A barge must carry steel pieces for a construction project such that the total weight of the steel pieces is under 1,500,000 kilograms (kg). Each steel piece is either a beam, which weighs 363kg or a connector plate, which weights 6kg. There must be at least 2 connector plates for each beam. If b is the number of beams and c is the number of connector plates, which of the following systems of inequalities must be true? a. 363 +6c < 1,500,000
b <= 2c
b. 363 +6c >= 1,500,000
2b <= c
c. 363b + 6c >= 1,500,000
b >= 2c
d. 363b + 6c >= 1,500,000
2b >= c

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: idk

step-by-step explanation:

step-by-step explanation:

the true ones are a b and d

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: