1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Korvikt [17]
3 years ago
11

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

true of the circle at the new location.
Mathematics
1 answer:
irga5000 [103]3 years ago
4 0

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 />

You might be interested in
A rectangular plot of ground is 30 meters longer than it is wide. its area is 10,000 square meters.
dimulka [17.4K]
A = W· L
10,000 = W ( W +30 ) = W² + 30 W
W² + 30 W - 10,000 = 0
W = \frac{-30+ \sqrt{900+40000} }{2}=  \frac{-30+202.24}{2} = 86.12
L = 86.12 + 30 = 116.12
Width of a plot is 86.12 m and lenght is 116.12 m.
Check : A = 116.12 · 86.12 ≈ 10,000
6 0
3 years ago
Whats the answer to 30 less than 10
Deffense [45]

We are looking for a new number which is 30 less than 10. We will get the new number by subtracting 30 from 10. We write it down as: 10-30=-20


And finally the solution for: What number is 30 less than 10? is -20 

Hope this helps!!
6 0
3 years ago
Read 2 more answers
Charlotte has been saving up to buy a home gym so she can work out at home without having to pay for a
Y_Kistochka [10]

The 15% discount for home gym, and the $889 cost of the Flex 3,000 gives;

1. f(x) = 0.85•x + 139.95

2.

  1. With the deal, Charlotte's before tax cost is $895.6
  2. The deal cost is more than the initial price making the deal not worth it.

3. The domain is; 889 < x < ∞

The range is; 895.6 ≤ f(x) ‹ ∞

<h3>How can the function notation for the cost be found?</h3>

1. The percentage discount Charlotte gets = 15% = 0.15

Cost of the 6 months subscription = $139.95

f(x) = Final before tax

x = Price of the home gym equipment

Therefore;

Given the 15% off, we get;

f(x) = (1-0.15)•x + 139.95

Which gives;

  • f(x) = 0.85•x + 139.95

2. Question 1

Cost of the Flex3000, <em>x</em> = $889

Therefore;

f(889) = 0.85 × 889 + 139.95 = 895.6

Charlotte's before–tax cost with the deal is therefore, $895.6

Given that the workout channel holds no value to Charlotte, and the deal cost is higher than the initial cost, it isn't worth it for her to pay for the subscription to get the 15% discount

3. The domain if the Awesome Flex is the cheapest option, is the possible initial price of the home gym equipment.

The domain is therefore;

  • 889 < x < ∞

The range is the possible values of the before tax cost.

The range is therefore;

  • 895.6 ≤ f(x) ‹ ∞

Learn more about writing equations here:

brainly.com/question/11331093

#SPJ1

5 0
1 year ago
Nancy's morning routine involves getting dressed, eating breakfast, making her bed, and driving to work. Nancy spends ⅓ of the t
devlian [24]

Answer: 26 minutes

Step-by-step explanation:

Assume that the total time spent in the morning which includes getting dressed, eating breakfast, making her bed, and driving to work is x.

Time getting dressed = ¹/₃x

Eating breakfast = 10 mins

Making bed = 5 mins

¹/₃x + 10 + 5 = 35 ½

¹/₃x + 15 = 35 ½

¹/₃x = 35 ½ - 15

¹/₃x = 20 ½

x = 20 ½ / ¹/₃

= 61.5 minutes

Total morning routine is is 61.5 mins

Time taken to drive to work is;

= 61.5 - 35 ½

= 26 minutes

8 0
2 years ago
FOR GEOMETRY PLEASE DONT WASTE ANSWERS PLEASE HELP URGENT ILL MARK BRAINLIEST
Igoryamba
I believe it’s the second one
5 0
3 years ago
Other questions:
  • Calculate the perimeter if the value of x is 5.
    12·2 answers
  • If a cone has a height that equals twice the diameter of its base,what is its volume in terms of the height
    15·1 answer
  • A wheelchair access ramp has an angle of elevation of 18°. If the ramp reaches the top of a 26 inch high porch, how long is the
    15·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%28%203%20-%20%28%20-%204%20%7Bx%7D%29%5E%7B2%7D%20" id="TexFormula1" title=" ( 3 - ( - 4 {
    15·1 answer
  • Can someone please explain to me how I do this?
    8·2 answers
  • Please help its math
    7·2 answers
  • Write 0.00005974 in scientific notation.
    13·2 answers
  • Find the volume and round to the nearest tenth as needed
    15·1 answer
  • The slope indicates how fast y increases or decreases as x increases.<br> O True<br> O False
    12·1 answer
  • Which of the following terms is defined as a set of all points in a plane that are a given distance from a point?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!