The result is: {5,6,9}
Step-by-step explanation:
Given
U = {0,1,2,......,10}
A = {5,6,9}
B = {0, 6, 7, 10}
We have to find
(A∩B)U(A∩B')
First of all,
<u>B':</u>
B' = U -B = {0,1,2,......,10} - {0, 6, 7, 10}
= {1,2,3,4,5,8,9}
<u>A∩B':</u>
A∩B' = {5,6,9} ∩ {1,2,3,4,5,8,9}
= {5,9}
<u>A∩B:</u>
A∩B = {5,6,9} ∩ {0, 6, 7, 10}
={6}
At the end we have to find union
(A∩B)U(A∩B') = {6} U {5,9}
(A∩B)U(A∩B') = {5,6,9}
Hence,
The result is: {5,6,9}
Keywords: Sets , Union
Learn more about sets at:
#LearnwithBrainly
145 blue paint are needed to make 28 pints of green paint
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0
As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81
Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2
So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2
A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.
3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.
So 2k^2 = 9 + 3k have two rational solutions (Option B).
Hope this Helps! :)
Answer:
l
Step-by-step explanation:
Answer:
Area of the wall to be painted = (11x² + 12x) square units
Step-by-step explanation:
The figure that should be attached to this question is missing. The figure was obtained and is attached to this solution provided.
From the image attached, it is given that the dimension of the rectangular wall to be painted is (4x+3) by (4x), the dimensions of the window is (2x) by (x) and the dimensions of the door is (x) by (3x).
Since, the window space and the door space cannot be painted along with the wall, the Area of the rectangular wall that will be painted will be given by the expression
(Total Area of the rectangular wall) - [(Area of window space) + (Area of door space)]
Area of a rectangular figure = Length × Breadth
Total area of rectangular wall = (4x+3) × 4x = (16x² + 12x) square units
Area of window space = (2x) × (x) = (2x²) square units
Area of door space = (x) × (3x) = (3x²) square units
Area of the wall to be painted = (16x² + 12x) - (2x² + 3x²)
= 16x² + 12x - 5x²
= (11x² + 12x) square units
Hope this Helps!!!
