6x+12y-6z+7x7y-28z= 13x+19y-34z
Answer:
Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Step-by-step explanation:
Let tap B fills the pool alone in the time = x hours
So in one hour part of pool will be filled = 
Another tap A when turned on, it takes time to fill the pool = x-5 hours
So in one hour part of the same pool filled = 
Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.
Part of the pool filled in one hour by both the taps = 
Now we form an equation
Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on



3(x - 4) = x(x - 5)
x² -5x = 3x - 12
x² - 8x + 12 = 0
x² - 6x - 2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
(x -2)(x - 6) = 0
x = 2, 6 hours
We will take higher value of x as x = 6 hours for tap B.
Time taken by tap A = 6 - 4 = 2 hours.
Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Answer:
Lines stay parallel or overlap
Step-by-step explanation:
AB and CD are parallel lines
Rotation around a point 90 degrees clockwise will make these lines perpendicular to their initial position but AB and CD will still be parallel to each other
They will overlap if the distance between them and point E is equal
Their initial slope is same and equal to m
Their final slope will be -1/m as a result of 90 degrees rotation
80 degrees. 145 = (4x+5) + (6x-10) = 10x-5... so 10x = 150, x = 15. LMN = 6x-10 = 6(15) - 10 = 80.