Find the midpoint of the line between the points (1 , 4) and (2,5)

According to the Mid-Point theorem, the mid point of any two points is given by the equation: x = (x1 + y1) /2 and y = (y1+y2)/2 Here, x1= 1, y1 = 4, x2 = 2, y2= 5 Putting these values in the equation, x= (1+2)/2 = 3/2 = 1.5 y= (4+5) /2 = 9/2 = 4.5 So, the midpoint of the given coordinates is ( 1.5, 4.5)

Simplify sin@ ( csc@ - sin@)

Put csc@ = 1/sin@ sin@ ( csc@ - sin@) = sin@ ( 1/sin@ - sin@) = sin@*1/sin@ - sin@*sin@ .... Distribute the brackets = 1 - sin^2@ = cos^2@ ... since sin^2@+cos^2 @ =1 So 1 - sin^2@ = cos^2@

Which of the following equations has the same solution as 5 x + 3 = 2x − 1?

5x+3 = 2x - 1 5x-2x+3 = 2x-2x -1 ... Subtract 2x from both sides 3x+3 = -1 3x+3-3 = -1 - 3 ... Subtract 3 from both sides 3x = -4 3x/3 = - 4 /3 ..... Divide by 3 on both sides x= -4/3