The total amount spent by some number of people on clothing and footwear in the years 2000-2009 can be modeled by the quadratic function f(x)equalsminus4.182xsquaredplus72. 85xplus96.42, where xequals0 represents january 1, 2000, xequals1 represents january 1, 2001, and so on, and f(x) is in billions of dollars. according to the model, in what year during this period was the amount spent on clothing and footwear a maximum?

This means that in the year 2008 the amount spent on clothing and footwear was a maximum.

Step-by-step explanation:

The quadratic function given is:

This is a quadratic function in the following format:

When , as in this problem, the vortex is a maximum.

The vortex of the function is the point , in which

According to the model, in what year during this period was the amount spent on clothing and footwear a maximum?

The year is x in the function. The year in which the amount spent is a maximum is 2000(the initial year) added to

In our secod order function, we have that . So

2000 + 8.71 = 2008.71.

This means that in the year 2008 the amount spent on clothing and footwear was a maximum.

option (a)

step-by-step explanation:

step 1:   take 2 number whose product equal to 25..

and sum of those two number are -10

step: 2 for example here if we take 5,5 are the number,,

5*5=25

and

5+5=10

but we need -10

so if we take   -5,-5

so -5*-5=25

and -5+(-5)=-10

s0

come the equation

replace -10x by these number

like -5x -5x+25

take common

x(x-5)-5(x-5)=0

(x-5)(x-5)=0