Select the correct answer for each statement.
will yield consecutive odd integers:
possible answers: k+10, k+12, k+14 or k+2, k+3, k+4
will yield consecutive integers:
possible answers: k+1, k+2, k+3 or k+6, k+8, k+10

k + 10 , k + 12 , k + 14 is correct statement for 1st.

k + 1 , k + 2 , k + 3 is correct statement for 2nd.

Step-by-step explanation:

Part 1).

We need to find statement which yield consecutive off integers.

k + 2 , k + 3 , k + 4 is incorrect as this will give consecutive integers.

We know that Consecutive odd integers have difference of 2.

So, k + 10 , k + 12 , k + 14 is correct statement.

Part 2).

We need to find statement which yield consecutive integers.

k + 6 , k + 8 , k + 10 is incorrect as this will give consecutive odd integers or even integers.

We know that Consecutive integers have difference of 1.

So, k + 1 , k + 2 , k + 3 is correct statement.

2.56 is the width of the garden

step-by-step explanation:

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!