Angle mpn is an isosceles triangle m=3x+1 and n=x-11 what is the measure of angle p?

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.

The difference of three and the reciprocal of a number is equal to the quotient of 20 and the number. find the number.

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.