, then a=0 or b=0. If the product of two factors is zero, then at least one of the factors must be zero.
pooja195
  • pooja195
thats eaasy
mathmate
  • mathmate
So if (x-3)(2x-5)=0, what are the possible values of x?
pooja195
  • pooja195
x=3 x=5/2
mathmate
  • mathmate
Excellent! Solve by factoring: \(\Large x^2-x-3=0\)
pooja195
  • pooja195
Cant do it .-.
mathmate
  • mathmate
sorry, it: \(\Large x^2-x-6=0\)
pooja195
  • pooja195
x=−2 or x=3
mathmate
  • mathmate
yes! perfect!
pooja195
  • pooja195
Are we done? :D
mathmate
  • mathmate
no
mathmate
  • mathmate
brb
mathmate
  • mathmate
sorry!
mathmate
  • mathmate
Do you need more practice on factoring a quadratic?
pooja195
  • pooja195
No
mathmate
  • mathmate
...apart from word problems?
pooja195
  • pooja195
No i think i have it all
mathmate
  • mathmate
Just to make sure, try factor \(2x^2-9x-35\)
pooja195
  • pooja195
(2x+5)(x−7)
mathmate
  • mathmate
Why, that's too fast!? Are you sure of your answer?
pooja195
  • pooja195
(2x+5)=0 (x−7)=0 x=-5/2 x=7
mathmate
  • mathmate
ok, now factor 3p^2+36p+108
mathmate
  • mathmate
Do you remember the first step in factoring?
pooja195
  • pooja195
GCF
pooja195
  • pooja195
in this case its 3
mathmate
  • mathmate
Excellent!!!!!!!
pooja195
  • pooja195
3(p+6)(p+6)
mathmate
  • mathmate
faster than I can type! Is the calculator there somewhere? lol
pooja195
  • pooja195
maybe ;) but not for the whole problem :P
mathmate
  • mathmate
xD
pooja195
  • pooja195
How did u know ? :P
pooja195
  • pooja195
too fast? :P xD
pooja195
  • pooja195
i didnt use it for the whole thing just to find the factors :/
mathmate
  • mathmate
Aren't you on your laptop with a camera?
pooja195
  • pooja195
xD yesh :P
mathmate
  • mathmate
xD
mathmate
  • mathmate
next: factor \(\large 4x^3+20x^2+24x\)
pooja195
  • pooja195
4x(x+2)(x+3)
mathmate
  • mathmate
Excellent!
mathmate
  • mathmate
I like it when you actually sweat it out!
pooja195
  • pooja195
xD
mathmate
  • mathmate
Now real cubic factors: \((x+y)^3 = (x+y)(x^2-xy+y^2)\) \((x-y)^3 = (x-y)(x^2+xy+y^2)\) I'll sho you the SOAP rule Nnesha taught me today!
pooja195
  • pooja195
i havent learned this ,-,
mathmate
  • mathmate
Sorry, wrong formulas: \(x^3+y^3 = (x+y)(x^2-xy+y^2)\) \(x^3-y^3 = (x-y)(x^2+xy+y^2)\)
mathmate
  • mathmate
Sure?
pooja195
  • pooja195
yes
mathmate
  • mathmate
ok, then Ch 10 is done!
pooja195
  • pooja195
O_O
pooja195
  • pooja195
lets learn SOAP
mathmate
  • mathmate
It has to do with the cubic factoring, you really want it?
pooja195
  • pooja195
yes yes
mathmate
  • mathmate
k, gimme a minute.
mathmate
  • mathmate
|dw:1433700122466:dw|
mathmate
  • mathmate
The same SOAP rule applies to x^3-y^3 and x^3+y^3.
mathmate
  • mathmate
It's all about signs only.
pooja195
  • pooja195
oooo ok
mathmate
  • mathmate
Pretty cute, isn't it?
pooja195
  • pooja195
yesh :3
mathmate
  • mathmate
So, shall we start Ch 11?
pooja195
  • pooja195
Maybe we should do more quadratic factoring
mathmate
  • mathmate
ok!
mathmate
  • mathmate
Find the product \(\large (d+2)(d^2-3d-10)\)
pooja195
  • pooja195
\[\huge~d^3−d^2−16d−20\]
mathmate
  • mathmate
Exactly! Have you done the grid method of multiplication?
pooja195
  • pooja195
nope
mathmate
  • mathmate
It makes your life easier, even without a calculator!
pooja195
  • pooja195
O-o
mathmate
  • mathmate
Here's how it works. Nothing magical, just helps you organize.
mathmate
  • mathmate
|dw:1433700861581:dw|
pooja195
  • pooja195
ooo thats neat :o
mathmate
  • mathmate
Yep!
pooja195
  • pooja195
whats next? :)
mathmate
  • mathmate
find product: (3x^3-5z^2+8)(z+2)
mathmate
  • mathmate
Be careful if you use the grid method, and treat the first factor as: (3z^3-5z^2+0+8) to fill the gap. and the first term is 3z^3, not 3x^3, sorry.
pooja195
  • pooja195
3x^3z+6x^3−5z^3−10z^2+8z+16
mathmate
  • mathmate
and simplify...
mathmate
  • mathmate
You mean 3x^4 at the beginning. :)
pooja195
  • pooja195
Right..
mathmate
  • mathmate
How about factor \(\large 30x^2+38x+12\)
pooja195
  • pooja195
2(5x+3)(3x+2)
mathmate
  • mathmate
Very good!
mathmate
  • mathmate
Last one for chapter 10 (if you get it without calculator) Factor \(\large 4x^2+44x+121\)
pooja195
  • pooja195
(2x+11)(2x+11)
mathmate
  • mathmate
Yep, excellent.
mathmate
  • mathmate
Unless there are questions, that's it for Ch 10.
pooja195
  • pooja195
nope thats all :P
pooja195
  • pooja195
mm chapter 11
mathmate
  • mathmate
11.1 Proportions ==========
mathmate
  • mathmate
solve \(\Large \frac{3}{y}=\frac{5}{8}\)
mathmate
  • mathmate
brb
pooja195
  • pooja195
8*3=24 5y 5y=24 y=24/5
mathmate
  • mathmate
Yep, that's good. That's cross multiplication.
mathmate
  • mathmate
We can extend the idea...
mathmate
  • mathmate
Solve \(\Large \frac{2}{x-3}=\frac{7}{x+2}\)
pooja195
  • pooja195
2(x+2) = 7(x-3) 2x+4=7x-21 2x=7x-25 -5x=-25 x=5
mathmate
  • mathmate
Excellent. Now try solve \(\Large \frac{x}{x-4}=\frac{6x}{x+1}\)
pooja195
  • pooja195
x(x+1)=6x(x-4) x^2+1x=6x^2-24x -7x^2+1x=-24x not sure...
mathmate
  • mathmate
x^2+1x=6x^2-24x is good, work from here.
pooja195
  • pooja195
idkk :/
mathmate
  • mathmate
x^2+1x=6x^2-24x subtract x^2+x on each side: x^2+x - (x^2-x) = 6x^2-24x -x^2 -x 0 = 5x^2-25x 0=5x(x-5) so x=0 or x=5
pooja195
  • pooja195
:/
mathmate
  • mathmate
Solve \(\Large \frac{5}{x+2}=\frac{3x-1}{x^2-1}\)
pooja195
  • pooja195
5(x^2-1) = (3x-1)(x+2) 5x^2−5=3x^2+5x−2 5x^2−5−(3x^2+5x−2)=3x^2+5x−2−(3x^2+5x−2) 2x^2−5x−3=0 (2x+1)(x−3)=0 2x+1=0 or x−3=0 x= -1/2 or x=3
mathmate
  • mathmate
Excellent, like a pro!
mathmate
  • mathmate
Any question on proportions?
pooja195
  • pooja195
nope
mathmate
  • mathmate
11.2 Direct and inverse variations. =====================
mathmate
  • mathmate
It's important to know what's what.
mathmate
  • mathmate
Can you give me an example of one of each?
mathmate
  • mathmate
Usually it's in the form y=.....
mathmate
  • mathmate
Direct variation: y=kx, example y=x, y=x/2, y=3.2x Inverse variation: xy=k, or y=k/x Example y=4/x, or xy=10
mathmate
  • mathmate
|dw:1433706731769:dw|
mathmate
  • mathmate
|dw:1433706794615:dw|
pooja195
  • pooja195
Direct variation: rule y=kx (when x is greater, y is greater) Inverse variation: rule xy=k (when x increases, y decreases, that's why inverse) right? This is from the other post.
mathmate
  • mathmate
That's true, exactly!
mathmate
  • mathmate
So if I give you: x y 1 3 2 6 3 9 Is this direct or inverse variation?
pooja195
  • pooja195
>_< can we not do these .-.
mathmate
  • mathmate
These are needed to solve word problems!
pooja195
  • pooja195
O_O
mathmate
  • mathmate
Say x=4/y, direct or inverse?
mathmate
  • mathmate
Ok, I'll put it another way. When the function is in the slope-intercept form, with \(b=0\), then it is direct variation.
mathmate
  • mathmate
if it is something to do with xy=something, it is inverse.
mathmate
  • mathmate
If it is in slope-intercept with intercept NOT equal to zero, it's partial (neither direct, nor inverse)
pooja195
  • pooja195
im so confused .-.
mathmate
  • mathmate
|dw:1433707362237:dw| This is the slope-intercept form with b=0 (y-intercept=0), so it is direct variation. (remember, y increases as x increases), and it is proportional.
pooja195
  • pooja195
I kinda get it .. . :/
mathmate
  • mathmate
so x y 1 3 2 6 3 9 The rule is y=3x, so it's a direct variation.
mathmate
  • mathmate
If I give you x y 1 20 4 5 5 4 10 2 You see that the rule is xy=20, so it is an inverse variation (also, y does not increase as x increases).
mathmate
  • mathmate
ok?
pooja195
  • pooja195
got it
mathmate
  • mathmate
Good, so tell me direct or inverse: 1. y=5x 2. y=50/x 3. xy=4 4. y/x=3
pooja195
  • pooja195
1) Direct 2 ) Direct 3) Inverse 4) Inverse
mathmate
  • mathmate
uh...uh Be careful. Try to convert the equation to either y=kx (direct), or xy=k (inverse) (k is a number) before deciding!
pooja195
  • pooja195
>_<
mathmate
  • mathmate
1. y=5x is direct (correct) 2. y=50/x is the same as xy=50, so ?
pooja195
  • pooja195
2) inverse?
mathmate
  • mathmate
Yes, how about 3)?
pooja195
  • pooja195
Direct?
mathmate
  • mathmate
3. xy=4 4. y/x=3 3 is xy=4, would that be ?
pooja195
  • pooja195
inverse .- .
mathmate
  • mathmate
right, how about 4). 4. y/x=3
pooja195
  • pooja195
inverse
mathmate
  • mathmate
Inverse is xy=something, here we have y/x = something, or y=something * x which is really in the slope-intercept form (with b=0). so...
pooja195
  • pooja195
direct ._.
mathmate
  • mathmate
ok. In any case, remember y=k/x is inverse, y=kx is direct. The rest is algebra that you have mastered quite well.
mathmate
  • mathmate
Direct relates to things like buying apples, 1 apple costs 40 cents 2 apples cost 80 cents 3 apples cost 1.20 dollars, etc.
mathmate
  • mathmate
Inverse variation is like splitting money between people. More people, less money. A hundred dollares split among 10 people = $10 each A hundred dollars split among 20 people = $5 each A hundred dollars split among 50 people = $2 each
mathmate
  • mathmate
Is that ok?
pooja195
  • pooja195
Yes
mathmate
  • mathmate
This will conclude 11.2 unless you have questions.
pooja195
  • pooja195
Nope thats all .
mathmate
  • mathmate
Ch. 11.3 Simplifying rational expressions ==========================
mathmate
  • mathmate
Simplify \(\Large \frac{2x-6}{4}\)
mathmate
  • mathmate
Don't bother with LaTex unless you want/need to.
mathmate
  • mathmate
But use proper parentheses.
pooja195
  • pooja195
Can you one as an example plz :) ?
mathmate
  • mathmate
yes!
mathmate
  • mathmate
\(\Large \frac{2x-6}{4}\) =\(\Large \frac{2(x-3)}{4}\) now divide out the common factor 2. =\(\Large \frac{x-3}{2}\) no more common factors, so that's the answer.
mathmate
  • mathmate
Notice that when we divide out the common factor 2, we're supposed to say that x\(\ne\)2, which is always true, so we don't need to give that as a condition.
pooja195
  • pooja195
Right :)
mathmate
  • mathmate
* 2\(\ne\)0
mathmate
  • mathmate
Do you find this thread draggy?
pooja195
  • pooja195
yea lets make a new one :P
mathmate
  • mathmate
ok! tag me!
mathmate
  • mathmate
So what fraction? rational functions?
pooja195
  • pooja195
The multiplying and dividing
mathmate
  • mathmate
like this? \(\Large \frac{c^2-64}{4c^3} \times \frac{c}{c^2+9c+8}\)
mathmate
  • mathmate
First factor, =\(\Large \frac{(c+8)(c-8)}{4c^3} \times \frac{c}{(c+8)(c+1)}\)
mathmate
  • mathmate
Then cancel, but give conditions for everything you cancelled. =\(\Large \frac{(c-8)}{4c^2(c+1)}~~~ x\ne -8,0\)
pooja195
  • pooja195
oh just as i thought :)
mathmate
  • mathmate
Good! With division, you only have to flip the fraction right after the division sign then \(multiply\)
pooja195
  • pooja195
Same thing just the flipping is diffrent right?
mathmate
  • mathmate
Like \(\Large \frac{1}{2}\div\frac{3}{4} = \frac{1}{2}\times\frac{4}{3} \)
pooja195
  • pooja195
Got it : )
mathmate
  • mathmate
That's it?
pooja195
  • pooja195
yes thats all

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