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3 years ago

Help with translations!

Mathematics

1 answer:

Vadim26 [7]3 years ago

3 0

Given:

The figure of a trapezoid.

The figure is translated down 5 units and then rotated 180 degrees clockwise.

To find:

The coordinates of the image of point W after these transformation.

Solution:

From the given figure it is clear that the coordinates of point W are (-6,3).

The figure is translated down 5 units. So,

$(x,y)\to (x,y-5)$

$W(-6,3)\to W'(-6,3-5)$

$W(-6,3)\to W'(-6,-2)$

After that the figure is rotated 180 degrees clockwise.

$(x,y)\to (-x,-y)$

$W'(-6,-2)\to W''(6,2)$

Therefore, the coordinates of point W after the given transformations are (6,2).

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A (0, 2) and B (6,6) are points on the straight line ABCD.

elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ , the distance is denoted by: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Let's find the distance between A and B:

d = $\sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}$

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = $\sqrt{(6-a)^2+(6-b)^2}$

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0

3 years ago

Read 2 more answers

Given the geometric sequence where a1=1 and the common ratio is 6, what is the domain for n?

kari74 [83]

We have been given that a geometric sequence's 1st term is equal to 1 and the common ratio is 6. We are asked to find the domain for n.

We know that a geometric sequence is in form $a_n=a_1(r)^{n-1}$ , where,

$a_n$ = nth term of sequence,

$a_1$ = 1st term of sequence,

r = Common ratio,

n = Number of terms in a sequence.

Upon substituting our given values in geometric sequence formula, we will get:

$a_n=1\cdot (7)^{n-1}$

Our sequence is defined for all integers such that n is greater than or equal to 1.

Therefore, domain for n is all integers, where $n\geq 1$ .

4 0

3 years ago

Please help me:) I don’t know what to do

Cloud [144]

Answer:

8 family members. Average of 2.6 fish per person.

Step-by-step explanation:

How many family members caught fish? Count only those members who caught at least 1 fish (that's all of them, because nobody caught 0 fish!).

3 + 1 + 0 + 4 = 8 family members.

Average number of fish caught <u>per person</u>. This is the total number of fish caught divided by the total number of people.

This is a little bit tricky because, for example, 4 people caught 4 fish, making 4 x 4 = 16 fish caught.

Multiply number of fish (column 1) by the number of people (column 2):

1 x 3 + 2 x 1 + 3 x 0 + 4 x 4 = 3 + 2 + 0 + 16 = 21 fish caught.

21 fish. 8 people. On average, that is 21 / 8 = 2.625 which rounds to 2.6 fish per person.

Hint: the word "per" means <u>divide</u>, so "fish per person" tells you to divide the total number of fish by the total number of people.

Good Luck!

5 0

2 years ago

A room is in the shape of a cube with 6.2-foot edge lengths.

Veronika [31]

---------------------------------------
Given information
---------------------------------------
It is a cube
Length = 6.2 ft

---------------------------------------
Find one surface
---------------------------------------
6.2 x 6.2 = 38.44 ft²

---------------------------------------
Find all 6 surfaces
---------------------------------------
38.44 x 6 = 230.64 ft²

---------------------------------------
Answer: 230.64 ft²
---------------------------------------

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3 years ago

198 cents to 234 cents

Anarel [89]

Answer:

i dont understand what ur asking

Step-by-step explanation:

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2 years ago