After simplification, the value of 1-2/1(1+2)-3/(1+2)(1+2+3)-4/(1+2+3) (1+2+3+4)-...-100/(1+2+...+99)(1+2+ ...+100) is a proper fraction in its lowest form. Find the difference of its numerator and denominator.

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

If the tip varies directly with the number of guest which equation represents between the tip,t, and the number of guest,g?

Yolanda wanted to buy a total of 6 pounds of mixed nuts and dried fruit for a party she paid 21.60 for mixed nuts and 11.90 for dried fruit did yolanda but enough mixed nuts and dried fruit for the party