Answer :
Option C (15, 7, 5) represents a possible solution for (x, y, z) because the sum of its components equals 26, which satisfies the given equation.
To see why the other options do not work, we can check their sums. Option A (12, 7, 4) has a sum of 23, which is less than 26. Option B (15, 7, 8) has a sum of 30, which is greater than 26. Option D (10, 27, 5) also has a sum of 42, which is greater than 26.
Therefore, only option C satisfies the equation x + y + z = 26. We can also note that there may be multiple solutions to this equation, but option C is the only one listed among the answer choices.
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Complete Question
Let x, y, and z be positive integers that satisfy the equation x + y + z = 26. Which of the following options represents a possible solution for (x, y, z)?
A. x=12, y=7, z=4
B. x=15, y=7, z=8
C. x=15, y=7, z=5
D. x=10, y=27, z=5
To find the distance between two points, we can use the distance formula which is derived from the Pythagorean theorem. The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where d is the distance between the two points, (x1, y1) and (x2, y2) are the coordinates of the two points.
Using this formula, we can find the distance between the two points (2, 1) and (-3, 4).
x1 = 2, y1 = 1, x2 = -3, y2 = 4
d = sqrt((-3 - 2)^2 + (4 - 1)^2)
= sqrt((-5)^2 + (3)^2)
= sqrt(25 + 9)
= sqrt(34)
Therefore, the distance between the two points (2, 1) and (-3, 4) is sqrt(34) or approximately 5.83 units.
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