Finite Math Examples

$c (x) = 900 + 25 x$ , $r (x) = 100 x - x^{2}$

Step 1

Set up the composite result function.

$c (r (x))$

Step 2

Evaluate $c (100 x - x^{2})$ by substituting in the value of $r$ into $c$ .

$c (100 x - x^{2}) = 900 + 25 (100 x - x^{2})$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$c (100 x - x^{2}) = 900 + 25 (100 x) + 25 (- x^{2})$

Step 3.2

Multiply $100$ by $25$ .

$c (100 x - x^{2}) = 900 + 2500 x + 25 (- x^{2})$

Step 3.3

Multiply $- 1$ by $25$ .

$c (100 x - x^{2}) = 900 + 2500 x - 25 x^{2}$

Step 4

Simplify the expression.

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Step 4.1

Move $900$ .

$c (100 x - x^{2}) = 2500 x - 25 x^{2} + 900$

Step 4.2

Reorder $2500 x$ and $- 25 x^{2}$ .

$c (100 x - x^{2}) = - 25 x^{2} + 2500 x + 900$