Adolphin is swimming to the surface of the ocean while at the same time a bird is flying towards the surface of the ocean. the function fx) models the position, in feet, of the dolphin x seconds after it starts swimming towards the surface. the function models the dolphin's position for the first 5 seconds the function g (x) models the position, in feet, of the bird x seconds after the bird begins flying towards the surface. the function models the bird's position for the first 5 seconds. a partial table of values for the two linear functions is shown. x f (x) g (x) 0.0-11 10 0.59 9 1.07 8 1.55 7 2.0 -3 6 2.5 -1 5 after how many seconds will the dolphin and bird be at the same position?

The dolphin and bird be at the same position will be at the same position after 3.5 seconds

Step-by-step explanation:

The general equation of a line is h(x) = m*x + b, where m is the slope and b is the y-axis interception. We can get m and b from data as follows. To get m, we need 2 points (x1,y1) and (x2, y2) and the next formula m = (y2 - y1)/(x2 - x1).  

For f(x), using (0.5, -9) and (0, -11)

m = (-9 - (-11))/(0.5 - 0) = 4

For g(x), using (0.5, 9) and (0, 10)  

m = (9 - 10)/(0.5 - 0) = -2

To get b, we need to see f(x) and g(x) values at x = 0. So, for f(x), b = -11 and for g(x), b = 10. Then,  

f(x) = 4*x - 11

g(x) = -2*x + 10

The dolphin and bird be at the same position when f(x) be equal to g(x). Mathematically :

f(x) = g(x)

4*x - 11 = -2*x + 10

4*x + 2*x = 10 + 11

6*x = 21

x = 21/6

x = 3.5 seconds

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.