Alice, bob & charlie are in competition to buy the two identical ford cars on offer in their college campus. their private held evaluation of the car's value is $12k, $11k and $10.5k. we don't know the reservation price of the seller and so the value created/value gap, etc. can you still find the price? what has to be true for your price to be the correct estimate?

Two positive integers are 3 units apart on a number line. their product is 108. which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108

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

Juanita wade's new car has an msrp of $28,902.11 including title and processing fees. the premier package which includes surround sound and dvd player costs three times the amount of the in-style package which includes leather seats and select wheels. the total cost of her new car was $34,290.08 which included the 6.5% sales tax. find the cost of the premier package to the nearest cent.