Answer:
Hence as long as x > 2/3, we can form a triangle from the three given sides.
Step-by-step explanation:
Given:
Length of 3 sides of triangle are ![x+3, 4x,3x-1](https://tex.z-dn.net/?f=x%2B3%2C%204x%2C3x-1)
Solution:
From the length of the 2nd side 4x, we know that x > 0
Let this be 1 st statement.
Now from the triangle inequality we can say that;
![x + 3 + 4x > 3x -1\\5x+3>3x-1\\5x-3x>-1-3\\2x>-2\\x>-1](https://tex.z-dn.net/?f=x%20%2B%203%20%2B%204x%20%3E%203x%20-1%5C%5C5x%2B3%3E3x-1%5C%5C5x-3x%3E-1-3%5C%5C2x%3E-2%5C%5Cx%3E-1)
No new information from this because of the 1st statement above.
Also,
![4x + 3x - 1 > x +3\\7x-1>x+3\\7x-x>3+1\\6x>4\\x>\frac{4}{6}\\\\x>\frac{2}{3}](https://tex.z-dn.net/?f=4x%20%2B%203x%20-%201%20%3E%20x%20%2B3%5C%5C7x-1%3Ex%2B3%5C%5C7x-x%3E3%2B1%5C%5C6x%3E4%5C%5Cx%3E%5Cfrac%7B4%7D%7B6%7D%5C%5C%5C%5Cx%3E%5Cfrac%7B2%7D%7B3%7D)
Lastly,
![x+3 +3x - 1 > 4x\\4x-2>4x\\4x-4x>2\\0>2](https://tex.z-dn.net/?f=x%2B3%20%2B3x%20-%201%20%3E%204x%5C%5C4x-2%3E4x%5C%5C4x-4x%3E2%5C%5C0%3E2)
and again no new information is obtained from this inequality.
Hence as long as x > 2/3, we can form a triangle from the three given sides.
Start at 107...
107 (-9) = 98
98 (- 8) = 90
90 (-7) = 83
83 (-6) = 77
77 (-5) = 72
72 (-4) = 68
68 (-3) = 65
Answer:
One solution (-1,2)
Step-by-step explanation:
Since these two linear equations have different slopes, different y-intercepts, and are indeed linear, these equations will only have one crossing when graphed, and hence one solution.
To find that solution, we can simply set the equations equal to each other.
y = -x + 1
y = 2x + 4
-x + 1 = 2x + 4
-3 = 3x
-1 = x
Now plug that value back into one of the equations:
y = -x + 1
y = -(-1) + 1
y = 2
So now you know the crossing for these two equations occurs at (-1,2).
Cheers.
Answer:
180
Step-by-step explanation: first base is 90 feet away so 90 x 2 = 180
The measure of angle G in terms of x is x+x degrees
<h3>Circle theorem</h3>
The measure of angle F and angle D is 90 degrees so that;
<GFD = <GDF = 90 - x
Since the sum of angle in a triangle is 180 degrees, hence;
<G + 90 - x + 90 - x = 180
<G + 180 - 2x = 180
<G = 2x
<G = x + x
Hence the measure of angle G in terms of x is x+x degrees
Learn more on circle theorem here: brainly.com/question/26594685
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