Answer: The answer is ![\dfrac{5}{3}.](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B3%7D.)
Step-by-step explanation: Given that the co-ordinates of point G and H are (3, -1) and (-2, 3) respectively.
We are to find the y-value of the point P that is located at two-third distance from point G to point H.
As shown in the attached figure, the ration in which the point P divides the line segment GH is 2 : 1.
Therefore, the co-ordinates of point P will be
![\left(\dfrac{2\times (-2)+1\times 3}{2+1},\dfrac{2\times 3+1\times (-1)}{2+1}\right)\\\\\\=\left(\dfrac{-4+3}{3},\dfrac{6-1}{3}\right)\\\\=\left(\dfrac{-1}{3},\dfrac{5}{3}\right).](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B2%5Ctimes%20%28-2%29%2B1%5Ctimes%203%7D%7B2%2B1%7D%2C%5Cdfrac%7B2%5Ctimes%203%2B1%5Ctimes%20%28-1%29%7D%7B2%2B1%7D%5Cright%29%5C%5C%5C%5C%5C%5C%3D%5Cleft%28%5Cdfrac%7B-4%2B3%7D%7B3%7D%2C%5Cdfrac%7B6-1%7D%7B3%7D%5Cright%29%5C%5C%5C%5C%3D%5Cleft%28%5Cdfrac%7B-1%7D%7B3%7D%2C%5Cdfrac%7B5%7D%7B3%7D%5Cright%29.)
Thus, the y-value of the point P is ![\dfrac{5}{3}.](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B3%7D.)
Take L.H.S sin2A+sin2B/sin2A-sin2B
= sin2A+sin2B/sin2A-sin2B
Put
[sinC+sinD = 2sin(C+D)/2cos(C-D)/2]
[sinC-sinD = 2cos(C+D)/2.sin(C-D)/2]
= 2 sin(2A+2B)/2 cos(2A-2B)/2 / 2 cos(2A+2B) sin(2A-2B)
= sin(A+B).cos(A-B)/cos(A+B).sin(A-B)
= sin(A+B)/cos(A+B) . cos(A-B)/sin(A-B)
= tan(A+B).cot(A-B)
= tan(A+B).1/tan(A-B)
= tan(A+B)/tan(A-B)
∴ Hence we proved sin2A+sin2B/sin2A-sin2B=tan(A+B)/tan(A-B)
This will have no equal sign because that is what an expression is. The sentence translated into numbers is:
<h3>(x-10)(x)</h3>
Answer:
30 degrees
Step-by-step explanation:
A linear pair of angles add upto 180
So, y+150=180
y=180-150
=30
Answer:
x<1
x>6
Step-by-step explanation:
solve 2x+8<10:
2x+8<10
2x<2
x<1
solve 2x+8>20:
2x+8>20
2x>12
x>6