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sleet_krkn [62]
3 years ago
12

Gina started with the circle (x−2)2+y2=16. She translated it 4 units left and 1 unit down. Then she reduced the radius by 1 unit

. What is the equation of her new circle?
Mathematics
1 answer:
olchik [2.2K]3 years ago
5 0

Answer:

(x + 2)² + (y + 1)² = 9

Step-by-step explanation:

Gina started with a circle with the given equation as,

(x - 2)² + (y - 0)² = 16

Since, standard equation of a circle is,

(x - a)² + (y - b)² = r²

Here (a, b) is the center of the circle and 'r' is the radius.

Therefore, from the given equation of the circle,

Center of the circle → (2, 0)

Radius of the circle → √16 = 4 units

She translated this circle 4 units left and 1 unit down.

Rule for the new center after translation will be,

(x, y) → (x - 4, y - 1)

(2, 0) → (2 - 4, 0 - 1)

         → (-2, -1)

Coordinates of the new center → (-2, -1)

Then she reduced the radius by 1 units.

Therefore, radius of the new circle = 4 - 1 = 3 units

Now we substitute these values in the standard equation of the circle to get the equation of the new circle.

(x + 2)² + (y + 1)² = 3²

(x + 2)² + (y + 1)² = 9

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Hey there!!

Let's take the number as x and y

Given,

The sum of x and y = 12

One number is 2 more than the other

Let's take y = x + 2

Equations

x + y = 12

As we know y = x + 2 , plug the value in

x + x + 2 = 12

2x + 2 = 12

Subtract 2 on both sides

2x = 10

Divide by 5 on both sides

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y = 7

The numbers are 5 and 7

Hope my answer helps!

3 0
3 years ago
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A student wrote and simplified an expression for the perimeter of the rectangle. (Using the picture provided.)
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Step-by-step explanation:

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2 years ago
A cookie factory monitored the number of broken cookies per pack yesterday.
trapecia [35]

Answer:

Confidence Interval - 2.290 < S < 2.965

Step-by-step explanation:

Complete question

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 50 cookies. The mean is 23.33 and the standard deviation is 2.6. Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

Solution

Given  

n=50

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X^2(a/2,n-1) = X^2(0.10, 49) = 63.17

sqrt(63.17) = 7.948

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