39. Folding paper. Each time you fold an ordinary sheet of paper in half, you double the thickness.

a. A single sheet of 20-pound bond paper is about a tenth of a millimeter

thick. How would you come up with this estimate? (Hint: Paper often

comes in reams of 500 pages.)

b. Find an exponential formula that gives the thickness of the sheet of paper

in part a after

f

folds in millimeters and in kilometers.

c. What would be the thickness in kilometers if you were physically able to

fold it 50 times? Note: For comparison, the distance from Earth to the Sun

is about

149,600,000

kilometers.

What is a graph with a never ending line called?

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

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