Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. ronald is preparing lemonade for his friends. to make 6 cups of lemonade, he needs 1 cup of lemon juice. to make 24 cups of lemonade, he needs to proportionally increase the amount of lemon juice to cups.

   4 cups

Step-by-step explanation:

Given the proportion

  6 cups lemonade : 1 cup lemon juice

you can multiply each number by 4 to see the required amount of lemon juice:

  24 cups lemonade : 4 cups lemon juice

___

You know this because you know that 24 is 4 times 6.

As an equation

You can let J stand for the number of cups of lemon juice required, and you can write the proportional relationship as ...

  (J cups of juice)/(24 cups of lemonade) = (1 cup of juice)/(6 cups of lemonade)

Multiplying by (24 cups of lemonade) gives ...

  (J cups of juice) = (1 cup of juice)·(24/6) = 4 cups of juice

He will need 4 cups juice

Step-by-step explanation:

We can use proportions to solve this problem.

cups of lemonade on top, lemon juice on the bottom

6 cups lemonade           24 cups lemonade

=

1 cup juice                 x cups juice

Using cross products

6x = 24

Divide by 6 on each side

6x/6 = 24/6

x = 4

He will need 4 cups juice

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.