Question

when you mix two colors of paint in equivalent ratios the resulting color is always the same. 1. how many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green explain or show your reasoning.2. make up a new pair of numbers that would make the same shade of green explain how you know they would make the same shade of green.3. what is the proportional relationship represented by the table?4. what is the constant of proportionality? What does it represent?

Answer 1

See explanation below

Step-by-step explanation:

1) let the number of cups of blue paint = x

the number of cups of yellow paint = y

Fromt the table, we have been frovided with data for both in the top part

when x = 2

y = 10

for the table to be proportional, we use the formula:

y = kx

where k = constant of proportionality

(2, 10) = (x, y)

10 = k(2)

k = 10/2

k = 5

For 2 cups of blue paint,

number of yellow paint to make green paint = 2 × 5 = 10

This means for 2 paint of blue, we need 10 paints of yellow

2) For one paint of blue, number of paint of green:

y = 5x

x = 1

y = 1 × 5 = 5

5 paints of yellow is needed

For a new pair, we can assign any number for x inorder to get value for y

if we use x = 5

y = 5x

y = 5 × 5 = 25

This means for 5 cups of blue paints, 25 cups of yellow paint is needed

The new pair (x, y) = (5, 25)

3) The proportional relationship represented by the table: y = 5x

4) since k is the constant of proportionality, the value of k we derived is 5

Hence, k = 5

k represents the constant value in the direct proportional relationship of x and y. It shows y is dependent on x. if x increses, y increases.