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3 years ago

1. Define a Transformations and a reflection. What is the difference between them?

Mathematics

1 answer:

ruslelena [56]3 years ago

6 0

Answer:

More advanced transformation geometry is done on the coordinate plane. The transformation for this example would be T(x, y) = (x+5, y+3). A reflection is a "flip" of an object over a line.

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Can someone help me with this math question.

Veronika [31]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Which equation is equivalent to startroot x^2 + 81 EndRoot = x + 10?

Nitella [24]

Answer:given below

Step-by-step explanation:

sqrt x^2 +81= x + 10

x^2 + 81 = (x+10)^2

x^2 + 81 = x^2 + 20x + 100

so answer is:

x^2 + 81 = x^2 +20x + 100

..HOPE IT HELPS YOU...ALL THE BEST

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3 years ago

How can the point (12, 16) be explained? The highest point of the mountain defined by the function is 12 feet. The highest point

Alex

Answer:

12 is the horizontal distance and 16 is the vertical distance

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3 years ago

What is the scale factor from L to S?

MariettaO [177]

Answer: While I don’t have the picture to actually know the answer I will explain how to get it.

Step-by-step explanation:

1. If the shapes are on a grid count the amount of grid squares that are located between each end point of the shape. If it’s not on a grid use a ruler to measure the side lengths. You will need to find out the side amounts for both shapes L and S.

2. From there if the L shape is SMALLER than the S shape, then take the S shape’s sides and divide it by the L shape’s sides, and whatever number you get from each of your division problems will be your scale factor. BUT If the L shape is BIGGER than the S shape then easiest way to find out your scale factor is to take the last scale factor you got and convert it into a fraction. For example, if you got 3 then it would be 1/3. Hope this helped!

8 0

2 years ago

Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)

Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

$\\$ AB = B - A = (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B = (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C = (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D = (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]

DA = -i - 4j - 3k

AC = C - A = (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD [AB is parallel to CD]

AC = BD This implies that AC || BD [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

Now let's calculate the area

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

$AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]$

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = $\sqrt{(-6)^2 + (-6)^2 + (10)^2}$

|AB X AC| = $\sqrt{172}$

|AB X AC| = 13.15

Area = 13.15 square units.

PS: ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0

3 years ago