The equation y = 0.4x2 + 2.04x + 50.07 models the number of Americans (in thousands) who are expected to be over 100 years old for selected years, x, starting at 2002. In what year will there be 158 Americans over the age of 100 years old?

2016

Step-by-step explanation:

Given the equation :

y = 0.4x2 + 2.04x + 50.07

y = number of Americans expected to be over 100 years

x = years starting from 2002

y = 158 ; calculate the year ;

158 = 0.4x2 + 2.04x + 50.07

0.4x2 + 2.04x + 50.07 - 158 = 0

0.4x2 + 2.04x - 107.93 = 0

Using a quadratic equation solver :

The roots obtained are :

-19.173 ; 14.073

X cannot be negative ; hence, x) 14.073

Hence, from the model, y = 158 after about 14 years ;

2002 + 14 = year 2016

60

step-by-step explanation:

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)