CPhill

Rate x Time = Distance

(65)3 + (400)2 = 995 miles

I'd say (a)....if the lion hasn't eaten in two years.....he's probably dead.......

4(2-4)^2 - 2(7-4)^2  =

4(-2)^2 - 2(3)^2  =

4(4) - 2(9)  =

16 - 18  =

-2

Let x be her little brother's age....so Maria's age now is 3x

And we're told that

5(x-5) = 3x - 5     simplify

5x - 25  = 3x - 5    add 25 to both sides and subtract 3x from both sides

2x  = 20         divide both sides by 2

x = 10.....and that's the age of her brother, now

So.....Maria's age now  = 3(10) = 30

Here's a "proof"

5^2 = 25

5^3  =  25 * 5  =  (20 + 5) (5) = 100 + 25

5^4  = 125 * 5  = (120 + 5) (5)  = (100 + 20 + 5) (5) = 500 + 100 + 25

5^5 = 625 * 5 =  (600 + 20 + 5) (5)  = (500 + 100 + 25)(5) = (500 + 100 + 20 + 5) (5)  = 2500 + 500 + 100 + 25

So it appears that the pattern  for 5^n = 

25 + 100*5^(0) + 100*5^(1) +.....+ 100*5^(n - 4) + 100*5^(n- 3)  for n ≥ 5 

And, in this series, all terms except the first one will end in the digits "00"...so adding 25 to this sum will always result in a number ending in "25"..........

It will calculate  10^308 but not 10^309.....strangely, though.....it will (seemingly) calculate.....

(10^308) (10^308) (10^308) (10^308) (10^308)......  

all day long......however it balks at (10^308)^2   (???)

Maybe one of our mods - Alan - can explain why this happens......he knows a lot about calculator operations

But, anyway.....it will probably handle most "normal" calculations just fine

It wasn't too much of a struggle.....but.......it does make me nervous when I get answers like 4.405....It defeats my "Nice Round Numbers"  theory........LOL!!!

We can find the answer just by getting the least common denominator between 12 and 20

12 = 2^2 x 3

20 = 2^2 x 5

And the LCD =  2^2 x 3 x 5 = 13 x 5 = 60 inches

So  60/12  = 5    and 60/20 = 3

When the length is 60 inches......3 of the 20 inch bocks will have been laid and 5 of the 12 inch blocks will have been laid.

Let x be the time (in hours) that B takes to fill the pool.....then( x - 5)  is the time it takes for A to fill the pool.

And every hour, B fills 1/x of the pool and A fills 1/(x -5) of the pool 

And we know that :

Rate per hour x time  = amount of job done....so.......

[(1/x) * 3]  + [1/(x -5) * 3]  = 1

3/x + 3/(x -5)  = 1

[ 3(x - 5) + 3(x)] = x(x - 5)

[6x - 15 ] = x^2 - 5x     simplify

x^2  - 11x + 15  = 0       and using the onsite solver, we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{11}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1.594\: \!875\: \!162\: \!046\: \!672\: \!8}}\\
{\mathtt{x}} = {\mathtt{9.405\: \!124\: \!837\: \!953\: \!327\: \!2}}\\
\end{array} \right\}$$

Reject 1.59......so A takes about (x - 5)= (9.405 - 5) = 4.405 hours to fill the pool working alone

Check....  (3/9.405) + (3/4.405) ≈ 1