A beverage company has just completed brewing a large batch of tea ( 1500 gallons). They will add sweentening to the tea, then bottle it and prepare it for distribution. Suppose 10 gallons of corn syrup is added to the mixture as a sweetener. What is the ratio of tea to corn syrup in the mixture? what if 50 gallons of corn is added instead?200?
Define a function f whose input x is the amount of corn syrup added (in gallons) and whose output R is the ratio of tea to corn syrup in the mixture. What is the practical domain for this function?
what happens to R as x-- 0+? why does this make sense?

12/11c

or

12

c

11

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!

well we know there are 4 clubs in 52 cards so it’s replaced so it should be 3/51

step-by-step explanation:

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

happy to

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