We know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)
Let
A------> Lincoln, NE
B------> Boulder, CO
C------> third city
we know that
in the triangle ABC
AB=500 miles
BC=200 miles
AC=x
Applying the Triangle Inequality Theorem
1) 500+200 > x------> 700 > x------> x < 700 miles
2) 200+x > 500----> x > 500-200------> x > 300 miles
the solution for x is
300 < x < 700
the interval is------> (300,700)
the possible distances, d, in miles, between Lincoln, NE, and the third city, are in the range between 300 and 700 miles
Answer:
x=−2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−3x−32=−2(5−4x)
−3x+−32=(−2)(5)+(−2)(−4x)(Distribute)
−3x+−32=−10+8x
−3x−32=8x−10
Step 2: Subtract 8x from both sides.
−3x−32−8x=8x−10−8x
−11x−32=−10
Step 3: Add 32 to both sides.
−11x−32+32=−10+32
−11x=22
Step 4: Divide both sides by -11.
−11x
−11
=
22
−11
Answer:
the coordinates of the center of rotation is (4 , 3)
Step-by-step explanation:
*The line which passes through points (4 , 1) and (4 , 5) is vertical because the points have same x coordinates and its length is 5 - 1 = 4
*The line which passes through points (2 , 3) and (6 , 3) is horizontal because the points have same y coordinates and its length is 6 - 2 = 4
*These two lines intersect each other at their mid-point and this mid-point is the center of rotation
*The mid point is 
or 
Answer:
180°
Step-by-step explanation:
cos(x) = - 1 has only 1 solution in the required interval , that is
x = 
(- 1) = 180°
82/100 or 41/50 if you simplify
