Question

the function f x =x2 +3x-10 models the area of a rectangle. a: describe the length and width of the rectangle in terms of x b: what is a rectangle in terms of x

Answer 1

A .$Length = x+5\\breadth = x-2$

B. domain of $f(x)= x^2+3x-10$ here is all values of x > 2 .

Step-by-step explanation:

Correct question is : the function $f(x)= x^2+3x-10$models the area of a rectangle. a: describe the length and width of the rectangle in terms of x b: what is a domain for above function in relation to rectangle . Let's solve:

a: describe the length and width of the rectangle in terms of x

Let's factorise $f(x)= x^2+3x-10$ :

⇒ $f(x)= x^2+5x-2x-10$

⇒ $f(x)= x(x+5)-2(x+5)$

⇒ $f(x)= (x+5)(x-2)$

Since , ⇒ $f(x)=length(breadth)$ So

$Length = x+5\\breadth = x-2$ .

b: what is a domain for above function in relation to rectangle

Since area is always > 0 , and (length , breadth)>0 So,

⇒ $f(x)= (x+5)(x-2)>0\\x>0 \\x>2$ Therefore, domain of $f(x)= x^2+3x-10$ here is all values of x > 2 .