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Find the center of this circle by completing the square. x^2+y^2-6x+8y+10=0
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Answers

Answer 1
Answer:

Answer:

Center: (3, - 4)

Step-by-step explanation:

We can start to solve this problem by converting this equation into standard form. In other words, by completing the square --- (1)

Subtract " 10 " from either side of the equation x² + y² - 6x + 8y + 10 = 0

x² + y² - 6x + 8y = - 10

Step 1: Complete the square for the expression " x² - 6x "

Using the quadratic equation ax² + bx + c we know that a = 1, b = - 6, c = 0. Assume that d = b / 2a. We have...

d = - 6 / 2(1) = - 6 / 2 = - 3

Now let's assume that e = c - (b²) / 4a...

e = 0 - (-6)² / 4(1) = 0 - 36 / 4 = 0 - 9 = 9 (Substitute values d and e)

(x - 3)² - 9

Step 2: Respectively we can complete the square for the remaining expression " y² + 8y "

Here a = 1, b = 8, c = 0

d = 8 / 2(1) = 8 / 2 = 4

e = 0 - (8)² / 4(1) = 0 - 64 / 4 = 0 - 16 = - 16 (Substitute values)

(y + 4)² - 16

This leaves us with the expression " (x - 3)² - 9 + (y + 4)² - 16 = - 10. " If we simplify this a bit further it leaves us with the following circle equation. Using this we can identify the center of the circle as well --- (2)

\mathrm{Standard}\:\mathrm{Circle}\:\mathrm{Equation} : (x - 3)^2 + (y +4)^2 = 15,\n\mathrm{General}\:\mathrm{Form} : (x - h)^2 + (y +k)^2 = r^2,\n\mathrm{Properties} : \mathrm{Center} = (3, - 4), \mathrm{Radius} = √(15)

As you can see our center here is (3, - 4)

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A fox leaves its den and travels 725 yards northeast, then 950 yards west. How far, in yards is the fox from its den

Answers

Using Pythagoras,the distanceof the fox from its den would be 533.26 yards

  • Hypotenus = 900 yards

  • Adjacent = 725 yards

  • Distance from den = opposite

Opposite = √hypotenus² - adjacent²

Distance = √(900)² - (725)²

Distance = √810000 - 525625

Distance = √284375

Distance = 533.26yards

Therefore, the fox is 533.26yards from his den.

Learn more : Opposite = √hypotenus² - adjacent²

Answer:

1,675

Step-by-step explanation:

add it

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?

Answers

Answer:

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

After 11 hours of burning, a candle has a height of 23.4 centimeters.

After 30 hours of burning, its height is 12 centimeters.

What is the height of the candle after 13 hours?

:

Assign the given values as follows:

x1 = 11; y1 = 23.4

x2 = 30; y2 = 12

:

Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29

m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19

:

Find the equation using the point/slope formula: y - y1 = m(x - x1)

y - 23.4 = -11.4%2F19(x - 11)

y - 23.4 = -11.4%2F19x + 125.4%2F19

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19

y = -11.4%2F19x + 570%2F19

y = -11.4%2F19x + 30, is the equation

:

What is the height of the candle after 13 hours?

x = 13

y = -11.4%2F19(13) + 30

y = -148.2%2F19 + 30

y = -7.8 + 30

y = 22.2 cm after 13 hrs

Anurak has nickels, dimes, and pennies in his pocket. The coins in Anurak's pocket have a total value of 75 cents. He has three more nickels than dimes and five times as many pennies as dimes. How many coins of each type does Anurak have?

Answers

Answer:

Anurak has 15 pennies, 6 nickels and 3 dimes.

Step-by-step explanation:

We must have these informations in mind:

1) A penny is a 1-cent coin.

2) A dime is a 10-cent coin.

3) A nickel is a 5-cent coin.

Let be x, y, z the quantities of pennies, nickels and dimes, respectively. From statement we get that to value in Anurak's pocket is represented by this mathematical expression:

0.01\cdot x + 0.05 \cdot y + 0.10\cdot z = 0.75(Eq. 1)

In addition, we get the following identities:

i)He has three more nickels than dimes

z + 3 = y(Eq. 2)

ii)And five times as many pennies as dimes

x = 5\cdot z(Eq. 3)

The system of linear equations is now reduced: (Eqs. 2, 3) in (Eq. 1)

0.05\cdot z +0.05\cdot z + 0.15 + 0.10\cdot z = 0.75

0.20\cdot z = 0.60

z = 3

The remaining variables are y = 6 and x = 15.

Anurak has 15 pennies, 6 nickels and 3 dimes.

Answer:

Anurak has 15 pennies, 6 nickels and 3 dimes.

Step-by-step explanation:

Solve for x.
8x=4x−32
A)x = 8
B)x = 4
C) x=−4
D) x=−8

Answers

Answer:

x=-8

Step-by-step explanation:

i took the quiz

Answerd

                     

Step-by-step explanation:

Dan will be 8X years next year. how old was Dan five years ago. give your answer in terms of X

Answers

If Dan is 8x years old next year then he must be 8x-1 years old this year
With the same logic, five years ago from this year, he must be 8x-1-5=8x-6

The answer should be 8x-6

A line with a slope of -1/2 passes thru the point (-4,3)...Which equation represents this line?

Answers

Here you go!! Hope this helps!!!!

Answer: Go to a website called m a t h w a y

Step-by-step explanation:

1. It's really good for all kinds of math problems

2. It lets you answers to one question in different ways to give you the best possible answer!!!

3. IT'S FREE!!!!!!!
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