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The cost of producing [tex]\( x \)[/tex] soccer balls in thousands of dollars is represented by [tex]\( h(x) = 5x + 6 \)[/tex]. The revenue is represented by [tex]\( k(x) = 9x - 2 \)[/tex].

Which expression represents the profit, [tex]\( (k - h)(x) \)[/tex], of producing soccer balls?

A. [tex]\( 14x - 8 \)[/tex]

B. [tex]\( 14x + 4 \)[/tex]

C. [tex]\( 4x - 8 \)[/tex]

D. [tex]\( 4x + 4 \)[/tex]

Sagot :

GinnyAnswer
To determine the profit function, we start by understanding the given cost and revenue functions.

The cost function [tex]\( h(x) \)[/tex] is defined as:
[tex]\[ h(x) = 5x + 6 \][/tex]

The revenue function [tex]\( k(x) \)[/tex] is defined as:
[tex]\[ k(x) = 9x - 2 \][/tex]

The profit function [tex]\( (k - h)(x) \)[/tex] is derived by subtracting the cost function from the revenue function:
[tex]\[ (k - h)(x) = k(x) - h(x) \][/tex]

Now, substitute the expressions for [tex]\( k(x) \)[/tex] and [tex]\( h(x) \)[/tex]:
[tex]\[ (k - h)(x) = (9x - 2) - (5x + 6) \][/tex]

Next, distribute the subtraction:
[tex]\[ (k - h)(x) = 9x - 2 - 5x - 6 \][/tex]

Combine like terms:
[tex]\[ (k - h)(x) = 9x - 5x - 2 - 6 \][/tex]
[tex]\[ (k - h)(x) = 4x - 8 \][/tex]

Thus, the expression that represents the profit function is:
[tex]\[ 4x - 8 \][/tex]

So, the correct answer is:
[tex]\[ \boxed{4x - 8} \][/tex]
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