Find the equation of the circle whose center and radius are given.

Mathematics

1 answer:

kiruha [24]3 years ago

4 0

Answer:

(x + 2)^2 + (y + 5)^2 = 1

Step-by-step explanation:

Since this circle is centered at (-2, -5), we have to add values within the squares. The standard form of a circle equation is:

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

So -2 is h and -5 is k. Substituting that in we get:

(x + 2)^2 + (y + 5)^2 = r^2

We are given the radius is 1, and one squared is one, so the final equation is:

(x + 2)^2 + (y + 5)^2 = 1

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Use complete sentences to describe why it is valid to say that both a function and its inverse describe the same relationship.

Serhud [2]

Answer:

Step-by-step explanation:

A comparison between a function and its inverse would show that the domain and range of the original function swap. The domain of the function becomes the range of the inverse, the range of the function becomes the domain of its inverse.

Looking at ordered pairs of the function and its inverse would look like this:

(2,4) on the original function becomes (4,2) on the inverse.

While the graph of a function and its inverse are noticeably different an important thing to note is that it is merely a reflection across the line y=x.

So even though they appear different you are looking at the same relationship just as y vs. x instead of x vs. y

I hope this helped you because i barley understood this myself.

Read more on Brainly.com - brainly.com/question/2834818#readmore

3 0

3 years ago

The vertices of shape K are at (4,7), (7, 7), (7,4) and (5, 5).

son4ous [18]

Answer:

To find the scale factor of the enlargement, compare the distance between a pair of corresponding points from both shapes.

Shape K

A = (4, 7)

B = (7, 7)

C = (7, 4)

D = (5, 5)

Horizontal distance between A (4, 7) and B (7, 7) = 3 units

Shape L

A' = (0, 11)

B' = (9, 11)

C' = (9, 2)

D' = (3, 5)

Horizontal distance between A' (0, 11) and B' (9, 11) = 9 units

9 ÷ 3 = 3

Therefore, Shape L is an enlargement of Shape K by scale factor 3.

To find the center of dilation (enlargement), draw two lines through 2 corresponding points (e.g. A and A', B and B') - the point of intersection of these lines is the center of dilation.

Therefore, the center of enlargement is (6, 5) (refer to the second attached image).