a map has a scale of 5 cm represents 3 km. Wich proportion would not allow you to find the actual distance between 2 cities if they are 7 cm apart on the map?

What are your choices?

To answer this question, we need to understand how the scale on a map works. The scale tells us the relationship between the distances on the map and the actual distances on the ground.

In the given map, we have a scale of 5 centimeters represents 3 kilometers. This means that for every 5 centimeters on the map, the corresponding actual distance on the ground is 3 kilometers.

Now, let's set up a proportion to find the actual distance between the two cities if they are 7 centimeters apart on the map. We can use the following proportion:

(Actual Distance)/(Map Distance) = (Scale of Map)/(Scale of Map)

Let's substitute the values we have:

(Actual Distance)/(7 cm) = (3 km)/(5 cm)

To find the actual distance, we can cross-multiply and solve for the variable:

Actual Distance = (7 cm)(3 km) / 5 cm

Simplifying this expression, we get:

Actual Distance = 21 km / 5

Calculating this division, the actual distance between the two cities is approximately 4.2 kilometers.

Now, let's analyze the proportions that would not allow us to find the actual distance:

1. (Actual Distance)/(7 cm) = (5 cm)/(3 km)
This proportion is incorrect because it swaps the positions of the map distance and the scale of the map.

2. (Actual Distance)/(7 cm) = (3 km)/(5 km)
This proportion is incorrect because it uses the incorrect scale of the map in the denominator.

Therefore, the proportion that would not allow us to find the actual distance between the two cities if they are 7 cm apart on the map is:
(Actual Distance)/(7 cm) = (5 cm)/(3 km)