The distance is 15, because -6 is 6 spaces away from zero and 9 is 9 spaces away from zero. You add the two distances to find the distance between the two numbers.
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The absolute value of |l-6| is the distance between the number 'l' and the number 6 on the number line, regardless of the direction. If l is greater than 6, the absolute value of |l-6| is l-6. If l is less than 6, the absolute value of |l-6| is 6-l. In either case, the absolute value function ensures that the result is always non-negative.
No, between 8 and 9, very close to eight.
The square root of 29 is an irrational number, close to (but not equal to) 5.385; on a number line, this is a point between 5 and 6 closer to 5 than 6. The number can also be represented as a continued fraction. You can find a link to an image of this representation below.
Points: (-6, 1) and (-2, -2) Distance: 5 units
If d is the distance between them, then d2 = (-6 -10)2 + (1 - (-8))2 = (-16)2 + 92 =256 + 81 = 337 so d = sqrt(337) = 18.36