The coordinates of point M which divides the line segment having end points (1,-2) and (10,3) in 5:1 are (17/2,13/6).
Given that the end points of line segment are X(1,-2) and Y(10,3) and the ratio in which the line segment is being divided is 5:1.
Line segment is a collection of points which when together joined joins two points on a surface.
The coordinates of point dividing a line segment with end points 
and ratio m:ncan be calculated using the below given formula:
(X,Y)=
.
We have to just put the values in the above formula to get the coordinates.
(X,Y)=(5*10+1*1/5+1,5*3-2*1/5+1)
=(50+1/6,15-2/6)
=(51/6,13/6)
=(17/2,13/6)
Hence the coordinates of point M which divides the line segment having end points (1,-2) and (10,3) in 5:1 are (17/2,13/6).
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Answer: 3x-7y
Step-by-step explanation:
9x-6x=3x you can't do anything with the y
There are 4 elements in the set A and 8 elements in set B that is n(A) = 4 and n(B) = 8
<h3>Cardinality of a set</h3>
This is the total number of elements in a set. Given the following sets;
A = {c, d, e, f}
B = {odd numbers greater than 5 and less than 23}
B = {7,9,11,13, 15, 17, 19, 21}
Since there are 4 elements in the set A and 8 elements in set B hence n(A) = 4 and n(B) = 8
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The roots of 54 are: 1 and 54, 2 and 27, 3 and 18, 6 and 9, then it restarts all over again.
The two numbers have to multiply up to 54, and add up to 3. 9 and 6 have a difference of 3, and the multiplied sum is negative, so this is your pair.
9 and -6 fit this criteria, since they add up to 3 and multiply to 64.
Answer:
k = 1 + sqrt(7/2) or k = 1 - sqrt(7/2)
Step-by-step explanation:
Solve for k over the real numbers:
4 k - 10/k = 8
Bring 4 k - 10/k together using the common denominator k:
(2 (2 k^2 - 5))/k = 8
Multiply both sides by k:
2 (2 k^2 - 5) = 8 k
Expand out terms of the left hand side:
4 k^2 - 10 = 8 k
Subtract 8 k from both sides:
4 k^2 - 8 k - 10 = 0
Divide both sides by 4:
k^2 - 2 k - 5/2 = 0
Add 5/2 to both sides:
k^2 - 2 k = 5/2
Add 1 to both sides:
k^2 - 2 k + 1 = 7/2
Write the left hand side as a square:
(k - 1)^2 = 7/2
Take the square root of both sides:
k - 1 = sqrt(7/2) or k - 1 = -sqrt(7/2)
Add 1 to both sides:
k = 1 + sqrt(7/2) or k - 1 = -sqrt(7/2)
Add 1 to both sides:
Answer: k = 1 + sqrt(7/2) or k = 1 - sqrt(7/2)
