What is m∠A? 45° 103° 77° 35°

Write the equation in standard form. Identity the center and radius. x² + y2 + 8x-4y-7=0

lorasvet [3.4K]

Answer:

equation;

$(x + 4) {}^{2} + (y - 2) {}^{2} = 27$

Center (-4,2)

Radius is

$3 \sqrt{3}$

Step-by-step explanation:

Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of

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

Where (h,k) is center

r is the radius

So first we group like Terms together

${x}^{2} + 8x + {y}^{2} - 4y - 7 = 0$

Add 7 to both sides

${x}^{2} + 8x + {y}^{2} - 4y = 7$

$( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7$

Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem

$(\frac{8}{2} ) {}^{2} = 16$

and

$( - \frac{4}{2} ) {}^{2} = 4$

so we have

${x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4$

${x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27$

$(x + 4) {}^{2} + (y - 2) {}^{2} = 27$

To find our center, h is -4 and k is 2

so the center is (-4,2)

The radius is

$\sqrt{27} = 3 \sqrt{3}$

So the radius is 3 times sqr root of 3.

8 0

2 years ago

a brand new candlestick has a length of one foot the candlestick is lit and left to burn at a rate of 1/2 inch per hour

Degger [83]

Answer:

24 hours

Step-by-step explanation:

One foot is 12 inches. 12÷1/2=24 so it will take 24 hours for the candle to burn down.

3 0

3 years ago

Which fraction shows the ratio 16:200 as a fraction simplified form

Molodets [167]

Answer:

16:200

4:50

2:25

So answer is C) 2/25

7 0

3 years ago

Read 2 more answers

Assume that long earlobes in humans are an autosomal dominant trait that exhibits 30% penetrance. A person who is heterozygous f

Bess [88]

Answer:

0.75

Step-by-step explanation:

Autosomal dominant: A pattern of inheritance in which an affected individual has one copy of a mutant gene and one normal gene on a pair of autosomal chromosomes

Heterozygous just means that a person has two different versions of the gene (one inherited from one parent, and the other from the other parent).

Being homozygous for a particular gene means you inherited two identical versions.

The trait is autosomal dominant so the characters pass into the next generation in a large ratio. the person who is heterozygous for the character have two type of allele which represents the trait for long earlobes and also for short earlobe.So a person is paired with homozygous individuals who have pure character for short earlobes.The percentage of their first child with long earlobes would be 75 percent. This is due to the dominance of the character in a generation.

3 0

3 years ago

Algebraic expression for 12 divided by t ?

Dimas [21]

Answer:

$\frac{12}{t}$

Step-by-step explanation:

To write an algebraic expression from words, translate each word into a symbol. Division can be shown with a division sign or a fraction sign. Create a fraction with a 12 in the numerator and the variable t in the denominator.

8 0

3 years ago