Alexa is constructing a circle inscribed in a triangle. she has partially completed the construction as shown below.
what should be her next step in the construction?

a. connect vertex b to the arc marking to complete the angle bisector
b. use the compass to find the angle bisector for angle a
c. connect three arc markings together to form the triangle
d. use the arc markings to determine the radius to construct the circle

The next step is to use the compass to find the angle bisector for angle A.

Step-by-step explanation:

To construct a circle inscribed in a triangle we have following step of construction.

Step 1: To construct incenter.

Firstly, it is given that Alexa has partially completed the construction in which she constructs the angle bisector of B. Now, in order to construct incenter we need two angle bisectors and the intersection point of two angle bisector gives incenter.

Hence, her next step in the construction should be to draw one more angle bisector i.e use the compass to ind the angle bisector for angle A

8

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!