The diagram shows three aid stations in a national park. Choose the values of x, y, and z that COULD represent the distances between the stations.
Responses
A x = 4 miles, y = 7 miles, z = 12 milesx
B x = 5 miles, y = 9 miles, z = 14
C x = 7 miles, y = 8 miles, z = 18 milesx
D x = 8 miles, y = 12 miles, z = 15 milesx
B x = 5 miles, y = 9 miles, z = 14 miles.
An angle's complement is 35°. Find the measure of its supplement.
Responses
A 155°155°
B 125°125°
C 180°180°
D 65°65°
E 55°
The complement of an angle is 90 degrees minus the angle, so in this case, the angle is 90 - 35 = 55 degrees.
The supplement of an angle is 180 degrees minus the angle, so the supplement of 55 degrees is 180 - 55 = 125 degrees.
Therefore, the answer is B) 125°.
To determine which set of values could represent the distances between the aid stations, we need to make sure they satisfy the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's use this theorem to verify each set of values:
A) x = 4 miles, y = 7 miles, z = 12 miles
To check if this set satisfies the triangle inequality theorem, we need to compare the sums of the two shorter sides with the longest side:
- x + y = 4 + 7 = 11 miles (less than z)
- x + z = 4 + 12 = 16 miles (greater than y)
- y + z = 7 + 12 = 19 miles (greater than x)
Since x + y is less than z, this set of values does not satisfy the triangle inequality theorem.
B) x = 5 miles, y = 9 miles, z = 14 miles
- x + y = 5 + 9 = 14 miles (equal to z)
- x + z = 5 + 14 = 19 miles (greater than y)
- y + z = 9 + 14 = 23 miles (greater than x)
This set satisfies the triangle inequality theorem.
C) x = 7 miles, y = 8 miles, z = 18 miles
- x + y = 7 + 8 = 15 miles (less than z)
- x + z = 7 + 18 = 25 miles (greater than y)
- y + z = 8 + 18 = 26 miles (greater than x)
Since x + y is less than z, this set of values does not satisfy the triangle inequality theorem.
D) x = 8 miles, y = 12 miles, z = 15 miles
- x + y = 8 + 12 = 20 miles (greater than z)
- x + z = 8 + 15 = 23 miles (greater than y)
- y + z = 12 + 15 = 27 miles (greater than x)
This set satisfies the triangle inequality theorem.
Therefore, the set of values that COULD represent the distances between the aid stations is:
B) x = 5 miles, y = 9 miles, z = 14 miles