A circle is defined by the equation x2 + y2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the length of the radius?

Answers

Answer 1

Answer:

The center of the circle is: (-4 ; -11) and the radius of the circle is r = 10

What is equation of circle?

The general equation for a circle is (x-a)² + (y-b)² = r², where ( a, b ) is the center and r is the radius.

Given:

x² + y² + 8x + 22y + 37 = 0.

Now, to find both coordinates and radius write the given equation in standard form:

(x-a)² + (y-b)² = r²

x² + 8x + y²+ 22y= -37

( x² + 2* x*4 + 4²)+( y² + 2*y* 11 + 11²) = -37 + 16 + 121

(x + 4)² + ( y+ 11)² = 100

(x + 4)² + ( y+ 11)² = 10²

So, center of the circle is: (-4 ; -11)

and the radius of the circle is r = 10

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Answer 2

Answer: We can say that:
8x = -2ax
8 = -2a
a = -4

22y = - 2by
22 = -2b
b = -11

37 = a² + b² - r²
37 = (-4)² + (-11)² - r²
r² = 16 + 121 - 37
r² = 100
r = 10

With all this information, we can say that:
The center of the circle is: (-4 ; -11)
and the radius of the circle is r = 10

P.S:
(a - x)² + (b-y)² = r²
a² - 2ax + x² + b² -2by + y² - r² = 0
x² + y² -2ax - 2by + a² + b² - r² = 0

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A container at a paper clip factory holds 2.1*10^3 pounds of paper clips. There are 9.6*10^5 paper clips in the container. Find the approximate weight of each paper clip in ounces. (1 pound= 16 ounces) Show Your Work.

Answers

Answer:

The approximate weight of each paper clip is 0.035 ounce.

Step-by-step explanation:

A container at a paper clip factory holds 2.1*10^3 pounds of paper clips.

= $2.1*1000=2100$ pounds

There are 9.6*10^5 paper clips in the container.

= $9.6*100000=960000$

Now we get that 960000 paper clips weigh 2100 pounds.

So, each paper clip will weigh = $(2100)/(960000)$ = 0.0021875 pounds

And 1 pound = 16 ounces

0.0021875 pounds = $16*0.0021875$ = 0.035 ounce

Hence, the approximate weight of each paper clip is 0.035 ounce.

Divide the total weight (2.1 * 10^3 lbs.) by the total quantity of things (9.6 * 10^5) to get the lbs./paperclip.

Then, multiply that number by 16 to get ounces/paperclip.

Which of the following is the best definition of the range of a relation? A. The set of all possible input values, or x-values
B. The set of all possible output values, or y-values
C. The set of all possible input values, or y-values
D. The set of all possible output values, or x-values

Answers

the answer is either a or c

What is the difference between -3 and five a number line

Answers

The answer to you’re question is 8

You are buying two kinds of coffee.1 pound of premium coffee costs $3.00.1 pound of regular coffee costs $2.00.You have $15.00 to spend and want to buy 1 pound of premium coffee.Use the number line to draw the solution set that shows all possible numbers of pounds of regular coffee that you could buy. Must be answered as an inequality: greater than, less than, greater than or equal to, less than or equal to, equal to.

Answers

Answer:

Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

$x\leq 7.5\ pounds$

Part 2) $m+n=(0.76x-0.28)$

Step-by-step explanation:

Part 1)

Let

x-----> the number of pounds of regular coffee

we know that

The inequality that represent the situation is

$2x\leq 15$

Solve for x

Divide by 2 both sides

$x\leq 15/2$

$x\leq 7.5\ pounds$

The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

The solution of the inequality is the interval ------> (-∞,7.5]

but the number of pounds cannot be a negative number

therefore

The solution is the interval -----> [0,7.5]

see the attached figure

Part 2) we have

$m=0.56x-0.25$

$m=0.20x-0.03$

Adds m and n

$m+n=(0.56x-0.25)+(0.20x-0.03)$

Group terms that contain the same variable

$m+n=(0.56x+0.20x)+(-0.25-0.03)$

Combine like terms

$m+n=(0.76x-0.28)$

What is 5*5+100-99*76

Answers

Answer:

-7399

Step-by-step explanation:

5*5+100-99*76

25 + 100 - 7524

= -7399

Answer:

-7399

Step-by-step explanation:

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( x − 3 )^2 as trinomial in standard form

Answers

Given (x - 3)^2, its trinomial in standard form, y = ax^2 + bx + c:

You must expand the binomial through FOIL method:

(x - 3)^2
x ^2 - 3x - 3x + 9

Combine like terms:

y = x^2 - 6x + 9
where a = 1, b = -6, and c = 9.

Please mark my answer as the Brainliest, if you find this solution helpful :)

Answer:

x^2 - 6x + 9

Step-by-step explanation:

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