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lakkis [162]
2 years ago
11

What are the center and radius of the circle given by x^2 + y^2 - 16x + 8y + 4 = 0?

Mathematics
1 answer:
lukranit [14]2 years ago
3 0

The center of the circle = (8, -4)

The radius of the circle =  \sqrt{76}

<h3>Finding the center and radius of a circle from the equation</h3>

The given equation of the circle is:

x^2+y^2-16x+8y+4=0

The equation can be expressed and simplified as:

x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76

The general equation of a circle is:

(x-a)^2+(y-b)^2=r^2

Comparing the two equations:

The center, (a, b) = (8, -4)

The radius, r = \sqrt{76}

Learn more on the equation of a circle here: brainly.com/question/1506955

#SPJ1

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USPshnik [31]

Answer:

\dfrac{8}{3}\ \text{cups of orange juice} or 2\dfrac{2}{3}\ \text{cups of orange juice} is used

Step-by-step explanation:

Daniel uses the proportions of \dfrac{2}{3} cups of orange juice and \dfrac{1}{4} cups of carrot juice to make a mixed juice.

Now, in the question 1 cup of carrot juice is used. So 4 times of the proportion of the carrot juice is used. Accordingly 4 times of the cups of orange juice will be used.

\dfrac{2}{3}\ \text{cups of orange juice}=\dfrac{1}{4}\ \text{cups of carrot juice}\\\Rightarrow 4\times \dfrac{2}{3}\ \text{cups of orange juice}=4\times \dfrac{1}{4}\ \text{cups of carrot juice}\\\Rightarrow \dfrac{8}{3}\ \text{cups of orange juice}=1\ \text{cup of carrot juice}

So for one cup of carrot juice \dfrac{8}{3}\ \text{cups of orange juice} or 2\dfrac{2}{3}\ \text{cups of orange juice} is used.

4 0
2 years ago
|-6+8| = simplify the expression
lilavasa [31]

Answer:

2

Step-by-step explanation:

|-6+8|

Add/subtract the numbers: -6 + 8 = 2

= |2|

Apply the absolute value rule: |a| = a, a ≥ 0

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8 0
2 years ago
Explain which variables would be included when using technology to calculate the present value of a lump sum and to calculate th
koban [17]

Answer:

a. Present value of a lump sum =

PV = FV / ( 1 + i )ⁿ

b. Present value of an annuity =

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)

Step-by-step explanation:

a. Present Value of a Lump sum =

PV = FV / ( 1 + i )ⁿ

Where variables in the formula are explained as follows

PV = Present Value of the given amount today

FV = Future Value of the given amount

i = Discount rate

n = Number of periods

b. Present value of an annuity is given as:

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)

The variables in the equation are explained as the follows:

P = the present value of annuity

PMT = Payment per period or the amount in each annuity payment

r =  the interest or discount rate

n = total number of periods or the number of payments left to receive

8 0
3 years ago
The blue figure is a translation of the black image. Write a rule to describe the translation.
vivado [14]

Answer:

The point at the Origin was moved down 4 and right 2

Step-by-step explanation:

5 0
2 years ago
Each pair of figures below is similar. Find the lengths of all unknown sides​
lions [1.4K]

Answer:

  a) w = 8; y = 5.25

  b) x = 10; z = 7.2

Step-by-step explanation:

a) Dimensions on the smaller figure are FA/F'A' = 3/4 times those on the larger figure.

  6 = (3/4)w

  w = 24/3 = 8

  y = (3/4)·7 = 21/4 = 5.25

__

b) Dimensions on the smaller figure are ER/E'R' = 9/15 = 3/5 times those on the larger figure.

  6 = (3/5)x

  x = 30/3 = 10

  z = (3/5)12 = 36/5 = 7.2

7 0
2 years ago
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