The supplement of an angle is six times as large as the complement of the angle. What is the measure of the angle to the nearest whole degree?
A. 18
B. 72
C. 39
D. 68
E. 44
Let's call the angle x.
The complement of the angle is 90 - x.
The supplement of the angle is 180 - x.
According to the problem, the supplement is six times as large as the complement:
180 - x = 6(90 - x)
Simplifying this equation:
180 - x = 540 - 6x
5x = 360
x = 72
Therefore, the angle is 72 degrees, which is answer choice B.
Which set of line segments can be used to construct a triangle?
A. 7 cm, 4 cm, and 1 cm
B. 8 cm, 3 cm, and 6 cm
C. 6 cm, 3 cm, and 2 cm
D. 9 cm, 2 cm, and 6 cm
To construct a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each set of line segments:
A. 7 cm, 4 cm, and 1 cm.
7 + 4 = 11, which is greater than 1.
7 + 1 = 8, which is also greater than 4.
But 4 + 1 = 5, which is NOT greater than 7.
Therefore, this set of line segments cannot be used to construct a triangle.
B. 8 cm, 3 cm, and 6 cm.
8 + 3 = 11, which is greater than 6.
8 + 6 = 14, which is greater than 3.
6 + 3 = 9, which is also greater than 8.
Therefore, this set of line segments can be used to construct a triangle.
C. 6 cm, 3 cm, and 2 cm.
6 + 3 = 9, which is greater than 2.
6 + 2 = 8, which is greater than 3.
3 + 2 = 5, which is NOT greater than 6.
Therefore, this set of line segments cannot be used to construct a triangle.
D. 9 cm, 2 cm, and 6 cm.
9 + 2 = 11, which is greater than 6.
9 + 6 = 15, which is greater than 2.
6 + 2 = 8, which is NOT greater than 9.
Therefore, this set of line segments cannot be used to construct a triangle.
The only set of line segments that can be used to construct a triangle is B: 8 cm, 3 cm, and 6 cm.
Which two numbers are 4 units away from 0 in any direction on the number line?
The two numbers that are 4 units away from 0 in any direction on the number line are -4 and 4.
On a number line, what is the distance between −17 and 9?
To find the distance between -17 and 9 on a number line, we need to calculate the absolute value of the difference between the two numbers:
|(-17) - 9| = |-26| = 26
Therefore, the distance between -17 and 9 on a number line is 26 units.