Melody

-7x-3(9-7x) if x=-1

   -7x        -3  (9   - 7 x)    if x=-1

= -7*-1    -3*(9  -  7*-1) 

= +7       -3*(9 - -  7   )

= 7         -3*(9 +  7  )

= 7        -3* 16

= 7    -   48

= -41

Could you put some brackets in please ?

simplified radical form of √208

\(\sqrt{208}=\sqrt{4*4*13}=4\sqrt{13}\)

0.6=3/30+x

\(0.6=\frac{3}{30}+x\\ 0.6=\frac{1}{10}+x\\ 0.6=0.1+x\\ 0.6-0.1=0.1-0.1+x\\ 0.5=x\\ x=0.5 \)

I needed a laugh,  thanks Rom  

Mmmm   What is the question?

What is between the x and the 10?

x 10exp(−0.17x)=1 what is the value of x

x ? 10^(-0.17x) = 1

Is it meant to be multiply??

\(x \times 10^{-0.17x} = 1\\ x \times \frac{10^{-0.17x}}{1} = 1\\ x \times \frac{1} {10^{0.17x}}= 1\\ x=10^{0.17x} \\ log x=0.17x\)

I am going to cheat a bit and get a graphical solution

I am graphing y=log(x)  and  y=0.17x

Looks to me like there is no solution since the 2 graphs don't intersect.

Can someone check this please?

Thanks Rom   

Thanks Heureka,

I didn't even see the tan(2x)      

g/h^2÷g^2/h^3

Are there meant to be any brackets here?

I will read your mind and put some in :)

\((g/h^2)÷(g^2/h^3)\\ =\frac{g}{h^2}\div\frac{g^2}{h^3}\\ =\frac{g}{h^2}\times \frac{h^3}{g^2}\\ =\frac{h}{g}\)

Find sin 2x, cos 2x, and tan 2x from the given information. tan x = −1/2 , cos x > 0

If a right angles triangle has the two short sides of 1 and 2 then the hypotenuse must be sqrt5

since tan is neg the angle is in the 2nd or 4th quads and since cos is pos, x must be in the 4th quad.

tan x = −1/2        cosx= +2/sqrt5         sinx= -1/sqrt5

sin2x= 2sinxcosx = 2* -1/sqrt5 * 2/sqrt5 = -4/5

cos2x= cos^2x-sin^2x =  4/5-1/5 = 3/5

I did it in my head so I hope I didn't do anything stupid.  You are capable of checking yourself. 

Any question, just ask. :)