A map scale indicates that 1 inch equals 175 miles. The distance between two points on the map measures 5 3/4 inches. What is the actual distance between those two points in kilometers? (1 mile = 1.61 kilometers.)

5.75 * 175 * 1.61 = 1620 km

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To calculate the actual distance between the two points in kilometers, you'll need to perform the following steps:

Step 1: Convert the map distance from inches to miles.
5 3/4 inches = 5.75 inches

Step 2: Find the actual distance in miles.
5.75 inches * 175 miles/inch = 1006.25 miles

Step 3: Convert the actual distance from miles to kilometers.
1006.25 miles * 1.61 kilometers/mile = 1623.06 kilometers

Therefore, the actual distance between the two points is approximately 1623.06 kilometers.

To find the actual distance between the two points in kilometers, we need to convert the given scale from miles to kilometers.

First, let's convert the scale from miles to kilometers. Given that 1 mile equals 1.61 kilometers, we can calculate the scale in kilometers by multiplying the scale in miles by 1.61:

1 inch = 175 miles
1 inch = 175 miles × (1.61 kilometers/mile)
1 inch = 281.75 kilometers

So, the scale in kilometers is 281.75 kilometers.

Next, we can find the actual distance between the two points by multiplying the map distance (5 3/4 inches) by the scale in kilometers:

Actual distance = Map distance × Scale in kilometers
Actual distance = 5 3/4 inches × 281.75 kilometers
Actual distance = (5 + 3/4) inches × 281.75 kilometers
Actual distance = 5 inches × 281.75 kilometers + 3/4 inches × 281.75 kilometers

To simplify the calculations, let's convert the mixed number 5 3/4 to an improper fraction:
5 3/4 = (4 × 5 + 3)/4 = 23/4 inches

Substituting back into the equation:

Actual distance = (23/4 inches) × 281.75 kilometers
Actual distance = (23 × 281.75)/(4 × 1) kilometers
Actual distance = 6577.25/4 kilometers
Actual distance = 1644.3125 kilometers

Therefore, the actual distance between the two points on the map measures approximately 1644.3125 kilometers.