Pablo and Johanna have to do a yearlong study for their biology course. After some discussion, they decide to try comparing their dogs and the diet that they feed them. Each has a dog from the pound, and both dogs are less than one year old. Pablo feeds his shepherd-mix dog a special diet of wet and dry foods from the local vet, while Johanna uses generic dry kibble from the supermarket for her bulldog. They want to see which diet results in bigger, healthier, faster-growing dogs. According to the information given, one dependent variable in this study will be .

a. the age of the dogs
b. the sex of the dogs
c. the type of food the dogs receive
d. how much the dogs grow
e. the breed of the dogs

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

The length of a rectangle is 5 times the width. if the perimeter is to be greater than 36 meters. what are the possible values for the width?

An angle bisector ac divides a trapezoid abcd into two similar triangles ? abc and ? acd. find the perimeter of this trapezoid if the leg ab=9 cm and the leg cd=12 cm.