Renee is simplifying the expression (7) (13/29) (1/7).she recognizes that 7 and 1/7 are reciprocals, so she would like to find their product before she multiplies by 13/29. which property will allow renee to do this without changing the value of the expression

There's one important property which states that when a number is multiplied by its reciprocal, equals 1.

The commutative property of multiplication states that two or more numbers can be multiplied in any order, therefore, the expression:  (7)×(13/29)×(1/7) can be changed to  (7)×(1/7)×(13/29) and the result won't be altered.

Now, given that 7 and 1/7 are reciprocals, the result is 1. Therefore, the result of the multiplication equals (13/29)

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!