Answer:
Angle A: 72°
Angle B: 108°
Step-by-step explanation:
Opposite angles are equal
Adjacent angles add up to 180
5y - 3 = 3y + 27
2y = 30
y = 15
Angle A:
5(15) - 3 = 72°
Angle B:
180 - 72 = 108°
The area of the triangle which is formed as described is; 60.
<h3>What is the area of the triangle formed?</h3>
According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).
It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.
Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.
Read more on area of a triangle;
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Answer:
25%
Step-by-step explanation:
From the boxplot Given, an earning of $25 or less is represented on the boxplot as the lower quartile of the distribution which is the point at the start of the box. The lower quartile value is the percentage value up to 25% that is the first 25% of the distribution.
Hence, the percentage required = 25%
Hence, Nicholas earned $25 or less about 25% of the time.
Answer:
Step-by-step explanation: 5795f
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.