The points a(2,b) and b(4,10) lie on a line. the line x + 3y - 6=0 is perpendicular to this line. what is the value of b?

The value of b is 6

Step-by-step explanation:

Given as :

The points of line AB is A  = ( 2 , b)   and B = ( 4 , 10 )

So , Slop of this line is ( m 1) =

Or,                                 ( m 1) =

Or,                                  ( m 1) =

Again, Another line is

x + 3y = 6

Or, 3y = - x + 6

Or   y =   x +  

SO, Slope of this line is ( m 2 ) =

∵  Both lines are perpendicular to each other

Then , ( m 1) × ( m 2) = - 1

or,       ( m 1 ) ×   = - 1

So,     ( m 1 ) = 3

Now,   ∵ ( m 1) =

          ∴   3     =

Or,          10 - b = 6

∴                  b = 10 - 6 = 4

Hence The value of b is 6  Answer

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.