Question

1. The lengths of three sides of a triangle are: n + 3, n + 6, and 3n – 6. Find the range of the possible lengths for n.
2. Find the value of x. https://www.connexus.com/content/media/464267-1122011-75457-PM-265560558.png
3. In ACE, G is the centroid and BE = 9. Find BG and GE. https://www.connexus.com/content/media/464267-1132011-53823-PM-153233918.png
5. /\ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Find the orthocenter of ABC.
6. Given ΔABC with A(–4, –2), B(4, 4), and C(18, –8), answer the questions 21–24. Write the equation of the line containing altitude BR in standard form.

Answer 1

for #1
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Using this:

(n + 3) + (n + 6) > (3n – 6) → 2n + 9 > 3n - 6 → -n > -15 → n < 15
(n + 3) + (3n - 6) > (n + 6) → 4n - 3 > n + 6 → 3n > 9 → n > 3
(n + 6) + (3n - 6) > (n + 3) → 4n > n + 3 → 3n > 3 → n > 1
The possible values of n are 3 < n < 15

Answer 2

#6
For step 1. m = (-2 - (-8))/(-4 - 18)
m=6/-22=-3/11
slope is m=11/3

Answer 3

sorry im not sure about the others

Answer 4

Well thank you, again:)

Answer 5

no problem pretty lady