Simplify the expression
1 answer:
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9514 1404 393
Answer:
m∠B < m∠A < m∠C
Step-by-step explanation:
We can work with the triangle inequality to find that the side measures form a triangle when n > 5/4. For the given value of n ≥ 4, we don't need to be concerned with whether a triangle is formed or not.
For n = 4, the side lengths are ...
a = 2(4) = 8
b = (4) +3 = 7
c = 3(4) -2 = 10
The longest side is opposite the largest angle, so the ordering of angles is ...
m∠B < m∠A < m∠C
_____
The triangle inequality requires all of these inequalities be true:
- a+b > c ⇒ 3n+3 > 3n-2 . . . always true
- b+c > a ⇒ 4n+1 > 2n ⇒ n > -1/2
- c+a > b ⇒ 5n-2 > n+3 ⇒ n > 5/4
That will be the case for n > 5/4. The attached graph shows the sides and angles keep the same order for n > 3.
Answer:
x = 25
Step-by-step explanation:
The three straight lines in the sides of the triangle means that ALL 3 SIDES ARE EQUAL.
This is an equilateral triangle. So all 3 angles are equal.
We know sum of 3 angles in a triangle is 180. Since 3 of the angles are equal, each angle is:
180/3 = 60
The top angle is given as "2x + 10", thus we can say "2x + 10" is equal to 60 degrees. Now we equate and solve for x:
The value of x is 25