Kayla has n marbles. she groups them by three and has one left over. she groups them by sevens and has four left over. kayla has more than five marbles. what is the least number of marbles kyla could have?

Given that (x-3) is a factor of f(x)=x^3+ax^2-x-6, find a and hence the number of real roots or the equation f(x)=0

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

Carson has only $20 bills and $10 bill in her wallet. the total value of the bills is $50. she has 1 more $20 bill than $10 bills. how many each kind of bill does carson have? a. one $20 and two $10 bills b. two $20 bills and one $10 bill c. one $20 bills and three $10 bills d. two $20 bills and two $10 bills