A heavy rope must be pulled onto the roof of a tall building. Each foot of rope weighs 3 pounds, and the rope is 20 feet long. At the start of the job, moving the rope by pulling it up requires 60 pounds of force. In the middle of the job, 10 feet of the rope is resting on the roof, and only 10 feet of rope must be lifted. Now, 30 pounds of force is required to move the second half of the rope by pulling it up. The force needed to pull the whole rope onto the roof is a variable force. Which equation r( x ) could describe the variable force needed to move the rope by pulling it up? The variable x represents the feet of rope that have already been lifted on to the roof.
Note, r (x) also describes the weight of the portion of rope that must still be lifted, when x feet of rope have already been lifted on to the roof.
a. r(x) = 3x
b. r(x) = 20x
c. r(x) = 3 (20 – x)

What additional information could be used to prove abc =mqr using sas? check all that apply.

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

Isaac wants the equation below to have no solution when the missing number is placed in the box. which number should he place in the box?