The floor of a storage unit is 8 meters long and 15 meters wide. what is the distance between two opposite corners of the floor?

17m

Step-by-step explanation:

Draw a picture for the situation:

  15m

  |                                                     |

b |                                                     |  8m

  ||

                             a

We can assume the floor is a rectangle. Cut the triangle diagonally in half.

The rectangles has all right angles and is composed of two right triangles.

Use the Pythagorean formula and solve for the length of the hypotenuse to find the distance between two the opposite corners. I labelled two of the sides a and b.

The formula is: a² + b² = c² , where c is the distance. Substitute the side lengths a and b and solve for c.

a² + b² = c²

15² + 8² = c²

Simplify:

225 + 64 = c²

c² = 289

c = √289

c = 17

The distance between two opposite corners on the floor is 17 metres.

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!