Answer:
2 hours
Step-by-step explanation:
first tap= 3hours
therefore work done is = 1/3
second tap= 6hours
therefore work done = 1/6
so, 1/3+ 1/6
=2/6 + 1/6
=3/6
=1/2
=2/1 hours
=2 hours
Answer:
140
Step-by-step explanation:
We have been given two fractions 
and 
. We are asked to find the least common denominator of both fractions.
To find the least common denominator of both fractions, we will find least common multiple of 20 and 28.
Prime factorization of 20: 
Prime factorization of 28: 
Least common multiple of 20 and 28 would be: 
.
Therefore, the least common denominator of both fractions would be 140.
AE = AC = 4
m<CAB = 60 (equilateral triangle)
m<CAE = 90 (square)
m<BAE = 150 (= 60 + 90)
Triangle BAE is isosceles since AB = AE;
therefore, m<AEB = m<ABE.
m<AEB + m<ABE + m<BAE = 180
m<AEB + m< ABE + 150 = 180
m<AEB + m<AEB = 30
m<AEB = 15
In triangle ABE, we know AE = AB = 4;
we also know m<BAE = 150, and m<AEB = 15.
We can use the law of sines to find BE.
BE/(sin 150) = 4/(sin 15)
BE = (4 sin 150)/(sin 15)
BE = 7.727
Answer:
p² -16pq + 36q²
Step-by-step explanation:
Given
(- 
p + 6q)²
= (- p + 6q)(- p + 6q)
Each term in the second factor is multiplied by each term in the first factor, that is
- p(- p + 6q) + 6q(- p + 6q)
= p² - 8pq - 8pq + 36q² ← collect like terms
= p² - 16pq + 36q²
So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter
Hope this helped!
