For what value of c does the following system have no solution?

1/2x+1/5y=2
5x+2y=c

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

Thanh and her crew are building a stage in the shape of a trapezoid for an upcoming festival. the lengths of the parallel sides of the trapezoid are 14 ft and 24 ft. the height of the trapezoid is 12 ft.what is the area of the stage? enter your answer in the box. ft²

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle