Consider the two expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$ a) show that the two expressions are equal to each other when $x=10.$ b) explain why these two expressions are not equal to each other when $x=-\dfrac12.$ c) show that these two expressions are equal to each other for all $x$ other than $-\dfrac12.$

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.