A manufacturing company has determined that the cost of labor for producing x transmissions is:

L(x) = 0.3x^2 + 400x + 550 dollars,
while the cost of materials is
M(x) = 0.1x^2 + 50x + 800 dollars.

Need to write a polynomial T(x) that represents the total cost of materials and labor for producing x transmissions.

Need to evaluate the total cost of polynomial for x=500

Need to find the cost of labor for 500 transmissions and the cost of materials for 500 transmissions.

(Any help would greatly be appreciated. I really don't understand any of this)

To find the polynomial T(x) that represents the total cost of materials and labor for producing x transmissions, you simply need to add the cost of labor (L(x)) and the cost of materials (M(x)).

So, T(x) = L(x) + M(x)

Substituting the given expressions for L(x) and M(x):

T(x) = (0.3x^2 + 400x + 550) + (0.1x^2 + 50x + 800)

Combining like terms:

T(x) = 0.4x^2 + 450x + 1350

To evaluate the total cost of the polynomial T(x) for x = 500, substitute x = 500 into the equation:

T(500) = 0.4(500)^2 + 450(500) + 1350

Simplifying the expression:

T(500) = 0.4(250000) + 225000 + 1350

T(500) = 100000 + 225000 + 1350

T(500) = 326350 dollars

Therefore, the total cost of producing 500 transmissions is 326350 dollars.

To find the cost of labor for 500 transmissions, substitute x = 500 into the equation for the cost of labor (L(x)):

L(500) = 0.3(500)^2 + 400(500) + 550

Simplifying the expression:

L(500) = 0.3(250000) + 200000 + 550

L(500) = 75000 + 200000 + 550

L(500) = 275550 dollars

Therefore, the cost of labor for producing 500 transmissions is 275550 dollars.

To find the cost of materials for 500 transmissions, substitute x = 500 into the equation for the cost of materials (M(x)):

M(500) = 0.1(500)^2 + 50(500) + 800

Simplifying the expression:

M(500) = 0.1(250000) + 25000 + 800

M(500) = 25000 + 25000 + 800

M(500) = 50800 dollars

Therefore, the cost of materials for producing 500 transmissions is 50800 dollars.