This table shows a proportional relationship between the number of cups of lemonade and strawberry juice used for strawberry lemonade.
Cups of
Lemonade
Cups of
Strawberry
juice
1
3
4
12
21
Enter the number of cups of lemonade used for 1 cup of strawberry juice.
cups

number of cups of lemonade used = 1/3 cups

Step-by-step explanation:

number of cups of lemonade : strawberry juice

= 1 : 3

Enter the number of cups of lemonade used for 1 cup of strawberry juice.

Let

x = number of cups of lemonade used

number of cups of lemonade : strawberry juice

= x : 1

Equate both ratios to get x

1 : 3 = x : 1

1/3 = x / 1

Cross product

1*1 = 3 * x

1 = 3x

Divide both sides by 3

x = 1/3 cu

number of cups of lemonade used = 1/3 cups

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3