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We all make mistakes 

Oh now i see it.It's 8:57 a.m. and im awake all night I was studying.I'm sorry!

Thanks for the observation!

This is not what the guest wants to prove, I think you confused the floor function with the absolute value function

\(\left |x \right | + \left |y \right | = \left |x \right | +\left |y \right |\)(1)

We know:

\(\left |x \right | + \left | y \right | \)>\(\left | x+y \right |\) (2) 

We (1)+(2) 

\(\left |2x \right | + \left | 2y\right |\) >\(\left | x \right | + \left | y \right | +\left | x+y \right |\)

We prove it!

Hope it helps! 

Off Topic.....Thanks!

We make concord the fractions before was 20/24 full and after is 9/24 the difference is 20/24-9/24

= 11/24 

The answer is 11/24 after - before practice!

Hope it helps! 

CPhill, didn't you forget about the V?

Since this is a dashed line.....we will have either   "< "  or  " > "

The points (3,1)  and (1, -2)  are on the graph boundary 

The slope of this dashed line is  [ -2 - 1 ] / [ 1 - 3 ]   = -3 / -2  = 3 /2

The equation of the dashed line is

y = (3/2)( x - 1) - 2

y = (3/2)x - 3/2 - 2

 y = (3/2)x - 7/2

We will either have 

y < (3/2)x - 7/2     or   y > (3/2)x  - 7/2

(0 ,0)  is in the feasible  [ yellow ] region

Putting this coordinate into the second equation makes this inequality true

So....the inequality  is

y > (3/2)x - 7/2     multiply through by 2

2y > 3x - 7     subtract 2y from both sides

0 > 3x - 2y - 7     which is the same as

3x - 2y - 7 <  0

I get it, Thank you!

We have the points  (0,1)  and (1, 0)  on the graph boundary

The slope of the  line is given by  [ 0-1 ] / [ 1 -0 ] = -1 / 1  = -1

Writing an eauation of this line, we have

y = -x  + 1 

But  we either have the inequality

y ≥ -x + 1    or    y  ≤ -x + 1

Testing a point in the yellow region  ...I'll choose  (x, y) =  (0,0)  in both equations 

shows that the second equation is correct

Rearranging this we have

x + y - 1  ≤ 0

There may be an algebraic way to do this.....but I think it can be done graphically like this :

https://www.desmos.com/calculator/4fhytbda6x

It can be shown that some corner point [ a point in the feasible region of all the graphs] will maximize x + y   [ the objective function]

Therea are two corner points here  (-5/9, 31/9)  and (5/9 , -31/9 )   

Testing both points in the objective function,the corner point  (-5/9,  31/9)  will maxmize x + y  =

-5/9 + 31/9  =

26/9

[ This is known as linear programming ]

We can use this formula to find each new point

new point  = (old point - center)*scale factor + center

So

[ (-1, 3) - ( -2 , -2) ] * 2 + (-2, -2)  = [ 1 , 5 ] *2 + (-2,-2)  = (2, 10) + (-2, -2)  = (0, 8)

[ (-5, 2) - ( -2, -2) ] *2 + (-2, -2)  =  [ -3, , 4]*2 + (-2,-2)  = ( -6, 8 ) + (-2, -2) = (-8, 6)

[(-4, -2) - (-2, -2) ] *2 + (-2, -2)  = [ (-2, 0) ]*2 + (-2, -2)  = (-4, 0) + (-2, -2) = (-6, -2)

[ (1,1) - (-2, -2)]*2 + (-2,-2)  = [ (3, 3]*2 + (-2, -2)  = (6, 6) + (-2, -2)  = (4, 4) 

Here's a pic :

2/3t - 1 < t +7 so

2/3t - t < 7 + 1

-1/3t < 8

t > -3(8) 

t > -24  

and t+7 < -2t +15 

t + 2t < 15 - 7 

3t < 8

t < 8/3 

Finally tE (-24,8/3] 

I did two of these for you... from what class are you getting these questions?

I was able to see the trick in the first two but this one seems truly complicated.

Is your class teaching any strategies for dealing with these?

He means with all numbers i understand with 5 numbers all the posible numbers we can take.I'm sorry ! :(

u wot mate?

disadvantages

1) they make me pay attention in class/to my online reading

2) they make me read my textbook

advantages

1) they make me pay attention in class/to my online reading

2) they make me read my textbook

If you are strictly enforcing 5 digits, as in no number can start with any number of zeros.

Then we have 

\(n = 9 \cdot 10^4 = 90000\)

In the form   ax^3 + bx^2 + cx + d

The sum of the roots  is   -b/a

So....in this case.....  -2/1  =   -2

First of all we eill find domain of equation. x ≠ -4, x ≠  -3 because if x = -4,-3 we will have in denominator 0 

After this we start

\((x+3)(x) = -(x+4)(9) <=>\)

\(<=> x^2+3x = -9x -36 <=> \)

\(<=> x^2 + 12x + 36 = 0 <=> \)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a} \)

x= -12/2 = -6 and

\(-6≠ -3,-6≠ -4 \) 

so \(x=-6\) is the answer.

Hope it helps! 

oh it was B

Its 5! = 1*2*3*4*5 = 120 different numbers with 5-digit numbers!

We have the avaiable letters

A  E  G   I   K   O   P   R   T  U   V

For the first letter, we can select either the G or K  =  2 choices

For the next letter, we can pick one of 8 letters  = 9 choices

For the next letter, can pick one of 7 letters = 8 choices

For the next letter, we can pick one of 6 letters = 7 choices

The last letter must be  a "T"

So....2 * 9 * 8 * 7  =    1008  plates

EDIT  to correct an errot

No its x power 2 

Like this: \(x^2\) or x*x  its means x multiply x 

Hope it helps!