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$1.29 x 4.7 = 6.063 Rounded to the nearest cent would be $6.06

|x|-2<=3    add 2 to both sides

l x l  <= 5       and we can set this up as

-5 <= x <= 5

So, the answer is

x = [ -5, 5 ]

WOW, that looks impressive Heureka    

"Product"  means "Multiply".......thus.......the "product" of 3 and 2   =  3 x 2   = 6

Sweet! That was really simple!

Thanks a lot :D

2x - y² + 3z³    ......x = 3, y = -2 and z = -1

2(3) - (-2)² + 3(-1)³  =        [remember that (-2)²  is positive, but the negative out front makes it negative.....  and that (-1)³  = -1  .....so 3 * - 1  = -3]

6  - 4 - 3   =

6 - 7  =

-1

2sinx+cosx=0   subtract cosx from both sides

2sinx = -cosx       square both sides

4sin'^2x   = cos^2x        and we can write cos^2x as  1 - sin^2x

4sin^2x = 1 - sin^2x     add sin^2x to both sides

5sin^2x   = 1       divide both side by 5

sin^2x  = 1/5      take the positive and negative square roots of both sides

sinx = plus/minus sqrt(1/ 5)

So, taking the sine inverse of both answers, we have

sin^-1 ( sqrt (1/5) )  = x =   about 26.565 °              and        sin^-1 (-sqrt (1/5) )  = x  =   about - 26,565 °

We can reject the first solution because the sin and cos are positive at 26.565 °   ......and this would make the original equation false

The second solution is correct

For more general solutions......here's a graph [ in degrees ]  ......https://www.desmos.com/calculator/cttwh9sjr2

One general solution is   x = [ - 26.565 °  + 180n ] °   where n is an integer

cos(2x-2.5)=0.75

Here's a graph of some solutions [in degrees].......https://www.desmos.com/calculator/dwdu9uf31p

The two general solutions appear to be, approximately

x = [22 + 180n] °       and x = [160.5 + 180n ] °      where n is an integer

Thank You

sin(6x-30)=0.5

This could have infinite answers, but one solution is based on the fact that the sine = 0.5 at 30°.........

6x - 30  = 30    add 30 to both sides

6x = 60            divide both sides by 6

x = 10

[ P.S.....other solutions could be 30, 70, etc.  ]

X^2-49

You need to be careful ChoZerr, there is no = sign in the question so there CANNOT be an answer.

Not like you have found anyway.

x^2-49 is already in its most simple form.

BUT

since it is of the from   x^2  -  7^2

it can very easily be factorised to give  (x-7)(x+7)

oh and IF

x^2 - 49 did really equal 0 then there are 2 answers,   x=7  or x=-7

jokes

Had trouble with this as well,

Its 17

I like to put in another step.

\(ln e^x =6\\ x*lne=6\\ x*1=6\\ x=6\)

Thank you so much! 

Is it a chain saw ????     

Did I win a banana or better still a banana daquiri,    

Hey Sir Phil La-TeX, do you make a mean banana daquiri like Sir Lancelot Link does.  mmm mmm.    

Our guest added 9 to both sides to make the LHS a perfect square.

he/she really added      (6/2)^2   which is 9 :))

CPhill's way is easier but it is good to understand lots of different ways if you can.

Thanks CPhill and thanks Guest for your great answers :))

Hi  Guest,

I do not know if you will even see this since you aske the question 24 hous ago, if you did not save the thread somewhere you have probably already lost track of it.

SO pleas join up and then you questions will be automatically put into you watchlist and you can aske for email notification if anyone answers you.

Anyway, to learn about polynomial long division it would be good for you to watch this video :))

how do you solve ln e^x =6

\(\begin{array}{rcll} \ln{ ( e^x ) } &=& 6 \\ x &=& 6 \end{array}\)

4.20 / 4 = 1.05$