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.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

read more on -

step-by-step explanation:

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)