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Mrrafil [7]
3 years ago
7

Which sequence of transformations confirms congruence by mapping shape I onto shape II?

Mathematics
2 answers:
Lubov Fominskaja [6]3 years ago
8 0

Answer:

  • Neither of the choices is correct.

Explanation:

<u>1. Coordinates of the vertices of the figure I (preimage):</u>

  • (10, - 5)
  • (15, -5)
  • (10, - 10)
  • (15, -10)

<u />

<u>2. Coordinates of the vertices of the figure II (image):</u>

  • (0,10)
  • (0,15)
  • (-5,10)
  • (-5, 15)

Since many different rigid transformations can map the figure I into the figue II, you will need to use trial and error.

The most important is to do it in an educated way.

I will start by eliminating some options.

The first option, a reflection across the x-axis and 15 units left, does not work, because the reflection across the x-axis would shift the figure to a lower position than what you need.

The third option, a 90º counterclokwise rotation about the origin then a translation 10 units up, would move the figure to the second quadrant, and we need it in the third quadrant.

I will try now with the second choice, a 90º clockwise rotation and then 25 units up:

First, a 90º clockwise rotation, which is the same that a 270º counterclockwise rotation, follows the rule (x, y) → (y, -x)

Then, that results in:

  • (10, - 5) → (-5, -10)
  • (15, -5) → (-5, -15)
  • (10, - 10) → (-10, -10)
  • (15, -10) → (-10, -15)

Now, you can see that shifting 25 units up will not work, because you need that two x-coordinates become 0 (zero). So, this is not the correct set of transformations either.

A 180º rotation about the origin and a translation 10 units right follow this chain of rules:

  • (x, y) → (-x, -y) → (-x + 10, -y)

That means:

  • (10, - 5) → (-10,5) → (-10 + 10, 5) = (0, 5)
  • (15, -5) → (-15, 5) → (-15 + 10, 5) = (-5, 5)
  • (10, - 10) → (-10, 10) → (-10 + 10, 10) = (0, 10)
  • (15, -10) → (-15, 10) → (-15 + 10, 10) = (-5, 10)

        These last points do not coincide either with the vertices of the figure II.

In conclusion, neither of the choices gives the correct answer to the question.

tensa zangetsu [6.8K]3 years ago
8 0

Answer:

b

Step-by-step explanation:

a translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin

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To find the quotient of 4 divided by 1/5, multiply 4 by <br> 1/5<br> 1/4<br> 4<br> Or <br> 5
alina1380 [7]

Answer:

5

Step-by-step explanation:

When dividing numbers by fractions, we can simply multiply the  umber by the reciprocal of the decimal. So,

4 ÷ 1/5 = 4 × (reciprocal of 1/5)

A reciprocal of a number is the same number written under 1. aka, 1 divided by that number, which simply is flipping the numerator and denominator of a number.

So the reciprocal of 1/5 is 5/1 = 5.

So 4 ÷ 1/5 = 4 × 5.

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hope it was useful!!! ;)

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3 years ago
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mario62 [17]

Answer:

1.sector 2. chords

Step-by-step explanation:

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3 years ago
The area of a rectangle is 6x^2-9x-15. And the length is (2x-5). Which expression best represents the rectangle’s width?
tester [92]
<h2><u>AnswEr :</u> </h2>

The area of the rectangle is of the form 6x² - 9x - 15

Factoring the given expression,

\sf \:  {6x}^{2}  - 9x - 15 \\  \\  \leadsto \:  \sf \:  3\bigg( {2x}^{2}  - 3x - 5 \bigg) \\  \\  \leadsto \:  \sf \: 3 \bigg( {2x}^{2}  - 5x + 2x - 5 \bigg) \\  \\  \leadsto \:  \sf \: 3 \bigg((2x - 5)(x + 1) \bigg)

Length of the rectangle is 2x - 5

Thus,

\leadsto \:  \sf \: (2x - 5)(3x + 3)

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Maksim231197 [3]

Answer:

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Step-by-step explanation:

7 0
2 years ago
3(2a + 1) = -5(a + 6)
Lemur [1.5K]
3(2a+1)=-5(a+6)
First expand the brackets.
6a+3=-5a-30
Now add 5a to both sides.
11a+3=-30
Then subtract 3 from both sides.
11a=-33
Finally divide both sides by 11.
a=- 33/11
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4 0
3 years ago
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