Asnack company makes three batches of a nut mix using the recipe shown.

each batch contains a different total amount of mix.

drag numbers to show how much of each type of nut should be used in each batch.
plz

how much of each type of nut should be used in each batch.

1/3 of the mix is almonds

1/6 is pistachios

1/2 is cashews

the first batch is

P.1cup

A.2cup

C.?

Batch 2 is

P.?

A.2/3

C.1

the Third batch is

P.4/6

A.?

C.?

The answers are Batch 1:  3 cups cashews; Batch 2:  1/3 cup pistachios; Batch 3:  4/3 cups almonds and 2 cups cashews

Step-by-step explanation:

Let’s represent the total amount of mix with y

Batch 1

Since the amount of pistachios is 1/6 of the total and that is 1 cup which gives us

1/6y = 1

The next step is to multiply both sides by 6:

1/6y(6) = 1(6)

y = 6

We have 6 cups total.  1/2 of the mix is cashews which mean 1/2(6) = 3 cups is cashews.

Batch 2

Since the amount of almonds is 1/3 of the total and that is 2/3 of a cup which gives us

1/3y = 2/3

The next step is to multiply both sides by 3:

1/3y(3) = 2/3(3)

y = 6/3 = 2

There are 2 cups of mix total.

1/6 of the mix is pistachios; this gives us 1/6(2) = 2/6 = 1/3 cup pistachios.

Batch 3

Since the amount of pistachios is 1/6 of the total mix and that is 4/6 of a cup which means

1/6y = 4/6

The next step is to multiply both sides by 6:

1/6y(6) = 4/6(6)

y= 24/6 = 4

Since there are 4 cups of mix total, we have  

1/3 of the mix is almonds which gives us 1/3(4) = 4/3 cups almonds.  

1/2 of the mix is cashews which gives us 1/2(4) = 2 cups cashews.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7

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!