Answer:
4:6
or 4/15 : 2/5
Step-by-step explanation:
Answer:
r =9
Step-by-step explanation:
7r-r=54
Combine like terms
6r = 54
6r/6 = 54/6
r =9
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
The answer is (D) <span>π (also known as pi) an Irrational Number</span>
Answer:
m∠ABG = 20 degrees
m∠BCA = 22 degrees
m∠BAC = 118 degrees
m∠BAG = 59 degrees
DG = 4
BE = 12.4
BG = 11.7
GC = 20.4
Step-by-step explanation:
The given parameters are;
m∠CBG = 20°, m∠BCG = 11°
The incenter of a triangle is the point where the three bisectors of ΔABC meets
m∠ABG = m∠CBG = 20° by definition of angle bisector
m∠ABG = 20°
m∠ACG = m∠BCG = 11° by definition of angle bisector
m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°
m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°
m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°
m∠BAG = m∠CAG by definition of angle bisector
m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG
2 × mBAG = 118°
m∠BAG = 118°/2 = 59°
m∠BAG = 59°
Given that "G" is the incenter of the triangle ABC, we have;
GF = GE = DG = The radius of the incircle of the triangle = 4
Therefore, by Pythagoras' theorem, we have;
BG = √(11² + 4²) = √137 ≈ 11.7
BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4
GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4