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3 years ago

Is it possible for the area of a figure to change after it is translated? Explain.

2 answers:

8 0

It is not possible for the area to change with a translation because translations are simply movements. They are not changing anything about the object's form, like something such as scaling does.

Sonja [21]3 years ago

8 0

Answer with explanation:

Translation means moving a geometrical shape in either direction in a coordinate plane without changing the shape and size of the geometrical object.

As, the coordinates of vertices of geometrical shape is translated in such a way that, The preimage and Image remains Congruent.

And, Congruent Shapes has equal Area.

So, it is Impossible for the area of a figure to change after it is translated.

You might be interested in

What is 11.52/128 show your work

grandymaker [24]

Answer:

The answer is

Step-by-step explanation:

11.5/128

First convert the decimal to an improper fraction

That's

$11.52 = \frac{288}{25}$

So we have

$\frac{288}{25} \div 128$

Change the division sign to multiplication sign and reverse the second number

That's

$\frac{288}{25} \times \frac{1}{128}$

Simplify

$\frac{288}{3200}$

Divide through by 32

The final answer is

$\frac{9}{100}$

Hope this helps you

6 0

3 years ago

25. John hired a plumber who charges a flat fee of $75 plus $55 per hour. The total charge

mestny [16]

Answer: 55x + 75 = 350; 5 hours

Step-by-step explanation:

What we know:

- A flat fee is $75

- John charges $55 an hour

- The total charge is $350

We need to write an equation to find how many hours John works.

<em>x </em>will represent hours worked.

55x + 75 = 350

We now need to solve for x.

Subtract 75 from both sides.

55x + 75 - 75 = 350 - 75

Simplify.

55x = 275

Divide 55 from both sides.

55x/55 = 275/55

Simplify.

x = 5

John worked 5 hours.

To check our work, we just plug in our x value!

55(5) + 75

275 + 75 = 350

3 0

3 years ago

a pond at a hotel holds 4290 gallons. the groundskeeper drains the pond at a rate of 78 gallons per hour. how long will it take

Studentka2010 [4]

55 hours to drain it

5 0

4 years ago

In the adjoining figure, area of trangle ABC is

Zepler [3.9K]

Answer:

$PQ=4\ cm$

Step-by-step explanation:

see the attached figure with the letter D to better understand the problem

we know that

The segment side AD is the height of triangle ABC

Triangles PBQ and ABD are similar by AA Similarity Theorem

The area of triangle ABC is equal to

$A=\frac{1}{2}(BC)(AD)$

we have

$A=48\ cm^2\\BC=12\ cm$

substitute

$48=\frac{1}{2}(12)(AD)$

$AD=8\ cm$

Remember that

If two triangles are similar then the ratio of its corresponding sides is proportional

$\frac{BP}{AB}=\frac{PQ}{AD}$

substitute the given values

$\frac{BP}{2BP}=\frac{PQ}{8}$

$\frac{1}{2}=\frac{PQ}{8}$

$PQ=4\ cm$

3 0

3 years ago

Consider the following probability distribution function of the random variable X which represents the number of people in a gro

Troyanec [42]

Answer:

(a) 3.55

(b) 3.45 and 1.86

(d) 0.016

Step-by-step explanation:

The random variable <em>X</em> denotes the number of people in a group (party) at a restaurant.

(a)

The formula to compute the mean is:

$\mu=\sum {x\cdot P(X=x)}$

Consider the Excel sheet attached.

The mean is, 3.55.

(b)

The formula to compute the variance is:

$\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}$

Consider the Excel sheet attached.

Compute the variance as follows:

$\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}\\\\=16.05-(3.55)^{2}\\\\=3.4475\\\\\approx 3.45$

The variance is, 3.45.

Compute the standard deviation as follows:

$\sigma=\sqrt{\sigma^{2}}\\\\=\sqrt{3.45}\\\\=1.85742\\\\\approx 1.86$

The standard deviation is, 1.86.

(c)

Compute the probability that the next party will be over 4 people as follows:

$P(X>4)=P(X=5)+P(X=6)+P(X=7)+P(X=8)\\\\=0.10+0.05+0.05+0.05\\\\=0.25$

Thus, the probability that the next party will be over 4 people is 0.25.

(d)

Compute the probability that the next three parties will each be over 4 people as follows:

It is provided that the three parties are independent.

P (Next 3 parties will be each over 4) = [P (X > 4)]³

$=(0.25)^{3}\\=0.015625\\\approx 0.016$

Thus, the probability that the next three parties will each be over 4 people is 0.016.

3 0

3 years ago