Evaluate (mn)(x) for x = − 3. (mn)(−3) =
2 answers:
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Answer:
For a clearer understanding, refer to the attached figure:
Step-by-step breakdown:
1. According to the unique line postulate, only one line segment can be created: BC
This is because a single line can only connect two distinct points.
2. Utilizing the definition of reflection, reflect BC across l.
To identify the line segment reflected over l, we will apply the reflection definition.
3. Based on the reflection definition, C remains as its own image and A represents the image of B.
The reflection definition states that a figure is transformed into a mirror image around a line. Thus, CD serves as the perpendicular bisector of AB, which makes A and B equidistant from D, producing their mirror images.
4. Because reflections maintain length, we find that AC = BC
In a reflection, the figure transforms to create a mirror image, ensuring the lengths remain unchanged.
Answer:
Tan(b°) = 3/4, which is equivalent to three fourths (C).
Step-by-step explanation:
Triangle JKL is a right triangle with angle K being the right angle and angle L equal to b°.
We will employ SOHCAHTOA principles from trigonometry to calculate the sides' values.
For triangle ∆JKL:
Sin(b°) = opposite/hypotenuse
Sin(b°) = 3/5
Cos(b°) = adjacent/hypotenuse
Cos(b°) = 4/5
Tan(b°) = 3/4.
From the earlier information, we have the values for each side of triangle ∆JKL.
Please refer to the attached diagram for the triangle (1).
Triangle ∆JKL is scaled with a factor of 2.
This implies multiplying each side of ∆JKL by 2, resulting in:
Opposite side = 2(3) = 6
Adjacent side = 2(4) = 8
Hypotenuse = 2(5) = 10.
To find tan(b°) for the new triangle, we use the tangent ratio:
Tan(b°) = opposite/adjacent.
Tan(b°) = 6/8.
Tan(b°) = 3/4.
Find the diagram for the new triangle included (2).
Diagram 3 provides a depiction of both triangles.
As shown, the angle remains unchanged when a triangle is scaled by a factor.
Thus, we conclude that tan(b°) = three fourths (C).
