Bronze is an alloy or mixture of the metals copper and tin. the properties of bronze depends on the percentage of copper in the mix. a chemist decides to study the properties of a given alloy of bronze as the proportion of copper is varied. she starts with 7 kg of bronze that contain 3.5 kg of copper and 3.5 kg of tin and either adds or removes copper. let f(x) be the percentage of copper in the mix if x kg of copper are add (x> 0) or removed (x< 0).
(
a. state the domain and range of f (assume that the chemist wants a non-negative amount of both copper and tin).
domain: range: what do each of the answers mean in the context of bronze?
the domain tells us the range tells us (
b. write a formula in terms of x for f(x). (
c. if the formula you found in part (
b. was not intended to represent the percentage of copper in an alloy of bronze, but instead simply defined an abstract mathematical function, what would be the domain and range of this function?
domain: range:

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

In which direction does the left side of the graph of this function point? a(x) = 3x - x2 + 4x - 2

Sanjay solved the equation below. which property did he use to determine that 7x+42=42 is equivalent to 7(x+6)=42 7x+42=42 7x=0 x=0