3. Represents the sets with a Venn diagram: U = {1,2,3,4,5,6,7,8,9, 10, 11, 12} A = {1,2,3,4,6, 12} B = {1,2,4,8}
1 answer:
Answer:
See explanation and picture attached
Step-by-step explanation:
A set can be described by<em> listing all of its elements</em>.
For example, A = { 2, 4, 6, 8}, which we read as
“A is the set whose elements are 2, 4, 6 and 8”.
The four elements of the set are separated by commas, and the list is enclosed between curly brackets.
A <em>set can also be described by writing a description of its elements</em> between curly brackets.
Thus the set A above can also be written as
A = { even natural numbers less than 9 }, which we read as
“A is the set of even natural numbers less than 9”.
A set can also be described graphically by using Venn diagrams, which are simply circle shaped drawings showing the elements inside.
In our case U={1,2,3,4,5,6,7,8,9,10,11,12} A={1,2,3,4,6,12} B={1,2,4,8}
See picture attached for the answer.
You might be interested in
Answer:
length of chord is 6cm
Step-by-step explanation:
Here, we are to calculate the length of the chord.
It should be understood that the chord has a length of 0.8cm from the center of the circle of radius 3cm, thereby forming two right-angled triangles with the radius 3cm being the hypotenuse of each and 0.8cm being the height of each.
Now, the chord is divided into 2 by this height dropping from the center of the circle. To calculate the first half, we use Pythagoras’ theorem with 3cm being hypotenuse and 0.8cm being the other side.
mathematically;
3^2 = 0.8^2 + l^2
9 = 0.64 + l^2
l^2 = 9-0.64
l^2 = 8.36
l = √(8.36)
l = 2.89 approximately
The length of the chord would be 2l = 2 * 2.89 = 5.78 cm which is 6cm to the nearest length
Answer:
The solution to the system is the pair (9, 6)
Step-by-step explanation:
Hi!
First, let´s write the system of equations:
-y² + 6y + x -9 = 0
6y = x +27
The solutions of the system are the pairs (x, y) that satisfy both equations.
Let´s take the second equation and solve it for x:
6y = x +27
Subtract 27 from both sides of the equation
6y - 27 = x
Now, we can replace x in the first equation and solve it for y:
-y² + 6y + x -9 = 0
-y² + 6y + 6y - 27 -9 = 0
-y² + 12y - 36 = 0
Notice that -y² + 12y - 36 = -(y - 6)², then:
-(y - 6)² = 0
y - 6 = 0
y = 6
(alternatively you can solve the quadratic equation using the quadratic formula).
Now let´s find the value of x:
x = 6y -27
x = 6·6 -27
x = 9
The solution to the system is the pair (9, 6)
Please see the attached figure. The point where the curves intersect is the solution to the system.
