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liq [111]
3 years ago
10

Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′.

Mathematics
1 answer:
andreev551 [17]3 years ago
7 0

When a triangle is rotated, it must be rotated through a center of rotation.

Assume the coordinate of LMN is

\mathbf{L = (1,1)}

\mathbf{M = (1,7)}

\mathbf{N = (3,6)}

The rule of 180-degree rotation is:

\mathbf{(x,y) \to (-x,-y)}

So, we have:

\mathbf{L' = (-1,-1)}

\mathbf{M' = (-1,-7)}

\mathbf{N' = (-3,-6)}

See attachment for the graphs of LMN and L'M'N

<u>(a) Describe the transformation</u>

When triangle LMN is rotated 180 degrees across the origin, the x and y coordinates of LMN are negated to form triangle L'M'N'

<u>(b) Lines LL' and MM'</u>

The distance between point L and the center of origin is the same as the distance between point M' and the center of origin

Similarly, the distance between point L and the center of origin is the same as the distance between point M' and the center of origin

<u>(c) Line NN'</u>

Line NN' will assume the same characteristics as lines LL' and MM'

Read more about transformations at:

brainly.com/question/11707700

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Fill in the blank (no word bank)
timofeeve [1]

Answer:

Alternate Interior Angles:

∠3 ≅ ∠5

Corresponding Angles:

∠3 ≅ ∠7

∠4 ≅ ∠8

Supplementary Angles:

∠3 is supplementary to ∠6

Step-by-step explanation:

7 0
3 years ago
On the basis of data collected during an experiment, a biologist found that the growth of a fruit fly population (Drosophila) wi
Ket [755]

Answer:

(a). 15

(b). 78

Step-by-step explanation:

Growth of the population of a fruit fly is modeled by

N(t) = \frac{600}{1+39e^{-0.16t} }

where t = number of days from the beginning of the experiment.

(a). For t = 0 [Initial population]

N(0) = \frac{600}{1+39e^{-0.16\times 0} }

       = \frac{600}{1+39}

       = \frac{600}{40}

       = 15

Initial population of the fruit flies were 15.

(b).Population of the fruit fly colony on 11th day.

N(11) = \frac{600}{1+39e^{-0.16\times 11} }

       = \frac{600}{1+39e^{-1.76} }

       = \frac{600}{1+39\times 0.172 }

       = \frac{600}{1+6.71}

       = \frac{600}{7.71}

       = 77.82

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On 11th day number of fruit flies colony were 78.

3 0
4 years ago
9+w&gt;7 what is the inequality?
Troyanec [42]

Answer:

w > -2

Step-by-step explanation:

9 + w > 7

Subtract 9 from both sides to end up with w alone on the left side.

w > -2

5 0
3 years ago
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snow_lady [41]
Angle n and angle l have the same degree so set them equal to eachother
7x+8=9x-8
-7x both sides
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x=8
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9 (8)-8
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4 0
3 years ago
Jimmy invests $4,000 in an account that pays 5% annual interest, compounded semiannually. What is his balance, to the nearest ce
masha68 [24]

Answer:

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4,000

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