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Ten to the 5th power is 100,000   it isn't a fraction

Well.....if the $34 hat is he more expensive, the other will be $12  less = $22

If the $34 hat is the less expensive, the other will be $12 more = $46

I'll be the type of person who will punch you and take pleasure in it, LOL!

Since the word cotainns four "E's"  and there are nine total letters.......we would expect that out of N draws, (4/9)  of them will be winners....

So.....with  45 draws......45(4/9)  = (45/9) * 4   =  5 * 4   = 20 students will be expected to win

Your nan

Yes, guest I suppose you are technically correct.....I assumed the term "made"  is what she charged for each shirt......who knows????

1/1,000,000 =   .000001   =   .0001 %

1/ 1x10^6  x 100  =  1/10^4 = .0001 %

10%  off means she paid 90%= .90 of the cost

20% off means that she paid 80% =.80  of the cost

So we have

43(.90)  + 35(.80) = $66.70

[The dress cost $38.70  and the hangbag cost $28]

Hmmmmm.....another poorly worded problem

if she TRULY made 84 dollars PROFIT   and she MADE 6 each shirt (it does NOT say she SOLD them for 6 ea) then 84/6 = 14 shirts    and expenses are irrelevant in this question.

if she MADE 6 for each shirt then she must have priced them @  (84 + 30)/14 = 114/14 =  8.14 ea   2.14 of which was expense and 6 of profit.

abs [5 - 11]   =   abs [ -6]    =  6

First, you make a proportion that the variable can be a part of. For example, if x is a hypotenuse in one triangle and the shorter leg in another, the proportion would be like so: x/smaller triangle's short leg= larger triangle's hypotenuse/ x. I know this is complicated, but I hope it makes sense! (BTW, what's half of 25.5?)

No prob, Solveit.....!!!!

Thanks CPhill !

f(x)  = 3x^4 − 7x^2 + 2x − 9       ......so.....

f(-x) = 3(-x)^4 - 7(-x)^2 + 2(-x)  - 9  =    3x^2 - 7x^2 - 2x  - 9

[  BTW.....This function is neither even nor odd....  ]

4 and two thirds of a ile every day

HUH???

5.   |x^2-x|=|x^2-1|      similar to the first one, we have

x^2 - x   = x^2 - 1                  or             x^2 - x  =  - (x^2 - 1)

-x = -1                                                   x^2 - x  = -x^2 + 1

x = 1                                                   2x^2 - x - 1  = 0

                                                           (2x +1)  ( x - 1)  = 0

                                                         Set each factor to  0

                                                            x = -1/2     [ x = 1    .....a repeated solution]

Here's the graph......https://www.desmos.com/calculator/kcbcpd3khj

9+10=19

Anol is giving a example of a simple argument.  But if he say it at my school the students will show up out of nowhere and lineup to punch him. I want to be first in line.  hahahaha

We do grow up Anol but it take time. Some of us will grow up to be cry babies and some will become bitter old farts like you. Most of us will be fine.

4 .   |2x-7|=|x-5|

2x - 7    =    x  - 5                    or          2x - 7   = -(x - 5)

x  =  2                                                    2x - 7  = -x  + 5

                                                              3x  = 12

                                                                x = 4

Again......these are easily verified

3. |4-x|=5       this one is easy

Either

4 - x   = 5                          or                      4 - x  = -5

-x  = -1                                                         -x   = -9

x = 1                                                              x = 9

These solutions are easily verified in the original problem

2.  3|x-2|=2|x-3|    divide both sides by 2

(3/2)|x-2|=lx-3|      as before, we have.....

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

                                                            (3/2)lx - 2 l  =  - x + 3

Multiply through by 2   in both equations.....

3(x -2) = 2x - 6                                     

3x - 6   = 4x - 6                                        3(x - 2)  = -2x + 6                               

The only solution to this is                     3x - 6    = -2x + 6

when x = 0  

                                                               5x  = 12

                                                                  x = 12/5  =  2 + 2/5  =  2.4

So the two solutions are  x = 0   and x  = 2.4

See the solution graphs, here.....   https://www.desmos.com/calculator/frf6guc36z

😕yall stupid its 2 😎

These are always a little difficult to wrap one's head around.....!!!

They are all solved in pretty much the same manner  ....!!!

1.  abs (x^2 - 1) = abs (x - 1)

We have two  equations that result

x^2 - 1  =  x - 1                       and       x^2 -1  = -(x - 1)            working on both, we have

x^2  = x                                               x^2  - 1   = -x + 1

x^2 - x = 0                                          x^2 + x - 2  = 0

x(x-1)  = 0                                          (x +2) ( x-1)  = 0

So  x = 0 , 1                                      So  x = -2  and x = 1

The solutions are  x = -2, x = 0 and x = 1

Look at the graph of the solutions, here.........https://www.desmos.com/calculator/sanncuv3uw