Jeff lives 12 miles east of Stan Jeff live 16 miles north of Wei what is the shortest distance that Stan and Wei can live from each other?
To find the shortest distance between Stan and Wei, we can use the Pythagorean theorem. The distance between Stan and Wei is the hypotenuse of a right triangle, with Jeff living 12 miles to the east and 16 miles to the north. Thus, we have a right triangle with sides of 12 miles and 16 miles.
Using the Pythagorean theorem, we can calculate the shortest distance:
(shortest distance)^2 = (12 miles)^2 + (16 miles)^2
(shortest distance)^2 = 144 miles^2 + 256 miles^2
(shortest distance)^2 = 400 miles^2
(shortest distance) = √400
(shortest distance) = 20 miles
Therefore, the shortest distance that Stan and Wei can live from each other is 20 miles.
Carl is a using figure to proof the Pythagorean theorem. She starts by writing the equation (a + b)^2 - c^2 = 4 (1/2 ab) Because she knows to equal ways to represent the area of the shaded region, which best describes the next steps Carl to take to complete his proof
To complete the proof of the Pythagorean theorem using the equation (a + b)^2 - c^2 = 4 (1/2 ab), Carl can follow these steps:
1. Expand the equation: (a + b)^2 - c^2 = 4 (1/2 ab)
2. Simplify the equation: a^2 + 2ab + b^2 - c^2 = 2ab
3. Rearrange the terms: a^2 + b^2 = 2ab + c^2
4. Notice that a^2 + b^2 represents the areas of two squares with side lengths a and b respectively, and 2ab represents the area of a rectangle with sides a and b.
5. Recognize that the right-angled triangle formed by the squares and rectangle has hypotenuse c.
6. By comparing the areas, conclude that the area of the two squares (a^2 + b^2) must be equal to the area of the square with side c (c^2) for the equality to hold.
7. Thus, the equation a^2 + b^2 = c^2 is obtained, proving the Pythagorean theorem.
Therefore, Carl has to continue with the above steps to complete his proof.
To find the shortest distance between Stan and Wei, we can use the Pythagorean theorem. Let's consider Stan and Wei as two points on a coordinate plane.
Let the coordinates of Stan be (0,0) and the coordinates of Jeff be (12,0). Wei's coordinates are therefore (12,16).
The distance between Stan and Wei can be calculated using the formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) are the coordinates of Stan and (x₂, y₂) are the coordinates of Wei.
Distance = √((0 - 12)² + (0 - 16)²)
= √((-12)² + (-16)²)
= √(144 + 256)
= √400
= 20
Therefore, the shortest distance between Stan and Wei is 20 miles.