The first triangle is dilated to form the second triangle select true or false for each statement a: the scale factor is 0.625 true or false? b: the scale factor is 1.6 true or false? ?

Part A) Is False

Part B) Is True

Step-by-step explanation:

we know that

the scale factor is equal to divide the length of the corresponding side of the second triangle by the length of the corresponding side of the first triangle

Let

z-----> the scale factor

x-----> the length side of the second triangle

y------> the length side of the first triangle

so

In this problem we have

substitute

------> is an enlargement

Verify the statements

Part A) the scale factor is

The statement is false, because the scale factor is

Part B) the scale factor is

The statement is True -----> see the procedure

answer: 12

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!