What is the relationship between the following two sequences? Sequence 1: 0, 1, 2, 3, 4, 5,…
Sequence 2: 0, 6, 12, 18, 24, 30,…
The terms of Sequence 2 are six times as large as the terms of Sequence 1.
The terms in Sequence 2 are three times as large as the terms in Sequence 1.
The terms in sequence 2 are half as large as the terms in sequence 1.
The terms in Sequence 2 are twice as large as the terms in sequence 1.

The 1st option

Step-by-step explanation:

Notice in sequence 1, it is 1,6; 2,12

That is sequence 1 * 6 = sequence 2.

Hope this helps! Have a nice day!

40 minutes

step-by-step explanation:

add the time and multiply by 2

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!