Point C is on line segment \overline{BD} BD
. Given CD=2x, CD=2x, BD=3x+4,BD=3x+4, and BC=2x-1,BC=2x−1, determine the numerical length of \overline{BD}.
BD
.

the numerical length of segment BD is = 19

Step-by-step explanation:

Given the information that point C is on the segment BD, and understanding that the total segment BD must equal the addition of the two parts on which it is divided by point C, we write the following equation:

BD = BC + CD

now we replace each of the above by their expression in x:

( 3 x + 4 ) = (2 x - 1 ) + (2 x)

and we solve for x in this equation:

3 x + 4 = 2 x + 2 x - 1

3 x +4 = 4 x - 1

4 + 1 = 4 x - 3 x

5 = x

Therefore, we can now obtain the length of segment BD:

BD = 3 x + 4 = 3 (5) + 4 = 15 + 4 = 19

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!

ur mom

step-by-step explanation: