jamiebookeater
  • jamiebookeater
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pooja195
  • pooja195
mathmate
  • mathmate
Finally, got here!
mathmate
  • mathmate
Start with quadratic equations, ok?

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More answers

pooja195
  • pooja195
ok :)
mathmate
  • mathmate
Solve \(x^2 -6x +9=0\)
pooja195
  • pooja195
a=1 b=-6 c=9
mathmate
  • mathmate
ok.
pooja195
  • pooja195
\[\huge~x=\frac{ -(-6)\pm \sqrt{(-6)^2-4(1)(9)} }{ 2(1) } \]
mathmate
  • mathmate
Great, now can you simplify that, because it will be greatly simplified when you put the numbers in there.
pooja195
  • pooja195
\[\huge~x=\frac{ 6\pm \sqrt{0} }{ 2}\]
pooja195
  • pooja195
\[\huge~\frac{ 6 }{ 2 }=3~~~~~x=3\]
mathmate
  • mathmate
Yes, that is the same as {3,3}, or 3 (twice)
mathmate
  • mathmate
It's called a double root, andthe graph looks like this:|dw:1433211976391:dw| the vertex just touches the x-axis.
mathmate
  • mathmate
ok so far?
pooja195
  • pooja195
ye
mathmate
  • mathmate
If you factored, you would have got (x-3)^2=0, which is the same as saying (x-3)=0, or x=3 (twice), or x={3,3}
mathmate
  • mathmate
Was wondering you still have the online textbook?
mathmate
  • mathmate
Can you dig some questions out of there, which will be more like what you have learned.
pooja195
  • pooja195
T_T but there are answers ,_,
mathmate
  • mathmate
You don't have to look at them, in any case, we are looking at the work, can check the answers at the end.
mathmate
  • mathmate
There may be word problems, which take more time to make. Using ready-made problems can help us do more.
pooja195
  • pooja195
mathmate
  • mathmate
Have you done anything like this? "A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?"
pooja195
  • pooja195
:/
pooja195
  • pooja195
no O_O
mathmate
  • mathmate
Always the numerical equations, and nothing like word problems?
pooja195
  • pooja195
no ._.
mathmate
  • mathmate
ok, so we can skip that.
pooja195
  • pooja195
:)
mathmate
  • mathmate
Whenever you solve quadratics, there are three ways to do it. If the teacher does not specify, you can use any method you want. If he/she specifies completing the square, you have no choice. the three are:
mathmate
  • mathmate
quad formula (just did) factoring (did over the weekend) completing the square Do youknow how to do the last one?
pooja195
  • pooja195
no :/ we havent learned it
mathmate
  • mathmate
ok, so we skip that too. Anything else you'd like to do on quadratic equations/
pooja195
  • pooja195
Nope.
mathmate
  • mathmate
So we will move onto system of linear equations. Have you done word problems?
pooja195
  • pooja195
yes but dont like those :/
mathmate
  • mathmate
How many ways do you know to solve system of linear equations?
pooja195
  • pooja195
Elmination Substituion :/
mathmate
  • mathmate
comparison?
pooja195
  • pooja195
eh?
mathmate
  • mathmate
When you have y=2x+3 y=4x-2 then you equate the right-hand sides (since they both equal y) to give 4x-2=2x+3 and solve for x. It is a form of elimination, but makes life easier. (called method of comparison)
pooja195
  • pooja195
i know that :P
mathmate
  • mathmate
Ok, so let go: Solve y = 36 – 9x 3x + y/3 = 12
mathmate
  • mathmate
*let's
pooja195
  • pooja195
3x+(36-9x)/3=12 6x+36/3=12 6x+12=12 x=0
mathmate
  • mathmate
...not finished! need y, and the final answer!
pooja195
  • pooja195
y=36-9(0) y=36-0 y=36? (0,36)
mathmate
  • mathmate
Excellent!
mathmate
  • mathmate
Solve the following system by substitution. 2x – 3y = –2 4x + y = 24 When you see a singleton y, or singleton x, then you can try substitution, as in the above case.
pooja195
  • pooja195
y=-4x+24 2x-3y=-2 2x-3(-4x+24)=-2 2x+12x-72=-2 14x-72=-2 14x=70 x=5 y=-4(5)+24 y=20+24 y=44 Final answer (5,44)
mathmate
  • mathmate
Something wrong here, otherwise all correct. y=-4(5)+24 y=20+24 y=44
pooja195
  • pooja195
y=4
mathmate
  • mathmate
yep! Solve the following system using addition (a kind of elimination) 2x + y = 9 3x – y = 16
pooja195
  • pooja195
x=5 2(5)+y=9 10+y=9 y=-1 (5,-1)
mathmate
  • mathmate
That was fast! You solved for x by inspection! But show work in exams!
mathmate
  • mathmate
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
pooja195
  • pooja195
O_O
pooja195
  • pooja195
Nooooooooooooooooo
mathmate
  • mathmate
With word problems, always define variables first, so you don't get confused at the end.
mathmate
  • mathmate
I'll do this one, ok?
mathmate
  • mathmate
Define variables: Number of children = c Number of adults = a (we'll could get confused using x,y, but never this way)
mathmate
  • mathmate
Admission for children = $1.50 Admission for adults = $4
mathmate
  • mathmate
"2200 people enter the fair and $5050 is collected" means c+a = 2200 1.50c + 4a=5050 = 15c+40a = 50500 (keep integers as long as possible Substitute (because c has a coefficient of 1) c=2200-a so 15(2200-a) + 40a = 50500 expand 33000 -15a + 40a = 50500
mathmate
  • mathmate
40a-15a = 50500-33000 25a = 17500 a=17500/25 = 700 c=2200-700=1500 Check 1.5c+4a=2250+2800=5050 good!
mathmate
  • mathmate
You will find that once the variables are defined, everything else look easy. What do you think?
pooja195
  • pooja195
It seems so complicated >_<
pooja195
  • pooja195
*-*
mathmate
  • mathmate
Do you want to tell me which part is harder to understand?
mathmate
  • mathmate
It looks complicated probably because I show all the work. If I skipped or jumped some steps, it will look easy, but a little harder to follow.
pooja195
  • pooja195
hmm.... :/
mathmate
  • mathmate
Now your turn! The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number
mathmate
  • mathmate
First define variables, use meaningful names, like t = tens digit u = units digit. so far so good?
mathmate
  • mathmate
When you have a number like 25, then t=2, u=5, and 10t+u = 25.
mathmate
  • mathmate
"The sum of the digits of a two-digit number is 7" can you form an equation with that?
pooja195
  • pooja195
7u+t=27?
mathmate
  • mathmate
Here, we are saying the equivalent of 2+5=7, so t+u=7 will do. now "When the digits are reversed, the number is increased by 27. "
pooja195
  • pooja195
t+u=27?
mathmate
  • mathmate
10t+u is the original number 10u+t is the number reversed (units digit becomes 10's digit) so 10u+t = 10t+u + 27 (increased by 27)
mathmate
  • mathmate
Simplifying this equation, we get 9u-9t=27 or u-t=3 combined with u+t=7 we solve for t=2, u=5, or the original number is 25.
mathmate
  • mathmate
Check: 52-25=27, ok.
pooja195
  • pooja195
:/
mathmate
  • mathmate
pooja195
  • pooja195
.
mathmate
  • mathmate
I'm typing up an example.
mathmate
  • mathmate
\(\large \frac{5}{x^2-1}+\frac{4}{x^2+2x+1}\)
mathmate
  • mathmate
So first factorize the denominators:
mathmate
  • mathmate
\(\frac{5}{(x+1)(x-1)}+\frac{4}{(x+1)^2}\)
mathmate
  • mathmate
Can you find the common denominator? between (x+1)(x-1) and (x+1)^2
pooja195
  • pooja195
it would be (x-1)
pooja195
  • pooja195
and then x+1 on the other side?
mathmate
  • mathmate
"common" denominator of two expressions must contain ALL the factors, and is the same for all the terms. So start with one of the two , say (x+1)(x-1) and add factors to it so that it contains every expression.
mathmate
  • mathmate
Say we start with (x+1)(x-1), surely it contains (x+1)(x-1) , which is the first expression.
mathmate
  • mathmate
Question is, does it contain the second expression (x+1)^2?
mathmate
  • mathmate
the answer is no. What do we need to do? Multiply by another (x+1), so we end up with a common denominator of (x+1)(x-1)(x+1).
mathmate
  • mathmate
So going back to the question: \(\Large \frac{5\color{red}{(x+1)}}{(x+1)(x-1)\color{red}{(x+1)}}+\frac{4\color{blue}{(x-1)}}{(x+1)^2\color{blue}{(x-1)}}\) notice that now both denominators are identical.
mathmate
  • mathmate
\(\Large \frac{5\color{red}{(x+1)}}{(x+1)^2(x-1)}+\frac{4\color{blue}{(x-1)}}{(x+1)^2(x-1)}\)
mathmate
  • mathmate
and that's the same as \(\Large \frac{5\color{red}{(x+1)}+4\color{blue}{(x-1)}}{(x+1)^2(x-1)}\)
mathmate
  • mathmate
Next step is to expand and simplify the numerator: \(\Large \frac{5x+5+4x-4}{(x+1)^2(x-1)}=\frac{9x+1}{(x+1)^2(x-1)}\) and that's the end of the calculations.
pooja195
  • pooja195
I read these but only half .-. @mathmate
mathmate
  • mathmate
Did you understand as far as you read?
pooja195
  • pooja195
yes but now we can start studying for the finals :P >_<
mathmate
  • mathmate
Here's the diagnostic test, as far as I have done. I will add other things on.
mathmate
  • mathmate
@pooja195 you there?
pooja195
  • pooja195
i iz here
mathmate
  • mathmate
ok, let's get started. Any questions on chapter 1?
mathmate
  • mathmate
Say, 4^d=64, what is "d".
mathmate
  • mathmate
need help?
pooja195
  • pooja195
yeah :/
mathmate
  • mathmate
4^0=?
pooja195
  • pooja195
1
mathmate
  • mathmate
Very good! 4^1=
pooja195
  • pooja195
4
mathmate
  • mathmate
Just two rules: Anything raised to the power of 0 is 1, anything raised to the power of 1 is the base itself, like 4^1=4
mathmate
  • mathmate
4^2=
pooja195
  • pooja195
16
mathmate
  • mathmate
Remember, \(4^2=4.4\), \(4^3=4.4.4\), \(4^4=4.4.4.4\), etc.
mathmate
  • mathmate
so 4^3=?
pooja195
  • pooja195
64
pooja195
  • pooja195
so 3?
mathmate
  • mathmate
compare 4^3=64, 4^d=64 so what is d? yes, d=3
mathmate
  • mathmate
Great! Now try 8=2^z. what is z?
pooja195
  • pooja195
2*2*2 2^3
mathmate
  • mathmate
and z=?
pooja195
  • pooja195
3
mathmate
  • mathmate
Good! Now a difficult one: \(-3^2=\)?
pooja195
  • pooja195
-9? or if its (-3)^2 it would be 9
mathmate
  • mathmate
Exactly, that's where many students make mistakes. when in doubt, use PEMDAS which says that exponentiation goes before subtraction (negative), so what you did was correct. (-3)^2 would raise the power of -3, so (-3)*(-3)=+9. Well done!
mathmate
  • mathmate
and -3^2=-9.
mathmate
  • mathmate
Try the following: 1^3= 3=3^j, j= 1=4^h, h= 3^r=81, r= (-2)^3=
mathmate
  • mathmate
Laws of exponent: 2^n = 2.2.2.....2 (n times) \(a^m \times a^n = a^{m+n}\) \(\large a^{-m}=\frac{1}{a^m}\) \(\large a^{\frac{1}{2}}=\sqrt a\) \(\Large a^{-\frac{1}{2}}=\frac{1}{\sqrt a}\)
mathmate
  • mathmate
Now practice: \(\Large (\frac{1}{2})^2=\) \(\Large (0.2)^3=(\frac{2}{10})^3=(\frac{1}{5})^3=\frac{1}{125}\) Express \(\large 3^{-8}\) with a positive exponent. \(\large 3^{-8}\) =
pooja195
  • pooja195
O_O
mathmate
  • mathmate
|dw:1433336557931:dw|
pooja195
  • pooja195
What is that??
mathmate
  • mathmate
Helps you see where numbers belong. R includes all numbers you're studying (i.e. does not include complex numbers) Inside of R is divided into Q (rational) and Q' (irrationals) Q' (irrationals) include numbers like sqrt(2), \(\pi\), sin(10\(^\circ \)), etc. Q (rationals) include \(all\) integers (Z), and all naturals (N). Decimals (2.5) repeating decimals (2.33333...), fractions (7/3) all belong to rationals, but not Z and N. All N belong to Z, but negative integers are in Z but not in N. See if you can read these relations from the diagram.
mathmate
  • mathmate
pooja195
  • pooja195
:)
mathmate
  • mathmate
Solve x+4<7 (page 324)
pooja195
  • pooja195
x<3
mathmate
  • mathmate
ok... too easy for you?
pooja195
  • pooja195
Yes xD
mathmate
  • mathmate
Write an inequality to show the max. no. of apples I can buy if I have $4.8 and apples cost $0.60 each.
mathmate
  • mathmate
* possible number of apples
pooja195
  • pooja195
O_O i dunno this...
pooja195
  • pooja195
x+0.60<4.8?
mathmate
  • mathmate
I have $4.80, and apples cost 0.60 each. So the maximum number of apples I can buy is $4.80/0.60 =?
pooja195
  • pooja195
8
mathmate
  • mathmate
Good, and the minimum?
pooja195
  • pooja195
would i subtract?
mathmate
  • mathmate
Well, the minimum would be zero. I don't have to buy any. So the answer would be:
pooja195
  • pooja195
x=8?
pooja195
  • pooja195
x<8
mathmate
  • mathmate
That's the maximum number of apples. If we ask for the possible number, then it would be:
pooja195
  • pooja195
4? o.L
mathmate
  • mathmate
I can buy anything from 0 to 8, so \(\large 0\le x \le 8\), where x is the number of apples.
pooja195
  • pooja195
ooo >_<
mathmate
  • mathmate
Does that make sense?
pooja195
  • pooja195
Yea
mathmate
  • mathmate
Word problems!
mathmate
  • mathmate
Try 4x-3=21
mathmate
  • mathmate
solve.
pooja195
  • pooja195
x=6
mathmate
  • mathmate
Excellent! now solve -5x+10=30
pooja195
  • pooja195
x=-4
mathmate
  • mathmate
Good!
mathmate
  • mathmate
now solve \(-5x+10\le30\)
pooja195
  • pooja195
\[\huge~x \ge-4\]
mathmate
  • mathmate
Very good!!! you actually know the rules!
mathmate
  • mathmate
Why is it \(\ge\) and not \(\le\) ?
pooja195
  • pooja195
because when you divide by a negative you always need to flip the signs
mathmate
  • mathmate
Excellent! What if you multiply by a negative?
pooja195
  • pooja195
Keep the sign as it is DO NOT change it :)
mathmate
  • mathmate
Is x/(-1) equal to x*(-1)? why would the rule be different?
pooja195
  • pooja195
idk its just like that .-.
mathmate
  • mathmate
Actually, whether you multiply or divide by a negative, you flip the direction of the > or < sign. You can remember that precisely because x*(-1) is the same as x/(-1). So can you now solve
mathmate
  • mathmate
\(\Large \frac{5}{3}(x-5)=6\)
pooja195
  • pooja195
\[\frac{ 5 }{ 3 }x-\frac{ 25 }{ 3 }=6\]
mathmate
  • mathmate
There is a trick to solving equations with fractional coefficients!
mathmate
  • mathmate
I would multiply by the denominator, or LCM of the denominator if there are many.
mathmate
  • mathmate
This way, we end up with an equation with integer coefficients.
mathmate
  • mathmate
\(\Large \frac{5}{3}(x-5)=6\) \(\Large 3*\frac{5}{3}(x-5)=3*6\) \(\Large 5(x-5)=18\) and then go from here
pooja195
  • pooja195
\[\huge~5x-25=18\] \[\huge~5x=43\] \[\huge~x=\frac{ 43}{ 5 }\]
mathmate
  • mathmate
Exactly!
mathmate
  • mathmate
Any questions before we move on to linear equations?
mathmate
  • mathmate
...and graphing?
pooja195
  • pooja195
no, but lets skip graphing :/
mathmate
  • mathmate
You're willing to forfeit the points?
pooja195
  • pooja195
nvm -_-
mathmate
  • mathmate
What is a linear equation in slope-intercept form?
pooja195
  • pooja195
y=mx+b
mathmate
  • mathmate
Good! Can you find a line with a slope of 2 that passes through (2,4)?
pooja195
  • pooja195
Point slope formula \[\huge~y-y1=m(x-x1)\] \[\huge~y-4=2(x-2)\] \[\huge~y-4=2x-4\] \[\huge~y=2x\]
mathmate
  • mathmate
Excellent. What form of equation did you use?
mathmate
  • mathmate
I call it point-slope form. Not many school teach this form.
mathmate
  • mathmate
*schools
pooja195
  • pooja195
i wrote it on top xD
mathmate
  • mathmate
Sorry, I didn't see it!
pooja195
  • pooja195
itz okz :-)
mathmate
  • mathmate
Now how about a line that passes through 2 points. Can you find it?
mathmate
  • mathmate
The points are (2,5), (7,15)
pooja195
  • pooja195
Find slope first \[\huge~\frac{ y2-y1 }{ x2-x1 }\] \[\huge~\frac{ 15-5 }{ 7-2}=\frac{ 10 }{ 5 }=5\] Point slope formula \[\huge~y-y1=m(x-x1)\] Pick a point right? \[\huge~y-5=5(x-2)\] \[\huge~y-5=5x-10\] \[\huge~y=5x-5\]
mathmate
  • mathmate
you got 90% for this one!
pooja195
  • pooja195
-_-
mathmate
  • mathmate
Spot the error!
pooja195
  • pooja195
i dont see it .-.
pooja195
  • pooja195
Wait i simplified
mathmate
  • mathmate
All the steps are perfect, but 10/5=2 !!!!
pooja195
  • pooja195
>_<
pooja195
  • pooja195
Are you going to make me redo all the work????? ;-;
mathmate
  • mathmate
That's no problem. That's how I would correct, more for steps.
mathmate
  • mathmate
No!
pooja195
  • pooja195
:)
mathmate
  • mathmate
If your steps are good, that's what's important.
mathmate
  • mathmate
But do be careful in tests and exams.
pooja195
  • pooja195
ok :)
mathmate
  • mathmate
Translate into a mathematical inequality: Ken's age (k) is at least four years older than Pete's (p).
pooja195
  • pooja195
\[\huge~K \ge 4+p\]
pooja195
  • pooja195
:/
mathmate
  • mathmate
Great! It wasn't easy for you, but you did it!
mathmate
  • mathmate
Now try: Liz (L) has at least 4 times less flowers than Priya (P).
mathmate
  • mathmate
At least 4 times could mean 5 times!
mathmate
  • mathmate
* could be
pooja195
  • pooja195
Idk know this one .-.
mathmate
  • mathmate
When in doubt, put numbers in. Say Liz has $10, how much should Priya have?
mathmate
  • mathmate
$40, $50, $60, anything $40 or more, right?
mathmate
  • mathmate
Sorry, change flowers to $...:(
mathmate
  • mathmate
So if L=10, P=40, so we write \(\Large 4L \le P\)
pooja195
  • pooja195
i knew it!
mathmate
  • mathmate
That's what you would have done?
pooja195
  • pooja195
i was thinking something similiar
pooja195
  • pooja195
4p
mathmate
  • mathmate
Good. Be careful, many students would write L\(\le\) 4P.
pooja195
  • pooja195
XD
mathmate
  • mathmate
so using numbers, you can check your work.
pooja195
  • pooja195
Right
mathmate
  • mathmate
How are we doing so far?
pooja195
  • pooja195
Great :)
mathmate
  • mathmate
Pace? 1=too slow, 10=too fast.
pooja195
  • pooja195
5
mathmate
  • mathmate
ok, we're on the right track.
mathmate
  • mathmate
Gimme a minute, I have to flip the pages. You can go get a glass of water, you talked a lot! lol
pooja195
  • pooja195
XD
mathmate
  • mathmate
Heard about compound inequalities? (6.5)
pooja195
  • pooja195
yes
mathmate
  • mathmate
Have you done interval notation?
pooja195
  • pooja195
no
mathmate
  • mathmate
Like (5,8(, or ]5, 8]
pooja195
  • pooja195
nope
mathmate
  • mathmate
They are usually used to solve compound inequalities.
mathmate
  • mathmate
Since you haven't done it, we'll describe by words.
pooja195
  • pooja195
You mean and and or ?
pooja195
  • pooja195
\[x+3<5~~or~~~5
pooja195
  • pooja195
like that?
mathmate
  • mathmate
Yes.
mathmate
  • mathmate
Can you try to solve x<-5 or x>-4
pooja195
  • pooja195
They are already solved. -
mathmate
  • mathmate
Excellent!
mathmate
  • mathmate
Change to and: Can you try to solve x<-5 and x>-4
pooja195
  • pooja195
still the same :/ ?
mathmate
  • mathmate
No, I'll draw the number line.
mathmate
  • mathmate
|dw:1433387503479:dw|
mathmate
  • mathmate
Solution for or is shown in the graph. But for and, there is no number that satisfies the and condition. No number can be less than -5 and greater than -4 at the same time, so answer is "no solution".
mathmate
  • mathmate
How about solving: x>4 and x<10 Use the number line if necessary
mathmate
  • mathmate
Feel free to show intermediate steps progressively. You don't have to wait till you typed up everything.
pooja195
  • pooja195
|dw:1433387789387:dw|
mathmate
  • mathmate
The answer is correct graphically. How would you write it mathematically?
pooja195
  • pooja195
x>4 and x<10
mathmate
  • mathmate
You can write it as \(4\lt x\lt10\) whe it is a range
mathmate
  • mathmate
But be careful about the difference between \(\le\) and \(\lt\) etc
mathmate
  • mathmate
Moving onto 6.6 unless you have questions.
mathmate
  • mathmate
Solve |x|=2
pooja195
  • pooja195
+2 -2
mathmate
  • mathmate
Very good. I see that your book does not write the answer in set notation, for example: x={-2,2}
mathmate
  • mathmate
Neither does your teacher?
pooja195
  • pooja195
Nope
mathmate
  • mathmate
ok, no problem. Solve |x|<2
pooja195
  • pooja195
x<2 and x>−2
mathmate
  • mathmate
Again, these two "and" inequalities make a range between -2 and +2 so we write -2
pooja195
  • pooja195
ok
mathmate
  • mathmate
solve |x-3| =5
pooja195
  • pooja195
x−3=5 x=8 x−3=−5 x=-2
mathmate
  • mathmate
So x=8 or -2 Good, you know your stuff! This is encouraging! what do you think?
pooja195
  • pooja195
Its easy :)
mathmate
  • mathmate
Even better!
mathmate
  • mathmate
now solve |2x-7| -3=6
pooja195
  • pooja195
add 3 to both sides 2x-7=9 x=8 2x-7=-9 x=-1
mathmate
  • mathmate
Very good! It's still easy?
pooja195
  • pooja195
yes
mathmate
  • mathmate
We move onto abs. inequalities.
mathmate
  • mathmate
solve |4-3x| -2 \(\le\) 7
pooja195
  • pooja195
Do you want me to show the work?
mathmate
  • mathmate
Not in this case, will save some time.
pooja195
  • pooja195
\[\huge~x \ge \frac{ -5 }{ 3} ~~~and ~~~x \le \frac{ 13 }{ 3 }\]
mathmate
  • mathmate
Can you check if it is x>=13/3
pooja195
  • pooja195
−3x+4−4≥−9−4 I subtracted 4 from both sides −3x≥−13 i divided and flipped the signs it should be \[\huge~\frac{ 13 }{ -3 }\]
mathmate
  • mathmate
I have 4-3x <= -9 (second case) -3x <= -13 3x >= 13 so x>=13/3 do you agree?
pooja195
  • pooja195
oh right the negatives cancel
mathmate
  • mathmate
yes, they do (after flipping sign)
pooja195
  • pooja195
and then u flipped .-.
mathmate
  • mathmate
xD
pooja195
  • pooja195
LOL
mathmate
  • mathmate
Looks like you're good till 6.7 (perhaps as you expected).
mathmate
  • mathmate
Sorry, didn't achieve 2 chapters, not even one, but we're efficient.
mathmate
  • mathmate
No dull moment. :)
pooja195
  • pooja195
:)
mathmate
  • mathmate
If we have time later on, we may go back to word problems.
pooja195
  • pooja195
NO
mathmate
  • mathmate
Sure, we'll continue with 6.8 then.
mathmate
  • mathmate
The NO is a tell-tale sign! :)
pooja195
  • pooja195
-_-
pooja195
  • pooja195
\(\color{blue}{\text{Originally Posted by}}\) @mathmate If we have time later on, we may go back to word problems. \(\color{blue}{\text{End of Quote}}\) NONONONONONON!!!
mathmate
  • mathmate
Not today. Want to do word problems when you're fresh. We'll move on to graphics in 2 variables. p.367
mathmate
  • mathmate
Can you tell me in a few words about graphing linear inequalities in two variables?
pooja195
  • pooja195
:/
mathmate
  • mathmate
Use words like region, feasible, vertical, horizontal lines, etc
mathmate
  • mathmate
ok, so I'll do it.
mathmate
  • mathmate
... another time! :)
pooja195
  • pooja195
yes :)

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