Maybe he's "auditioning".........

Are you enjoying answering your own questions anon?      

Sorry, mchow.....there may be a "trick," but I don't know what it might be.....I certainly don't see it....!!!

If something "hits me" later on, I'll message you.......(maybe some other answerer might see something I don't....)

@CPhill The question is correct, but apperntly my teacher said there is a trick. He won't tell us though. It'd be great of you could figure out the seconf part. Thank you for helping me with the irst though!

3x^2 - 7x + 12 = 0    this doesn't factor......using the onsite solver, we have

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{95}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{7}}\right)}{{\mathtt{6}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{95}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}\right)}{{\mathtt{6}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1.624\: \!465\: \!724\: \!134}}{i}\right)\\
{\mathtt{x}} = {\frac{{\mathtt{7}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1.624\: \!465\: \!724\: \!134}}{i}\\
\end{array} \right\}$$

The sum of the roots =  (14 / 6) =( 7 / 3 )

The product of the roots is

(1/36)[(7 - (√95)i] [ (7 + (√95)i ] =

(1/36) [49 - 95i²] =

(1/36) [ 49 + 95] =

(1/36)[144] =  4

I guess I have to dig out my compound interest formula :P

$${\mathtt{A}} = {{P}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{r}}\right)}}^{\,{\mathtt{n}}}$$

Where A is the amount,

P is the original value and,

r is the rate and

n is the number of compound periods.

So, lets fill out the stuff we know.

$${\mathtt{1\,000}} = {\mathtt{500}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.06}}\right)}^{{\mathtt{n}}}$$

This might not be correct but I believe it would be rearranged as so,

$${\mathtt{n}} = {\sqrt{{\mathtt{500}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.06}}\right)}} \Rightarrow {\mathtt{n}} = {\mathtt{23.021\: \!728\: \!866\: \!442\: \!676\: \!4}}$$

Thats how many compound periods it would take.

To find the answer in years divide by the amount of compound periods in a year.

Good luck! 

$${\frac{{\mathtt{39}}}{\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right)}} = {\mathtt{52}}$$

If you didn't add the brackets the calculator would interpret it as:

$${\frac{{\frac{{\mathtt{39}}}{{\mathtt{3}}}}}{{\mathtt{4}}}} = {\frac{{\mathtt{13}}}{{\mathtt{4}}}} = {\mathtt{3.25}}$$

Best of luck!

@geno3141 I tried graphing it but the graph is on the negative side which is pretty much impossible. I'm really stuck and don't know what to do :(

microwaves are electromagnetic waves, so to calculate the frequency of the wave, we should follow this formula:

c=f*λ

being  λ the wavelength and c the speed of light (equal to all electromagnetic waves)

c= 3*10^8 m/s

526mm=0.526m, then

$${\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{8}}}\right)}{\left({\mathtt{0.526}}\right)}}$$ = 5.7*10^8 Hz or (s^-1)

or it could be

570 MHz

9351.8032485719030978

√(2) / 2

A = (-1, 6)         B = (4, 5)         C = (-3, -4)

Use the distance formula to find the distance of each side:  d  =  √[ (x2 - x1)² + (y2 - y1)² ]

AB:  (x1, y1) = (-1, 6)         (x2, y2) = (4, 5)     --->  d  =  √[ (4 - -1)² + (5 - 6)² ]  

       --->   d  =  √[ (5)² + (-1)² ]     --->   d  =  √( 25 + 1)     --->     d  =  √26

BC:  (x1, y1) = (4, 5)         (x2, y2) = (-3, -4)     --->  d  =  √[ (-3 - 4)² + (-4 - 5)² ]  

       --->   d  =  √[ (-7)² + (-9)² ]     --->   d  =  √( 49 + 81)     --->     d  =  √130

AC:  (x1, y1) = (-1, 6)         (x2, y2) = (-3, -4)     --->  d  =  √[ (-3 - -1)² + (-4 - 6)² ]  

       --->   d  =  √[ (-2)² + (-10)² ]     --->   d  =  √( 4 + 100)     --->     d  =  √104

Since AB² + AC²  =  BC², this is a right triangle with sides AB and AC.

To find the area:  Area  =  ½ · AB · AC  =  ½ · √26 · √104 =  ½ · √2704  =  ½ · 52  =  26

NO!!!....a negative exponent just indicates a reciprocal....for instance......

3² = 9    but..... 3^-2 = 1 / 3² = 1 / 9

Note that an answer could be negative but not because of the negative exponent itself...for instance

(-3)³  = -27   and......  (-3)^-3  = 1 / (-3)³  = 1 / -27 = -1 / 27

-5 and -7 seem to work OK........

product = multiply              a number = x              increased by = add

3x + 7  =  23

Subtract 7:

3x  =  16

Divide by 3:

  x  =  16/3

They are separate functions. Is there some relation between the two that you need to know (such as: when are they equal? ) ?

A  =  P · [ ( 1 + r/n ) ^ (n·t) - 1 ] · (n/r)

A  =  final amount

P  =  deposit per time period  -- if weekly, amount deposited per week

r  =  rate (as a decimal)

n  =  number of times compounded per year  -- if weekly, use 52

t  =  number of years

Great explaination there Chris 

It means that if you have 27 lollies, how do you divide them equally between you and your friend.

Well you can have 13 lollies each but there is 1 left over.  you will have to cut that one in half and have a half each. 

SO

$$27\div 2 = 13\frac{1}{2}$$

you get 13 and a half lollies each :)

8  =  (-1/10)(6) + b

8  =  (-6/10) + b

8  =  -3/5 + b

Add 3/5 to both sides:

8 3/5  =  b

Add the numbers and divide by 10.......

0.025 x (his body weight)  =  (amount he eats)

0.025 x (his body weight)  =  45 pounds

Divide both sides by 0.025

            his body weight  =  45 ÷ 0.025

            his body weight  =  1800 pounds 

You can use the onsite calculator to evaluate this....