CPhill

C = (5/9)(F-32)      multiply both sides by 9/5

(9/5)C =  F - 32     add32 to both sides

(9/5)C + 32   = F

Thanks, Hayley

Let 462 = 480

Let  77  = 80

So

480 / 80  = 6

Notice that 462 / 77  = 6 as well  !!!!!!

In this case, our estimate was spot on  !!!!

 About -62.2859°   =   about 297.7141°

1/2(-4+6x)=1/3x+2/3(x+9)     multiply through by the common denominator of 2 and 3  = 6

3(-4 + 6x)  = 2x  + 4(x + 9)      simplify

-12 + 18x  = 2x  + 4x  + 36

-12 + 18x  = 6x  + 36       add12 to both sides, subtract 6x from both sides

12x  = 48      divide both sides by 12

x = 4

Love that pic, Hayley....!!!

5sin70=7sinB    divide both sides by 7

(5/7)sin70  = sinB    take the sine inverse to find B

sin^-1 [ (5/7)sin70]  = B  = about 42.16°

Shades......see Melody's and my answers under your original post....

Show that replacing k with k + 1 in 1 - 1/2^k gives an expression equivalent to 1 - 1/2^k + 1/2^(k+1)

1  -  1/ [2^(k + 1)]  =

1 - 1 / [2^k * 2] =

1 - 1/2^k (1/2)  =

1 + (-1/2)(1/2^k) =                     [notice that  -1/2  =  -1  + 1/2]

1 + [ -1 + 1/2] [ 1/2^k]  =

1 - 1/2^k  + (1/2)(1/2^k)  =

1 - 1/2^k + 1 / [ 2^k *2]  =

1 - 1/2^k +  1/ 2^(k + 1)

Thanks, rarinstraw.....

If 1.2 is meant to be hours........this expression could also represent the distance that the car traveled in 1.2 hours