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

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.