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goldenfox [79]
3 years ago
12

Which of the following transformations fit the definition of isometry?

Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0

Answer: Rotations, reflections, translations (A, C, and E)

Imagine you had a camera aimed at a triangular figure on a piece of paper. If you rotate the camera, then the image of the triangle appears to rotate. In reality it's the other way around. What this means is that the triangle is not changing at all. It keeps the same size, shape, area, perimeter, etc. This applies to when the camera pans left or right, ie shifts from side to side. The triangle will translate but again the triangle isn't changing at all. It's merely an illusion. Reflections are the same way. Imagine having a piece of glass or a mirror that reflects the image which is an identical copy; although everything is flipped.

Dilations are not isometries because the image is a different size then the pre-image. The same shape is maintained though. Note: the scale factor must be some number other than 1.

another note: "isometry" breaks down into "iso+metry" with "iso" meaning "same" or "equal", and "metry" meaning "measure". So if you had 2 identical yard sticks, then they are isometrical or equal in length.

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You push your younger sister on a swing one time and then allow your sister to
Ber [7]

Answer:

My sister will swing the total distance = 40 feet

Step-by-step explanation:

On the first swing my sister travels a distance of 8 feet.

In every successive swing she travels 80% of the distance of the previous distance.

So the sequence formed by the distance traveled in every swing will be a geometric sequence.

First term of the sequence 'a' = 8 feet

common ratio 'r' = 0.80

Since this sequence is an infinite geometric sequence,

Sum of this sequence = \frac{a}{(1-r)}  [Since r < 1]

                                     = \frac{8}{1-0.8}

                                     = \frac{8}{0.2}

                                     = 40 feet

Therefore, my sister will cover the total distance = 40 feet

7 0
2 years ago
What are the roots of the polynomial equation x3-7x=6x-12?
Ilia_Sergeevich [38]
This is not a polynomial equation unless one of those is squared.  As it stands x=-.833.  If you can tell me which is squared I can help solve the polynomial.

Ok, that is usually notated as x^3 to be clear.   I'll solve it now.

x^3-13x-12=0

Then use factor theorum to solve x^3-13x-12/x+1 =0
So you get one solution of x+1=0
x=-1

Then you have x^2-x-12 now you complete the square.

Take half of the x-term coefficient and square it. Add this value to both sides. In this example we have:

The x-term coefficient = −1

The half of the x-term coefficient = −1/2

After squaring we have (−1/2)2=1/4

When we add 1/4 to both sides we have:

x2−x+1/4=12+1/4

STEP 3: Simplify right side

x2−x+1/4=49/4

STEP 4: Write the perfect square on the left.

<span>(x−1/2)2=<span>49/4
</span></span>

STEP 5: Take the square root of both sides.

x−1/2=±√49/4

STEP 6: Solve for x.

<span>x=1/2±</span>√49/4

that is,

<span>x1=−3</span>

<span>x2=4</span>

<span>and the one from before </span>

<span>x=-1</span>

7 0
3 years ago
Read 2 more answers
Simplify the polynomial 3x5-2x+4-x5+x2
MariettaO [177]

Answer:

-65 is answer if we will solve it then it will be answer

4 0
2 years ago
Which of the following is not a correct name for the line shown?
Talja [164]

Answer:

D

Step-by-step explanation:

The line can be named with small latin letters or with two large latin letters which represent two points lying on the line.

Consider all options:

A. Points V and X lie on the line, so you can name the line as VX (true option)

B. Points W and X lie on the line, so you can name the line as WX (true option)

C. p represents the line (small letter given on the diagram) - (true option)

D. You cannot name the line using point V and line p, so this option is false

3 0
3 years ago
Read 2 more answers
Using the figure below, select the two pairs of alternate interior angles.
algol [13]

Answer:

B :point 2 and point 3

Step-by-step explanation:

The only interior angles are 6, 2, 3, and 7

The angles equal to each other are 6 and 7 or 2 and 3

6 and 7 is not an option so 2 and 3 are the correct answer.

7 0
3 years ago
Read 2 more answers
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