CPhill

x+y=9 y=2x

Subbing the second equation into the first for y, we have

x + (2x)  = 9    simplify

3x = 9             divide by 3 on both sides

x = 3

And y = 2x  = 2(3)  = 6

So....our solution is

(3, 6)

y = x + 3

y - 3 = x

In the second equation we can rearrange it as 

y = x + 3

This is the same as the first equation........so we have infinite solurions on this line

The total outcomes possible = C(9,2)  = 36

But, we're just interested in choosing 2 of the 3 dimes = C(3, 2)  = 3

So....the probability  is 3 / 36  =  1 / 12    =  8.33 %

15.6%  = .156

So

.156N = 13   divide both sides by .156

N = 13/ .156  = 83 1/3

400 = e^(3t)   take the ln of each side

ln 400  = ln e^(3t)    and we can write

ln 400 = (3t) ln e       and ln e = 1  so we can disregard this.....so we have

ln 400 = 3t      divide both sides by 3

ln 400 / 3  = t = about 1.997

Let x be each side of the fountain....so we have

L x W = 700

(x + 7)(x + 7)  = 700  simplify

x^2 + 14x + 49 = 700

x^2 + 14x - 651  = 0

Using the on-site solver, we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{651}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}{\mathtt{\,-\,}}{\mathtt{7}}\\
{\mathtt{x}} = {\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}{\mathtt{\,-\,}}{\mathtt{7}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{33.457\: \!513\: \!110\: \!645\: \!905\: \!9}}\\
{\mathtt{x}} = {\mathtt{19.457\: \!513\: \!110\: \!645\: \!905\: \!9}}\\
\end{array} \right\}$$

So...each side of the fountain is about 19.46 ft

And the area is (19.46)^2  = 378.7 sq ft

10^100

In other words......1 followed by 100 zeroes.....

N/6 + 8 - 3  = 7   simplify

N/6 + 5 = 7      subtract 5 from both sides

N/6  = 2           multiply both sides by 6

N = 12    .....and that's the number