The first number is 6, second is 29, and the third is 16.
Answer:
![22 < X < 46](https://tex.z-dn.net/?f=22%20%3C%20X%20%3C%2046)
Step-by-step explanation:
Given
Two sides of a triangle; 34 and 12
Required
Determine the range of the third side
Represent the third side with X
To determine the range of the third side; two of the following conditions must be satisfied'
![34 + X > 12](https://tex.z-dn.net/?f=34%20%2B%20X%20%3E%2012)
![34 + 12 > X](https://tex.z-dn.net/?f=34%20%2B%2012%20%3E%20X)
![12 + X > 34](https://tex.z-dn.net/?f=12%20%2B%20X%20%3E%2034)
Solving 34 + X > 12
<em>Subtract 34 from both sides</em>
![34 - 34 + X> 12 - 34](https://tex.z-dn.net/?f=34%20-%2034%20%2B%20X%3E%2012%20-%2034)
![X > -22](https://tex.z-dn.net/?f=X%20%3E%20-22)
Solving 34 + 12 > X
![34 + 12 > X](https://tex.z-dn.net/?f=34%20%2B%2012%20%3E%20X)
![46 > X](https://tex.z-dn.net/?f=46%20%3E%20X)
Solving 12+ X > 34
<em>Subtract 12 from both sides</em>
![12 - 12 + X > 34 -12](https://tex.z-dn.net/?f=12%20-%2012%20%2B%20X%20%3E%2034%20-12)
![X > 22](https://tex.z-dn.net/?f=X%20%3E%2022)
Write out the results
![X > -22](https://tex.z-dn.net/?f=X%20%3E%20-22)
![46 > X](https://tex.z-dn.net/?f=46%20%3E%20X)
![X > 22](https://tex.z-dn.net/?f=X%20%3E%2022)
The first inequality will be discarded because it accommodates negative digits;
<em>So, we're left with</em>
and ![X > 22](https://tex.z-dn.net/?f=X%20%3E%2022)
This can be rewritten as
and ![22 < X](https://tex.z-dn.net/?f=22%20%3C%20X)
Combine both inequalities;
![22 < X < 46](https://tex.z-dn.net/?f=22%20%3C%20X%20%3C%2046)
Hence, the range of the third length is ![22 < X < 46](https://tex.z-dn.net/?f=22%20%3C%20X%20%3C%2046)
<LMP and <NMP are supplementary angles so sum = 180
<LMP + <NMP = 180
(-16x + 13) + ( - 20x + 23) = 180
-16x + 13 - 20x + 23 = 180
-36x + 36 = 180
-36x = 144
x = -4
<LMP = -16x + 13 = -16(-4) + 13 = 77
<NMP = - 20x + 23 = - 20(-4) + 23 = 103
Answer
<LMP = 77°
<NMP = 103°
Answer:
c
Step-by-step explanation:
Answer:
boxes 1, 3, and 4
Step-by-step explanation: