Claire and richard are both artists who use square canvases. claire
uses the polynomial 50%? + 250 to decide how much to charge for her paintings
and richard uses the polynomial 40x² + 350 to decide how much to charge for
his paintings. in each polynomial, x is the height of the painting in feet.
a. how much does claire charge for a 20-foot-tall painting?
b. how much does richard charge for a 15-foot-tall painting?
c. to the nearest tenth, for what height will both claire and richard charge
the same amount for a painting? explain how to find the answer.
d. when both claire and richard charge the same amount for a painting,
how much does each charge?

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

(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: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

47 - 90 = 43

43 - 180 = x

x = 137