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2 years ago

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

Mathematics

2 answers:

Lubov Fominskaja [6]2 years ago

8 0

Answer:

Neither of the choices is correct.

Explanation:

1. Coordinates of the vertices of the figure I (preimage):

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

2. Coordinates of the vertices of the figure II (image):

(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]2 years ago

8 0

Answer:

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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Anon25 [30]

No, the system is inconsistent.

Step-by-step explanation:

If the last column is a pivot column, then that row gives an equation that looks something like 0x+0y+0z=1 , meaning , 0=1. Clearly, this is false.

So, the system of linear equations is inconsistent.

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2 years ago

Jennifer can run 12 miles in 2 hours, and she can bike 33 miles in 3 hours. What is Jennifer’s biking speed?

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Answer:

11 miles per hour

Step-by-step explanation:

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2 years ago

Which expression can be used to convert 100 USD to Japanese yen

Montano1993 [528]

As of 12:04 EST U.S.

$1=112.624847Yen

So:

100USD(112.624847Y/1USD)=11262.62 Yen

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1 year ago

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A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

1 year ago

30,45,x,100; The median is 51

Alex Ar [27]

To solve for x, you must first understand how the median was calculated out of the given set of numbers. Without looking at the given median value, we can see that we cannot get the median by process of elimination since there are an even amount of numbers in this particular set. Therefore, we must average the two closest values to what should be the median.

In this case, the values are "45" and "x". If we pretend that we know the value of the variable "x" (for example we will pretend that x is 55), then we should have an equation that looks like this: (45+55) ÷ 2 = [median]. What this equation is doing is adding the two closest values to the median (45 and 55) and dividing it by 2, the number of values we are averaging. Now we can solve this equation and simplify it to 100 ÷ 2 which is 50, our median.

So if they give us the median instead of the x value, then we can rewrite the equation to fit your request: (45+x) ÷ 2 = 51. Now we can solve for x:

1. Multiply by 2
(45+x) = 102

2. Subtract 45
x = 57

The x value for your question is 57.

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