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RUDIKE [14]
2 years ago
7

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and

calculations to receive credit.
x2 + 4x + y2 − 6y = −4
Mathematics
1 answer:
valentinak56 [21]2 years ago
8 0

The Center of the given circle is at (-2, 3) and radius of circle is 3.

<h3>How to use the method of completing the square?</h3>

The general form of equation of a circle is;

(x - h)² + (y - k)² = r²

Where h and k are the center and r is the radius of the circle;

The given equation of the circle is;

x² +  4x +  y² - 6y = -4

Add 4 to both sides to get;

x² +  4x +  4 + y² - 6y = 0

Factoring the x part gives;

(x + 2)² + y² - 6y = 0

Add 9 to both sides to get;

(x + 2)² + y² - 6y = 0

Factoring the y part gives;

(x + 2)² + (y - 3)² = 9

⇒ (x + 2)² + (y - 3)² = 3²

Comparing the above with the general circle equation form gives;

(h, k) = (-2, 3) and r = 3

Thus;

Center of circle is at (-2, 3) and radius of circle is 3.

Read more about Completing the square at; brainly.com/question/3350489

#SPJ1

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Katrina had a bookcase that holds 200 books. She can put 20 books on each shelf. If 20% of the bookcase is empty, how many shelv
Tom [10]

Answer:

First, find 20% of the 200 books. Then, subtract that amount by the total and divide that amount by 20 to receive your answer.

Step-by-step explanation:

20 x 200

/100  = 40

Therefore, there are 40 books missing.

200-40 = 160

160/20 = 8 shelves are filled with books.

There are 10 shelves in total: 160 books are on 8 shelves and 40 books are missing for 2 shelves

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3 years ago
Suppose marginal benefit of your first cup of coffee is $4 of your second is $3, and your third is $2 . If the price of coffee i
enot [183]
I would buy 69 cups of coffee
7 0
2 years ago
in the usa, the shoe sizes or men are approximated by the equation 3f-s=24, where f represents the length of the foot in inches
Otrada [13]

Answer:

x intercept = 8

y intercept = -24

Step-by-step explanation:

In the USA, the shoe sizes or men are approximated by the equation 3f-s=24, where f represents the length of the foot in inches and s represents the shoe size.

<u>When we represent this equation using a graph, we mark the independent variable on the x axis and the dependent variable on the y axis.</u>

Here the foot length is the independent variable and the shoe size is the dependent variable. Hence we take foot length on x axis.

To get x intercept put y=0, f = \frac{24}{3} = 8 inches .

This is the point from which where we start our shoe size.

The y intercept , s = -24.

8 0
4 years ago
The sum of three numbers is 104. The first number is 10 less than the second. The third number is 4 times the second. What are t
AnnyKZ [126]

Answer:

The numbers are 9, 19 and 76.

Step-by-step explanation:

Let's take the second number and make it a variable, like x. Now let's find all the other numbers in terms of x.

The first number in terms of x:

x - 10

The second number in terms of x:

4x

If we add them all up, these 3 numbers in terms of x must be equal to 104, so:

x + (x - 10) + (4x) = 104 \\ x + x - 10 + 4x = 104 \\ 6x - 10 = 104 \\ 6x = 114 \\ x = 19

Now that we know the second number, we can find the other numbers since we already figured out their values in terms of x:

19 - 10 = 9

4 \times 19 = 76

The first number is 9, second number 19 and the third number 76.

6 0
3 years ago
What is the answer to the problem I am stuck on?
liubo4ka [24]

Answer:

A

Step-by-step explanation:

1*1/4 is One lap, but you want 23 laps so exchange the 1 with a 23:

23*1/4

A

6 0
3 years ago
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