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Harlamova29_29 [7]
3 years ago
10

Use math drawings to make pictures equal

Mathematics
1 answer:
gavmur [86]3 years ago
5 0
Well, what are the pictures??
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A circle is translated 4 units to the right and then reflected over the x-axis. Complete the statement so that it will always be
irga5000 [103]

Answer:

The statement is now presented as:

\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}

In other words, this mathematical statement can be translated as:

<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>

Step-by-step explanation:

Let C = (h,k) the coordinates of the center of the circle, which must be transformed into C'=(h', k') by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:

(x-h)^{2}+(y-k)^{2} = r^{2}

Where r is the radius of the circle, which remains unchanged in every operation.

Now we proceed to describe the series of operations:

1) <em>Center of the circle is translated 4 units to the right</em> (+x direction):

C''(x,y) = C(x, y) + U(x,y) (Eq. 1)

Where U(x,y) is the translation vector, dimensionless.

If we know that C(x, y) = (h,k) and U(x,y) = (4, 0), then:

C''(x,y) = (h,k)+(4,0)

C''(x,y) =(h+4,k)

2) <em>Reflection over the x-axis</em>:

C'(x,y) = O(x,y) - [C''(x,y)-O(x,y)] (Eq. 2)

Where O(x,y) is the reflection point, dimensionless.

If we know that O(x,y) = (h+4,0) and C''(x,y) =(h+4,k), the new point is:

C'(x,y) = (h+4,0)-[(h+4,k)-(h+4,0)]

C'(x,y) = (h+4, 0)-(0,k)

C'(x,y) = (h+4, -k)

And thus, h' = h+4 and k' = -k. The statement is now presented as:

\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}

In other words, this mathematical statement can be translated as:

<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>

<em />

4 0
3 years ago
Can someone please help me I really need help please help me help thank you
KiRa [710]
That is a isosceles triangle, therefore x and the top angle are the same.

There’s 180 degrees in a triangle.

Therefore:

(180 - 38)/2 = x
142/2 = x
71 = x
7 0
3 years ago
Read 2 more answers
PLEASE HELP ILL GIVE BRAINLIEST Which set of ordered pairs represents a function?
jenyasd209 [6]

Answer:

the 2nd on (B)

Step-by-step explanation:

The x does not repeat

4 0
3 years ago
Read 2 more answers
Tax returns filled manually have a 20% chance of containing errors while tax returns filled electronically have a .05% chance of
Travka [436]

Answer:

538,650

Step-by-step explanation:

We must first find how many errors there will be if filed manually and if filed electronically

Manually: 2,700,000*20% or 2,700,000*.2

Answer: 540,000 errors

Electronically: 2,700,000*.05% or 2,700,000*.0005

Answer: 1,350 errors

We must then find the difference; 540,000-1,350=538,650

7 0
3 years ago
Read 2 more answers
A man bought a bicycle for $400 and sold it at a loss of 35%. How much money did he lose?
DedPeter [7]
If he bought the bike for $400 and lost 35% of his profit, you would divide 35 by 100. Next, you would multiply that number (0.35) by 400. When you do that, you get an answer of $140. In conclusion, if he bought the bike for $400 and sold it at a loss of 35%, he would lose $140 from that $400. 

Additionally, if you wanted to know what exactly he sold it for, you would simply subtract 140 from 400. Which would be $260.

So, he bought the bike for $400, but when he resold it, he lost $140 of that pay. Basically, he resold the bike for $260. 

I hope this helps! :) Let me know if you need help with anything else!
8 0
3 years ago
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