Grant reads a story about a turtle that swam 25 feet in 40 seconds. He assumes the time, t, that it takes the turtle to swim a distance of d feet is a proportional relationship Grant starts to create the table shown for other times and distances the turtle swims.
Enter the missing numbers in the table to represent the proportional relationship
Time
(seconds)
Distance
(feet)
1
10
30
40
25

Time(t)      Distance(d)

  1                   0.625

 16                   10

  30                  18.75

  40                  25

Step-by-step explanation:

We are given table values and they are in proportional relationship.

Time(t)      Distance(d)

  1                   a

  b                   10

  30                  c

  40                  25

Since they are in proportional relationship. Let's form a proportion and missing values (a, b , c) using t = 40 and d = 25.

Cross multiplying, we get

1(25) = a(40)

25 = 40a

a =  

a = 0.625

Now let's find b.

25b = 40(10)

25b = 400

Dividing both sides by 25, we get

b =  

The value of b = 16

Now let's find c.

30(25) = 40c

40c = 750

Dividing both sides by 40, we get

c =  

The value of c = 18.75

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!