Answer:
(a) Theorem 9
Step-by-step explanation:
Any of the given theorems can be used to prove lines are parallel. We need to find the one that is applicable to the given geometry.
<h3>Analysis</h3>
The marked angles are between the parallel lines (interior) and on opposite sides of the transversal (alternate).
Theorem 9 applies to congruent alternate interior angles.
The critical points of the function graphed are given as follows:
<h3>What are the critical points of a function?</h3>
The critical points of a function are the values of x for which:
![f^{\prime}(x) = 0](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%200)
In a graph, they are turning points, and are classified as follows:
- Local maximum, if the functions changes from increasing to decreasing.
- Local minimum, if the functions changes from decreasing to increasing.
Looking at the graph, the turning points are approximately:
More can be learned about critical points at brainly.com/question/2256078
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Answer:
<u>CIRCLE : CIRCLE</u>
Ratio of area is the scale factor squared. So find the radii of the two circles, square both values, and simplify the ratio.
<u>SQUARE : SQUARE</u>
Ratio of area is the scale factor squared, So find the side lengths of the two squares, square both values, and simplify the ratio.
<u>SQUARE : CIRCLE</u>
Using the formulas A = s*s and A = pi*r^2, find the areas of the circle and the square. Then simplify the ratio.
Answer:
![LN = 55](https://tex.z-dn.net/?f=LN%20%3D%2055)
Step-by-step explanation:
Given
![LN = 12w + 7](https://tex.z-dn.net/?f=LN%20%3D%2012w%20%2B%207)
![LP = 15w - 5](https://tex.z-dn.net/?f=LP%20%3D%2015w%20-%205)
Required
Determine LN
Since LM is a bisector, then we have:
(See attachment for illustration)
![15w - 5 = 12w + 7](https://tex.z-dn.net/?f=15w%20-%205%20%3D%2012w%20%2B%207)
Collect Like Terms
![15w - 12w = 5 +7](https://tex.z-dn.net/?f=15w%20-%2012w%20%3D%205%20%2B7)
![3w = 12](https://tex.z-dn.net/?f=3w%20%3D%2012)
Solve for w
![w = 12/3](https://tex.z-dn.net/?f=w%20%3D%2012%2F3)
![w = 4](https://tex.z-dn.net/?f=w%20%3D%204)
LN is calculated as thus:
![LN = 12w + 7](https://tex.z-dn.net/?f=LN%20%3D%2012w%20%2B%207)
Substitute 4 for w
![LN = 12 * 4 + 7](https://tex.z-dn.net/?f=LN%20%3D%2012%20%2A%204%20%2B%207)
![LN = 48 + 7](https://tex.z-dn.net/?f=LN%20%3D%2048%20%2B%207)
![LN = 55](https://tex.z-dn.net/?f=LN%20%3D%2055)