CPhill

w= the squar root of z^y

y=11+x

x=z-12

z=y-w+x

z also equals

600/30-50+y

w+x+y+z= 1200

This has no solution.....to see why......

y = 11 + x   → y =  11 + [ z - 12] → y =   z - 1 → y + 1 = z

But

z = 600/30 - 50 + y 

z = 20 - 50 + y

z  = -30 + y

z = y - 30

So

z = z   implies that

y + 1  = y - 30

But this is impossible......1 added to something can't equal the same thing as 30 subtracted from it......so, y has no definable real number value.......

The annual interest rate = (1.045)^2 - 1  = 1.092 - 1  = .092 = about 9.2%

C is the logical answer

The number of cubic ft =

pi (3/2)^2 * 2  = about 14.4 ft^3

Multiply this by 59  to get your answer

5x+2y= -8

Here's one method :

Let x = 0   ...so we have

5(0) + 2y = -8

0 + 2y = -8

2y = -8     divide both sides by 2

y = -4        so....we have the point (0, -4) on the graph

Next...let y = 0   and we have

5x + 2(0)  = -8

5x  = -8    divide both sides by -5

x = -8/5      so......the point  (-8/5, 0)  is also on the graph

Plot the two points  and draw a line through them......that's your graph....!!!

We need to find  the effective rate of monthly depreciation......we can do this,as follows :

(.88)^8  = (r)^(12*8)

(.88)^8  = r^(96)  take the log of both sides

log(.88)^8  = log (r)^96   and we can write

8log(.88) = 96 log (r)     divide both sides by 96

(1/12) log(.88)  = log r  

This says that

10^[(1/12) log(.88)]  = r = about .9894

So.....A would be correct, as Spawn said

Guest is correct....let's see how he/she arrived at that answer

Note :  the output [y]  changes by 2 every time the input [x] changes by 1

And the slope of a line = change in y  change in x =  2 / 1   = 2

So,  using  the form

y - y1  = 2 ( x - x1)       we can write an equation for this line

Let  (x1, y1)   =  any of the  ( Input, Output) values....I'll use the first one.... (0, 3)...so we have...

y - 3  = 2(x - 0)

y  - 3  = 2x          add 3 to both sides

y = 2x + 3

Just as "guest" said......

Thanks, Spawn....

( √2 , 1)  ( √3 , 2)

Distance

sqrt [ ( √3 - √2)^2  + (2 -1)^2 ]  =

Notice,Spawn    ( √3 - √2)^2   =   ( √3 - √2) * ( √3 - √2)  =

√3*√3 - 2√3*√2  + √2 *√2    =

3   - 2√6  + 2 

So we have.....

sqrt [ 3 - 2√6 + 2 + 1 ]  =

sqrt  [ 6 - 2√6 ]  =  about  1.049 units

Midpoint

 [ ( √3 + √2 ) / 2  ,  (2 + 1) / 2 ]  =

[ ( √3 + √2 ) / 2 ,  3 / 2 ]      [this is exact, Spawn ...!!!  ]

( √2 , 1)  ( √3 , 2)

Distance

sqrt [ ( √3 - √2)^2  + (2 -1)^2 ]  =

sqrt [ 3 - 2√6 + 2 + 1 ]  =

sqrt  [ 6 - 2√6 ]  =  about  1.049 units

Midpoint

 [ ( √3 + √2 ) / 2  ,  (2 + 1) / 2 ]  =

[ ( √3 + √2 ) / 2 ,  3 / 2 ]      [this is exact, Spawn ...!!!  ]