The function f(x)equalsx squared plus 3 x minus 10 models the area of a rectangle.

a. Describe the length and width of the rectangle in terms of x.

b. What is a reasonable domain and range for the situation? Explain.

Step-by-step explanation:

The function f(x)equalsx squared plus 3 x minus 10 models the area of a rectangle.

factor the right side of the expression to find length and width

product is -10

and sum is +3

Area of the rectangle is f(x)

Area = length times width

Length is x+5

width is x-2

the value of x  cannot be negative

width is x-2, so x should be greater than 2

Domain is x>2

range is all positive values of y that is area

so range is f(x)>0

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft