Answer:
A 61377
B 87405
Step-by-step explanation:
If sum of the digits of a number is divisible by 3, then that number is also divisible by 3.
Option A:
Given number is: 61377
Sum of the digits = 6+1+3+7+7 = 24
24 is divisible by 3, hence 61377 is also divisible by 3.
Option B:
Given number is: 87405
Sum of the digits = 8+7+4+0+5 = 24
24 is divisible by 3, hence 87405 is also divisible by 3.
Option C:
Given number is: 30898
Sum of the digits = 3+0+8+9+8 = 28
28 is not divisible by 3, hence 30898 is also not divisible by 3.
Similarly, sum of the digits of the numbers in options D, E and F are 8, 22 and 26 respectively, which are not divisible by 3, hence the numbers 6020, 29830 and 75932 are also not divisible by 3.
X=-7
AB=-37
BC=73
AC=-49
I pretty sure
Answer: C. Two of the side lengths add to a sum that is less than the third side length, so these lengths cannot be used to draw any triangles.
Explanation:
Those two sides in question are 8 and 12. They add to 8+12 = 20, but this sum is less than the third side 24. A triangle cannot be formed.
Try it out yourself. Cut out slips of paper that are 8 units, 12 units, and 24 units respectively. The units could be in inches or cm or mm based on your preference.
Then try to form a triangle with those side lengths. You'll find that it's not possible. If we had the 24 unit side be the horizontal base, so to speak, then we could attach the 8 and 12 unit lengths on either side of this horizontal piece. But then no matter how we rotate those smaller sides, they won't meet up to form the third point for the triangle. The sides are simply too short. Other possible configurations won't work either.
As a rule, the sum of any two sides of a triangle must be larger than the third side. This is the triangle inequality theorem.
That theorem says that the following three inequalities must all be true for a triangle to be possible.
where x,y,z are the sides of the triangle. They are placeholders for positive real numbers.
So because 8+12 > 24 is a false statement, this means that a triangle is not possible for these given side lengths. Therefore, 0 triangles can be formed.
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