demonstrate any vocabulary word, type of problem, on integers and absolute value.
Sure! Let's demonstrate a problem involving the concept of absolute value.
Problem:
Find the distance between the points A(-8, 3) and B(4, -5) on a coordinate plane.
Solution:
To find the distance between two points on a coordinate plane, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the coordinates of points A and B:
d = √((4 - (-8))² + (-5 - 3)²)
= √(12² + (-8)²)
= √(144 + 64)
= √208
Now, let's simplify further by finding the square root of 208 using its prime factorization:
208 = 2² × 2 × 13
We can take out pairs of identical factors from under the square root:
√208 = √(2² × 2 × 13)
= √(2²) × √(2 × 13)
= 2 × √(26)
Thus, the distance between points A and B is 2√26 units.