FREE POINTS Alright, there are no free points but you do get points if you answer this question

A small container and its lid are shown below.
A rectangular prism has a length of 4 centimeters, width of 8 centimeters, and height of 5 centimeters. A rectangular pyramid has a base of 4 centimeters by 8 centimeters and a height of 2 centimeters.

Which correctly describes the dimensions of the figures that make up the container and its lid?

A) a rectangular prism measuring 4 cm by 5 cm by 8 cm and a rectangular pyramid with the dimensions of 2 cm by 4 cm by 8 cm
B) a rectangular prism measuring 2 cm by 4 cm by 8 cm and a rectangular pyramid with the dimensions of 4 cm by 5 cm by 8 cm
C) a rectangular prism measuring 4 cm by 5 cm by 8 cm and a rectangular pyramid with the dimensions of 2 cm by 5 cm by 8 cm
D) a rectangular prism measuring 2 cm by 5 cm by 8 cm and a rectangular pyramid with the dimensions of 4 cm by 5 cm by 8 cm

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!

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

step-by-step explanation: