Extra credit (turn in separately! ): find an equation for the plane that passes through the point (1; 2; 3) and cuts o the least volume in the rst octant (i. e., the part of r3 where all coordinates are non-negative). note: the volume of a pyramid is one third times the area of the base times the height. hint: it may be easiest to use the points of intersection of the plane with the three axes as the three variables. that is, assume the plane intersects the three axes at (a; 0; 0); (0; b; 0); (0; 0; c). 1

To which set of numbers does the number –5 belong? select all that apply. integers natural numbers rational numbers real numbers whole numbers

Iam a rectangle. my perimeter is 60 feet. how much are do i cover?

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