Answer:
c = 3(b + 1)
Step-by-step explanation:
c = 4b - 1b + 3
4b - 1b = 3b
c = 3b + 3
3 is a common factor of both terms on the right hand side
Factorizing the expression
c = 3(b + 1)
Answer:
A
Step-by-step explanation:
There is a not so well-known theorem that solves this problem.
The theorem is stated as follows:
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides" (Coxeter & Greitzer)
This means that for a triangle ABC, where angle A has a bisector AD such that D is on the side BC, then
BD/DC=AB/AC
Here either
BD/DC=6/5=AB/AC, where AB=6.9,
then we solve for AC=AB*5/6=5.75,
or
BD/DC=6/5=AB/AC, where AC=6.9,
then we solve for AB=AC*6/5=8.28
Hence, the longest and shortest possible lengths of the third side are
8.28 and 5.75 units respectively.
Answer:
(a) P = 4x+10
(b) x = 6
Step-by-step explanation:
(a) The perimeter is the sum of the side lengths:
P = AB +AC +BC = 2x +2x +10
P = 4x+10
__
(b) For P=34, the value of x is ...
34 = 4x +10 . . . .substitute given value for P
24 = 4x . . . . . . . subtract 10
6 = x . . . . . . . . . .divide by 4