Carrie is considering three different types of materials for her chairs. Depending on the price she sets for each chair, the costs and revenues for each type of material will generate different costs and revenues for her business. In the functions in the table, x is the price of each chair. The functions give the revenue (R) and costs (C) that Carrie’s business can expect in a year at a given price for the item. Use graphing tools to examine the graphs for each set of equations. Then select the correct answer from each drop-down menu.

Material 1 Material 2 Material 3
R(x) = 200,000x - 2,000x2 R(x) = 160,000x - 1,000x2 R(x) = 54,000x - 270x2
C(x) = 5,000,000 - 20,000x C(x) = 4,000,000 - 10,000x C(x) = 2,000,000 - 5,000x

Material (1 2 3) can deliver the highest profit of about ($500,000 $2,055,000 $3,225,000 $4,125, 000)
.

Material (1 2 3) earns profit for the widest range of prices.

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graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

the answer is a.

step-by-step explanation:

in three games of golf, alex shot two under par four times.

explanation:

step-by-step explanation:

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answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)