(MARKING BRAINLIEST) For Alexandra's lemonade recipe, 8 lemons are required to make 4 cups of lemonade. Fill out a table of equivalent ratios and plot the points on the coordinate axes
provided.

2 1

8 4

10 5

Step-by-step explanation:

We already know that it takes 8 lemons to make 4 cups of lemonade. So, to get the number of lemons needed to make 1 cup of lemonade, we divide the lemons and cups by 4.

8 divided by 4 = 2 and  4 divided by 4 = 1. Therefore, it takes 2 lemons to make 1 cup of lemonade.

By this logic, to figure how many cups are needed for 10 lemons, and since we know 2 lemons = 1 cup of lemonade, we multiply the lemons and cups by 5. 2 times 5 is 10 (lemons) and 1 times 5 is 5 (cups). Therefore, 10 lemons are needed to make 5 cups of lemonade.

To plot this on the coordinate axes, the first point goes (2,1) second being (8,4) and third point being (10,5).

side note - is this delta math? I feel your pain

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!

x equals 1

step-by-step explanation:

f(4)=f(×)

x=1