Ms. Omar runs the school tennis club. She has a bin of tennis balls and rackets For every 5 tennis balls in the bin, there are 3 tennis rackets. Draw a model to show the ratio of tennis balls to tennis rackets write the following ratios tennis balls to tennis rackets tennis balls to total pieces of tennis equipment

see the explanation

Step-by-step explanation:

Let

x ----> number of tennis balls

y ----> number of tennis rackets

Part 1) Write the following ratios tennis balls to tennis rackets

we know that

To find out the ratio of tennis balls to tennis rackets, divide the number of tennis ball by the number of tennis rackets

In this problem we have

so

That means

The number of tennis balls is three-fifths times the number of tennis rackets

see the attached figure to better understand the problem

Part 2) Write the following ratios tennis balls to total pieces of tennis equipment

we know that

To find out the ratio of tennis balls to total pieces of tennis equipment, divide the number of tennis ball by the total pieces of tennis equipment

we have

total pieces of tennis equipment=x+y

so

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

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!