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AlekseyPX
3 years ago
7

Which sequence of similar transformations could map △ABC onto △A'B'C'?

Mathematics
2 answers:
nadya68 [22]3 years ago
7 0

Answer:  A sequence of similar transformations of dilation and translation could map △ABC onto △A'B'C'.


Step-by-step explanation:

Similar transformations:  If one figure can be mapped onto the other figure using a dilation and a congruent rigid transformation or a rigid transformation followed by dilation then the two figures are said to be similar.

In the attachment △ABC mapped onto △A'B'C' by a sequence of dilation from origin and scalar factor k followed by translation.

PilotLPTM [1.2K]3 years ago
7 0

<u>A dilation and a translation </u>could have occurred to map {\Delta \;\text{ABC}} to {\Delta \;\text{A''B''C''}}.

Further Explanation:

Given:

The options are as follows,

(A). A dilation and a reflection

(B). A dilation and a translation

(C). A translation and a rotation

(D). A translation and a reflection

Explanation:

The reflection symmetry is defined as a line that divides the Figure into two equal parts.

Translation can be defined as to move the function to a certain displacement.

Rotation is defined as a movement around its own axis. A circular movement is a rotation.

A dilation and a translation could have occurred to map {\Delta \;\text{ABC}} to {\Delta\; \text{A''B''C''}}.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

  1. If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard brainly.com/question/2479097.
  2. Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? brainly.com/question/1446243.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Geometry

Keywords: sequence, similar, Transformation, reflection, dilation, rotation, translation, rigid, motion, rigid motions.

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Answer:

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Step-by-step explanation:

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Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10
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The approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

<h3>What is depreciation?</h3>

Depreciation is to decrease in the value of a product in a period of time. This can be given as,

FV=P\left(1-\dfrac{r}{100}\right)^n

Here, (<em>P</em>) is the price of the product, (<em>r</em>) is the rate of annual depreciation and (<em>n</em>) is the number of years.

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.

Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is n_1. Thus, by the above formula for the first car,

0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}

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Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.

Thus, the depreciation price of the car is 0.6y. Let the number of year is n_2. Thus, by the above formula for the second car,

0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}

Take log both the sides as,

\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14

The difference in the ages of the two cars is,

d=4.85-3.14\\d=1.71\rm years

Thus, the approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

Learn more about the depreciation here;

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Step-by-step explanation:

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