1. A rectangle has an area given by A=x^2+5x+6. Find expressions for the possible lengths and width of the rectangle.

2. The profits of a company are found by subtracting the company's costs from it's revenue. If a company's cost can be modeled by 14x+120,000 and it's revenue can be modeled by 40x-0.000x^2, what is the expression for the profit?

Question

04-02-2018
Mathematics

contestada

1. A rectangle has an area given by A=x^2+5x+6. Find expressions for the possible lengths and width of the rectangle.

2. The profits of a company are found by subtracting the company's costs from it's revenue. If a company's cost can be modeled by 14x+120,000 and it's revenue can be modeled by 40x-0.000x^2, what is the expression for the profit?

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JaySL JaySL · Answer 1 · 2018-02-05T02:09:38+01:00

1. [tex]x^2+5x+6 = (x+3)(x+2)[/tex], which implies that the sides could be [tex]x+3[/tex] and [tex]x+2[/tex]. (There are theoretically an infinite number of side-lengths, though--in general, for any polynomial or reciprocal of a polynomial [tex]P(x)[/tex], [tex]\frac{x+3}{P(x)}[/tex] and [tex]P(x)(x+2)[/tex] is valid. However, the set provided makes the most sense.)

2. Profit is the difference between cost and revenue. For revenue, [tex]0.0000x^2 = 0[/tex], so revenue equals [tex]40x[/tex], so profit equals [tex]26x-120,000.[/tex]