Final answer:
The total perimeter of Anna and Tamara's suitcases is represented by the algebraic expression 11x - 1. For Marta's squares, the area of the larger square is four times the area of the smaller one due to the scaling factor impact on area. When using a scale factor, it's used to determine proportional dimensions on scale drawings, such as mapping a 15-meter distance to 10 centimeters using a 1/150 scale factor.
Step-by-step explanation:
When Anna's suitcase has a perimeter of 3x + 2, and Tamara's suitcase has a perimeter of 8x - 3, to find the total perimeter of the suitcases, we simply add these two algebraic expressions together:
Total Perimeter = (3x + 2) + (8x - 3)
Combine like terms:
Total Perimeter = 3x + 8x + 2 - 3
Total Perimeter = 11x - 1
The algebraic expression for the total perimeter of both suitcases is 11x - 1.
Marta's problem with the squares is a great way to understand scale factors and their impact on area. The original square side length is 4 inches; scaling it by a factor of 2 gives a new side length of 8 inches for the larger square. As the area of a square is given by the formula side length squared (a²), the area of the larger square with a side length of 8 inches is 8² = 64 square inches. This is four times larger than the smaller square, which has an area of 4² = 16 square inches, since the scaling factor of 2 applies to both dimensions, and area scales with the square of the scaling factor.
With multiplication, it's important to understand that when two positive numbers are multiplied, the result is positive, and similarly for two negative numbers. However, when numbers of opposite signs are multiplied, the result is negative.
Lastly, when portraying distances on a scale drawing, if Anna's room is 15 meters from the kitchen and the scale factor is 1/150, the distance on the diagram would be 15 meters times 1/150, which equals 0.1 meters or 10 centimeters.