the new toaster division in the company has a production cost per toaster represented by $r(x)=\frac{350…

the new toaster division in the company has a production cost per toaster represented by $r(x)=\frac{350 - 3x}{x - 2}$. recall that your original divisions production - cost - per - toaster function is $p(x)=\frac{4x + 1400}{x}$. suppose both divisions make the same number of toasters weekly. then $t(x)=p(x)+r(x)$ would represent the production cost to make one toaster from each division. which of the following are correct expressions for $t(x)$? select all that apply.\n$square t(x)=\frac{350 - 3x}{x - 2}+\frac{4x + 1400}{x}$\n$square t(x)=\frac{(350 - 3x)+(4x + 1400)}{x(x - 2)}$\n$square t(x)=x + 1750$\n$square t(x)=\frac{x^{2}+1742x - 2800}{x(x - 2)}$\n$square t(x)=\frac{x(350 - 3x)+(x - 2)(4x + 1400)}{x(x - 2)}$

the new toaster division in the company has a production cost per toaster represented by $r(x)=\frac{350 - 3x}{x - 2}$. recall that your original divisions production - cost - per - toaster function is $p(x)=\frac{4x + 1400}{x}$. suppose both divisions make the same number of toasters weekly. then $t(x)=p(x)+r(x)$ would represent the production cost to make one toaster from each division. which of the following are correct expressions for $t(x)$? select all that apply.\n$square t(x)=\frac{350 - 3x}{x - 2}+\frac{4x + 1400}{x}$\n$square t(x)=\frac{(350 - 3x)+(4x + 1400)}{x(x - 2)}$\n$square t(x)=x + 1750$\n$square t(x)=\frac{x^{2}+1742x - 2800}{x(x - 2)}$\n$square t(x)=\frac{x(350 - 3x)+(x - 2)(4x + 1400)}{x(x - 2)}$

Answer

Answer:

  • A. $T(x)=\frac{350 - 3x}{x - 2}+\frac{4x + 1400}{x}$
  • D. $T(x)=\frac{x(350 - 3x)+(x - 2)(4x + 1400)}{x(x - 2)}$
  • E. $T(x)=\frac{x^{2}+1742x - 2800}{x(x - 2)}$

Explanation:

Step1: Write the formula for $T(x)$

$T(x)=P(x)+R(x)=\frac{350 - 3x}{x - 2}+\frac{4x + 1400}{x}$

Step2: Find a common - denominator

The common denominator of $x - 2$ and $x$ is $x(x - 2)$. So, $T(x)=\frac{x(350 - 3x)}{x(x - 2)}+\frac{(x - 2)(4x + 1400)}{x(x - 2)}=\frac{x(350 - 3x)+(x - 2)(4x + 1400)}{x(x - 2)}$

Step3: Expand the numerator

Expand $x(350 - 3x)+(x - 2)(4x + 1400)$: [ \begin{align*} x(350 - 3x)&=350x-3x^{2}\ (x - 2)(4x + 1400)&=4x^{2}+1400x-8x - 2800=4x^{2}+1392x - 2800 \end{align*} ] Combining them: $-3x^{2}+350x + 4x^{2}+1392x - 2800=x^{2}+1742x - 2800$. So $T(x)=\frac{x^{2}+1742x - 2800}{x(x - 2)}$