The values of x and y that will make LMNO a parallelogram are: x = 9, y = 1.5.
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Properties of a Parallelogram</h3>
- The opposite sides of a parallelogram are parallel to each other and are also of equal lengths.
- Diagonals of a parallelogram are congruent to each other and also bisect each other into equal halves.
Therefore:
ON = LM
Substitute
7x - 5 = 6x + 4
Add like terms
7x - 6x = 5 + 4
x = 9
OL = NM
Substitute
8y + 3 = x + 6
Plug in the value of x
8y + 3 = 9 + 6
8y + 3 = 15
8y = 15 - 3
8y = 12
y = 12/8
y = 1.5
Therefore, the values of x and y that will make LMNO a parallelogram are: x = 9, y = 1.5.
Learn more about parallelogram on:
brainly.com/question/7200842
First find the x and y values because where the lines will intersect, they share the point of the intersection so they will share the x and y coordinates.
Rearrange equations
To cancel y, we must do equation 1 minus equation 2. Similarly:
So the x coordinate is 3.
The y coordinate can be found with substitution of x into one of the equations:
So where the two lines intersect is at the point (3, 7), which is the solution to the equations.
36 equally-likely outcome: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)
Solution:
Outcomes with first number being old number and second being even number: (1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6) = 9 outcomes
P(old,even) = 9/36 =1/4 = 0.25
There are (5 C 1) = 5! / (5 - 1)! = 5 ways of drawing a red marble, and (11 C 1) = 11! / (11 - 1)! = 11 ways of drawing any marble, so that the probability of drawing a red marble is 5/11.
After putting back the first marble, the probability of drawing another red is again 5/11.
So the probability of drawing 2 red marbles with replacement is (5/11)² = 25/121.
