The length of the hypotenuse of a right triangle is 157 units. the length of one leg of the triangle is 132. lara wrote the following step to find the length of the unknown leg:

length of the unknown leg = 1572 − 1322 = 24,649 − 17,424 = 7,225 units

which statement best explains whether lara's step is correct or incorrect?

a. it is correct because the length of the unknown side is the difference of the lengths of the sides.
b. it is correct because the length of the unknown side is the difference of the squares of the sides.
c. it is incorrect because the length of the unknown side is the square root of 42,073.
d. it is incorrect because the length of the unknown side is the square root of 7,225.

-4

step-by-step explanation:

(-4+8)=-(4-8)=-8+4=-4

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!