The difference between two positive rational numbers is 2/9 . The numerator of the first number is 4 times larger than the numerator of the second, and its denominator is 3 times larger. Find the largest of these rational numbers?

Express the following as a function of a single angle. cos(60) cos(-20) - sin(60) sin(-20)

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

Carl is hanging pictures in his home. there is a space on a wall that has a width of 4 feet. carl has pictures with different widths. which picture width would fit in the space on the wall? a. 46 inches b. 60 inches c. 50 inches d. 54 inches