CPhill

Let  H  be the height of the flagpole  and B the height of the building

And we have that

tan (28)  = B / 100  →   100 tan (28)   = B      (1)

tan (39.75)  =   ( B + H) / 100   →   100 tan (39.75)  =  B + H     (2)

Sub (1)  into (2)

100 tan (39.75)  =    100 tan (28)  + H        rearrange

100 tan (39.75)   -  100 tan (28)   =   H

100 (tan (39.75)  - tan (28) )   =  H  ≈  30 ft

Answered here :  https://web2.0calc.com/questions/math_75712

1/8 of a lawn  in 1/4 hour

Multiply both by 8

1 whole lawn  in 2 hrs

2 (2.50)  + 1 (4.00)  + B (4.00)  =  25.00

Where B is the number of bags of chips

A  =   10 * 3ⁿ       Where A  is the amount of money in the account after  n  months

23 + 2/9   =  209 / 9

209 / 9   *  9  =

(209 / 9)  * ( 9 / 1)  =

(209 / 1)  * (9 / 9)  =

209  * 1    =

209

(5/3)  / 3   =

(5/3)  / (3/1)     invert the second fraction and multiply

(5/3) * (1/3)   =

5 / 9

 6 / 2(1+2)

By the order of operations......the division  of 6 / 2    occurs first.....= 3

So

3 ( 1 + 2)   =

3 ( 3)   = 9

But

6 / [  2 ( 1 + 2) ]   =

6 /  [  2 (3) ]  =

6 / 6  =   

1

This points up the importance of parentheses.............and the lack of their use often changes the nature of the problem.....!!!!!!

25 feet  

1 ft  =  12 inches

So

25 ft  x  12 inches / ft  =   300  inches

One of our regulars, hectictar, pointed out to me that this might be :

(3 x + 7)  / (x + 7)      if so, we have

               3

x + 7   [   3x +  7   ]

               3x  + 21 ]

              ________

                      -14

The result is   3  + [ -14 / ( x + 7) ]

Thanks , hectictar  !!!!!