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3 years ago

Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations?

Mathematics

1 answer:

kirill115 [55]3 years ago

8 0

Answer: HG, CD, and PN

Step-by-step explanation:

The only transformations that we have are:

Reflections, rotations and/or translations.

You should notice that none of these transformations are dilations/contractions. This means that the length of the segment will remain constant.

Then the possible images of AB after the sequence of transformations, are the segments that have the same length as AB.

The length of AB is 4 units.

The segments with the same length are:

HG, CD and PN

So any of those could be the image of AB after the transformations.

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to arrive at 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution. How many liters of eac

CaHeK987 [17]

Answer:

800 liters of 90% saline solution and 1200 liters of 40% saline solution should be used.

Step-by-step explanation:

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At 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution.

Now, to find the number of liters of saline solution each should be used.

Let the liters of 90% saline solution mix be $x.$

And let the liters of 40% saline solution mix be $y.$

So, the total number of liters:

$x+y=2000.$

$y=2000-x\ \ \ ....(1)$

Now, the total percentage of saline solution:

$90\%\ of\ x+40\%\ of\ y=60\%\ of\ 2000$

$\frac{90}{100}\times x+\frac{40}{100}\times y=\frac{60}{100}\times 2000$

$0.9x+0.4y=1200$

Substituting the value of $y$ from equation (1) we get:

$0.9x+0.4(2000-x)=1200$

$0.9x+800-0.4x=1200$

$0.5x+800=1200$

Subtracting both sides by 800 we get:

$0.5x=400$

Dividing both sides by 0.5 we get:

$x=800.$

The liters of 90% saline solution mix = 800.

Now, substituting the value of $x$ in equation (1) to get the liters of 40% saline solution:

$y=2000-x$

$y=2000-800$

$y=1200.$

Thus, the liters of 40% saline solution = 1200.

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Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations? ​

Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations?