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AleksAgata [21]
3 years ago
6

Sometimes two transformations, one performed after the other, have a nice description as a single transformation. For example, i

nstead of translating 2 units up followed by translating 3 units up, we could simply translate 5 units up. Instead of rotating 20 degrees counterclockwise around the origin followed by rotating 80 degrees clockwise around the origin, we could simply rotate 60 degrees clockwise around the origin.
Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis?
Mathematics
1 answer:
almond37 [142]3 years ago
6 0

Answer:

We rotate the point counterclockwise by an angle θ = tan⁻¹ (y/x)

Step-by-step explanation:

If we have the point (x, y), its reflection along the x-axis (x,-y). The reflection of the point (x, -y) along the y - axis is (-x, -y). So, the angle between the initial point (x, y) and the final point (-x, -y) is θ = tan⁻¹ [(-y - y)/(- x -x)] = tan⁻¹ [(-2y/(-2x)] =  tan⁻¹(y/x).

So, the point (x, y) is rotated counterclockwise by an angle of  θ = tan⁻¹ (y/x) to perform both reflections.

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16/9(1.2b)=4.8(20/3)<br> solve
mart [117]

\frac{16}{9}(1.2b)=4.8( \frac{20}{3})

Multiply 4.8 into (20/3), and multiply 16/9 with (1.2b)

\frac{19.2b}{9} = \frac{96}{3}

\frac{19.2b}{9} = 32  Multiply 9 on both sides

19.2b = 32(9)

19.2b = 288          Divide 19.2 on both sides

b = 15

4 0
3 years ago
The scale on a trail map is 0.5 cm : 1 km. The straight distance between 2 huts on the trail is 16.9 cm. What is the actual dist
sesenic [268]

We have been given that the scale on a trail map is 0.5 cm : 1 km. The straight distance between 2 huts on the trail is 16.9 cm. We are asked to find the actual distance between 2 huts.

We will use proportions to solve our given problem.

\frac{\text{Actual length}}{\text{Scale length}}=\frac{\text{1 km}}{\text{0.5 cm}}

\frac{\text{Actual length}}{\text{16.9 cm}}=\frac{\text{1 km}}{\text{0.5 cm}}

\frac{\text{Actual length}}{\text{16.9 cm}}\times \text{16.9 cm}=\frac{\text{1 km}}{\text{0.5 cm}}\times \text{16.9 cm}

\text{Actual length}=\frac{\text{1 km}}{\text{0.5}}\times \text{16.9}

\text{Actual length}=33.8\text{ km}

Therefore, the actual distance between both huts is 33.8 km.

6 0
3 years ago
Find the slope and the y-intercept of the line. y=4x-5
dusya [7]

\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hspace{6em}\underset{y-intercept}{\stackrel{slope}{y=\stackrel{\downarrow }{4}x\underset{\uparrow }{-5}}}\qquad \qquad \begin{cases} slope\\ \qquad 4\\ y-intercept\\ \qquad (0,-5) \end{cases}

6 0
3 years ago
HELP!!! I can't figure out what do do or how to solve the last part!!
koban [17]

Answer:

Use what you used for the first one and you should get the right answer.

Step-by-step explanation:

3 0
3 years ago
I need help with number 26 too
emmasim [6.3K]
So if one bag has 8 apples and each apple weights 5 ounces then the whole bag weights 40 ounces (8*5).

But now you have 2.5 bags so multiply (8*5) by 2.5.

Expression is 8*5*2.5
3 0
3 years ago
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