Answer:
Step-by-step explanation:
We require 2 equations with the repeating decimal after the decimal point in both equations.
The bar above 136 indicates that 136 is being repeated
let x = 0.136136...... → (1) Multiply both sides by 1000
1000x = 136.136.... → (2)
Subtract (1) from (2) to eliminate the decimal part
999x = 136 ( divide both sides by 999 )
x =
1st digit: 9 possibilities (can’t have 0)
2nd digit: 10 possibilities
3rd digit:10
4th digit:10
5th digit:10
6th digit: 4 possibilities (it can only be even)
9•10•10•10•10•4 =360,000 possibilities
He should set up the refreshment stand on the incenter of the obtuse triangle. The incenter of a triangle is described as the intersection between the angle bisectors of a triangle. The inradius are the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal. The inradius is depicted as the radius of an inscribed circle in the triangle. Therefore, the shortest equal distance from his stand to each road is C. on the incenter.
First, find out x
x+15+2x+15=180
3x+30=180
3x=150
x=50
so the two angels are x+15=65(let's name is ∠5 for convenience), and ∠6= 2x+15=115
notice the two inner lines are marked as congruent, so
∠4=∠5=65
∠1=180-∠4-∠5=180-65-65=50
Name the right bottom angle ∠7, ∠3=∠7 and ∠3+∠7=the exterior angle 100 degree, therefore, ∠3=50
∠2+∠3=∠4, therefore, ∠2=∠4-∠3=65-50=15
∠1=50, ∠2=15, ∠3=50, ∠4=65
