Melody

$$\left({\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{50}}}{{\mathtt{60}}}}\right){\mathtt{\,\times\,}}{\mathtt{7}} = {\frac{{\mathtt{413}}}{{\mathtt{6}}}} = {\mathtt{68.833\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

i think that you mean 'trial and improvement"

Given that X lies between 5 and 6 use trail and improvement to solve X^3- 6X=126.

0=x^3-6x-126

try x=5.5

$${{\mathtt{5.5}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5.5}}{\mathtt{\,-\,}}{\mathtt{126}} = {\frac{{\mathtt{59}}}{{\mathtt{8}}}} = {\mathtt{7.375}}$$

try 5

$${{\mathtt{5}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{126}} = -{\mathtt{31}}$$

So it is between 5 and 5.5

Try 5.2

$${{\mathtt{5.2}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5.2}}{\mathtt{\,-\,}}{\mathtt{126}} = {\mathtt{\,-\,}}{\frac{{\mathtt{2\,074}}}{{\mathtt{125}}}} = -{\mathtt{16.592}}$$

So it is between 5.2 and 5.5

try 5.4

$${{\mathtt{5.4}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5.4}}{\mathtt{\,-\,}}{\mathtt{126}} = {\mathtt{\,-\,}}{\frac{{\mathtt{117}}}{{\mathtt{125}}}} = -{\mathtt{0.936}}$$

So it is between 5.4 and 5.5

Try 5.45

$${{\mathtt{5.45}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5.45}}{\mathtt{\,-\,}}{\mathtt{126}} = {\mathtt{3.178\: \!625}}$$

So it is between 5.4 and 5.45

So to 1 decimal place it is 5.4

Thanks Chris  :))

$${\frac{{\mathtt{37}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{3\,851\,799}} = {\mathtt{1\,425\,165.63}}$$

Example

$$7\frac{2}{3}\;=\;\frac{7*3+2}{3}\;=\;\frac{21+2}{3}\;=\;\frac{23}{3}$$

Thank you Gino for providing this web address.

I hope to put it to good use in the future.  :)

To answer this question you go wher Gino sent you

Yes - but yours is more impressive.  :)

$$y=a^2+6a-7$$

This is a concave up parabola  (I can explain why if you ask)

$$y=(a+7)(a-1)$$

The roots are a=-7 and a=1

The axis of symmetry is  a=(-7+1)/2 = -3

The minimum value

$$\\y=(-3)^2+6*(-3)-7\\
y=9-18-7\\
y=-16$$

The minimum value is -16

ALTERNATIVELY

It would have been easier to solve this using calculus.   

$$\\\frac{3k}{5}-\frac{1k}{10}=\frac{1k}{2}+1\\\\
10\left(\frac{3k}{5}-\frac{1k}{10}\right)=10\left(\frac{1k}{2}+1\right)\\\\
\frac{30k}{5}-\frac{10k}{10}=\frac{10k}{2}+10\\\\
6k-k=5k+10\\\\
5k=5k+10\\\\
0=10\\\\
$No solution$$$

what is the % of 4000000.897 in 4000000.897?

4000000.897/4000000.897*100  

then write the percent sign at the end.

Use the site calc on the home page. :)