x2+y2-4+2y-11=0 what are the center and radius of the circle?

Answers

Answer 1

[tex] x^2 + y^2 - 4x + 2y - 11 = 0 [/tex]

You need to complete the square for both x and y.

[tex] x^2 - 4x + y^2 + 2y = 11 [/tex]

[tex] x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 [/tex]

[tex] (x - 2)^2 + (y + 1)^2 = 16 [/tex]

[tex] (x - 2)^2 + (y + 1)^2 = 4^2 [/tex]

The center is (2, -1).
The radius is 4.

Related Questions

Madeline is financing $321,800 to purchase a house. How much money will she save over the life of a 20 year fixed rate loan by buying five points with the rate of 4.23% instead of not buying points with the rate of 5.18%? Round to the nearest dollar. (show work)

A= $39,984
B= $23,894
C= $36,697
D= $36,766

Answers

Did you get an answer yet?

Below is the graph of y=b^x. Find b.

Answers

y = b^x

when x = 1
y = b^1
y = b

Therefore, the value of b is the same as the value of y when x =1
From the graph,
When x = 1, y = 0.5
Therefore, b = 0.5

To confirm this

From the graph,

When x = -1, y = 2
Since y = b^x
2 = b^-1
2 = 1/b
2b = 1
b = 0.5

When x = -2, y = 4
Since y = b^x
4 = b^-2
4 = 1/(b^2)
b^2 = 1/4
b = √(1/4)
b = 1/2
b = 0.5

Therefore, it is conformed that b = 0.5

Functions can be represented as equations, and equations can be represented as functions.

The value of b is 1/2

The graph is given as:

[tex]\mathbf{y = b^x}[/tex]

From the graph, we have the following point:

(x,y) = (-1,2)

Substitute these values in the function

[tex]\mathbf{2 = b^{-1}}[/tex]

Rewrite as:

[tex]\mathbf{2 = \frac{1}{b}}[/tex]

Multiply both sides by b

[tex]\mathbf{2b = 1}[/tex]

Divide both sides by 2

[tex]\mathbf{b = \frac{1}2}[/tex]

Hence, the value of b is 1/2

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Which kind of function best models the data in the table? Use differences or ratios.

A. linear
B. quadratic
C. exponential
D. none of the above

Answers

The data in the table represents a C. exponential function. In an exponential function, as x-values increase, y-values get greater and greater. The y-values increase more rapidly as x-values increase linearly.

The answer would be B. Hope this helps :)

helppp how do u do 12

Answers

B is the correct answer

[tex] \frac{x}{100} = \frac{53}{106} \\ x = \frac{53 \times 100}{106} = \frac{5300}{106} = 50[/tex]

good luck

[tex]\begin{array}{ccc}\$53.00&-&106\%\\\$x&-&100\%\end{array}\\\\cross\ multiply\\\\106x=53\cdot100\\\\106x=5,300\ \ \ \ |:106\\\\\boxed{x=50}\\\\Answer:\ \boxed{\$50} [/tex]

There are 5 cars to be displayed in 5 parking spaces, with all the cars facing the same direction. of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. if the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

Answers

For questions like these, I believe you use permutations. Basically you mutiply all the numbers in the set together. so in this case there are five, so you multiply numbers 1-5 together in order to get the total arrangements possible.

For example :
[tex]1 \times 2 \times 3 \times 4 \times 5 = 120[/tex]
There you go :)

Final answer:

The question relates to combinatorial mathematics and asks for possible arrangements of 5 cars of three different colors. Treating identical colors as one entity, we find that there are 6 ways to arrange the color groups and another 6 ways to arrange the red cars among themselves, resulting in 36 possible arrangements.

Explanation:

The subject of this question is combinatorial mathematics. We're asked how many different arrangements there are if we have 5 cars to be displayed in 5 parking spaces, with the condition that the cars are identical besides their color; 3 of them are red, 1 is blue, and 1 is yellow.

Since three cars are identical (red ones), we treat them as one. So initially, we have three 'entities' to arrange: the red group (of 3 cars), the blue car, and the yellow car. These can be arranged in 3! (which means 3 factorial, or 3 * 2 * 1) = 6 ways.

However, within the red group, those 3 red cars can be arranged amongst themselves in 3! = 6 ways.

Therefore, to get the total number of arrangements, we multiply these results together, giving us: 6 * 6 = 36 different arrangements.

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"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"

Answers

Given that only the top 1% are admitted, the cutoff will be as follows:
the z-score is given by:
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
P(x>X)=1-P(z<Z)=0.01
⇒P(z<Z)=1-0.01=0.99
thus:
the value of z that corresponds to 0.99 is 2.33
thus:
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8
thus the cutoff was 739.8

Algebra question ( Matrices and Determinants ) 20 points

Answers

The correct answer is option A

The answer is as following
The new matrix is 2 rows and 2 columns . i.e. it is 2*2 matrix
The element a₁₁ =5*2 + 0*2 = 10
The element a₁₂ = 5*-1 + 0*-2 = -5
The element a₂₁ = 3*2 +-5*2 = -4
The element a₂₂ = 3*-1 + -5*-2 = 7

The new matrix will be [tex] \left[\begin{array}{ccc}10&-5\\-4&7\end{array}\right] [/tex]

What does the underlined conjunction connect in the sentence? The family enjoyed fishing, but they loved hiking during their trip. A. sentences B. predicates C. subjects D. direct objects

Answers

the answer is c objects

An irregularly shaped stone was lowered into a graduated cylinder holding a volume of water equal to 20mL. The height of the water rose to 30.2mL. If the mass of the stone was 25g what was its density?

Answers

Answer:
density = 2.4509 g/ml

Explanation:
1- getting the volume of the stone:
since the stone has an irregular shape, the volume of the stone would be equal to the increase in the volume of the stone after placing the stone in it.
Initial volume of water = 20 ml
Final volume of water = 30.2 ml
volume of stone = final volume of water - initial volume of water
volume of stone = 30.2 - 20 = 10.2 ml

2- getting the density of the stone:
we have:
volume of stone = 10.2 ml
mass of stone = 25 g
Therefore, we can get the density as follows:
density = mass / volume
density = 25 / 10.2
density = 2.4509 g/ml

Hope this helps :)

Final answer:

To find the density of the stone, subtract the initial volume of water from the final volume, then divide the mass of the stone by the volume. The density of the stone is 2.45 g/cm³.

Explanation:

In order to find the density of the stone, we first need to calculate its volume. The volume can be determined by subtracting the initial volume of water in the graduated cylinder from the final volume with the stone submerged. In this case, the volume of the stone is 30.2 mL - 20 mL = 10.2 mL.

Next, we can use the formula for density: density = mass/volume. Plugging in the given values, we have density = 25 g/10.2 mL.

Since density is mass divided by volume, we need to convert mL to g/cm³. 1 mL is equal to 1 g/cm³. Therefore, the density of the stone is 25 g/10.2 mL = 2.45 g/cm³.

What do the graphs of sine and cosine have in common with the swinging you see?
Which reasons did you think of?

Answer:
The high and low points repeat in a pattern.
The cycle repeats at equal time intervals.
The swinging motion is smooth, unabrupt.

Answers

Final answer:

The graphs of sine and cosine functions have similarities with the swinging motion such as repeating patterns at equal time intervals and smoothness.

Explanation:

The graphs of sine and cosine functions have several similarities with the swinging motion you observe:

Both the high and low points in the graphs of sine and cosine functions repeat in a pattern, just like the motion of a swing repeating from its highest to lowest points.The cycle of both graphs repeats at equal time intervals, just like the swinging motion of a swing that takes the same amount of time to swing back and forth.The swinging motion of a swing is smooth and uninterrupted, just like the graphs of sine and cosine functions.

These similarities are because simple harmonic motion, which includes swinging, is closely related to sine and cosine waves.

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In this figure, angle 3 = (2x+15) and angle 6 = (3x+10)

What value of x makes a || b?

Answers

[tex]\angle3+\angle6=180^o\\\\\text{substitute}\\\\(2x+15)+(3x+10)=180\\\\2x+15+3x+10=180\\\\5x+25=180\ \ \ |-25\\\\5x=155\ \ \ |:5\\\\\boxed{x=31}[/tex]

5 plus 5 divided by 2 times 300032 plus 6

Answers

750,091
5/2=2.5
2.5x300,032
750,080+11
750,091

5 + 5/2 * 300032 + 6

STEPS:

DIVIDE AND MULTIPLY:

5 + 5/2 (300032) + 6

= 5 + 750080 + 6

ADD:

= 750085 + 6

= 750091

FINAL ANSWER: 750091

You flipped a coin 70 times and recorded 23 heads. What is the experimental probability of flipping tails?

ANY HELP IS APPRECIATED!
Please show work

Answers

The experimental probabilities relies on the fact of actual occurrence of the experiment and events. It is the ratio of the number of times an event is occurring to the total number of times that activity has been repeated for.
thus:
experimental probability of our case will be:
P(H)=(# of times of occurrence of the event)/(# of trials)
=23/70
So the probability of getting a head in the experiment is 23/70=0.33

Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be?

15°

30°

45°

60°

Answers

Answer:

It would be 30

Step-by-step explanation:

I did it on plato

A toy company produces two kites whose shapes are geomaetrically similar. Find the length of the missing size of similar kite.

Answers

your answer is x=17.5

Joy started with 2.75 gallons of milk. She used 1.5 pints to make mashed potatoes and another cup to make cookies. How much milk does joy have left?

Answers

Amount of cups Joy has=2.75
1 cup=0.0625 gallons
1 pint=0.125 gallons
amount used to make mashed potatoes:
1.5×0.125=0.1875 gallons
amount used to make cookies=0.0625 gallons
total amount of milk used:
0.0625+0.1875=0.25

Remaining amount
=2.75-0.25=2.5 gallons

Isabel is purshing a 5 pound bag of dog food.how many 8- ounce servings can she feed her dog (1lb=16oz

Answers

1 pound = 16 ounces
16 ounces / 8 ounces = 2 servings per pound

5 pound bag x 2 servings per pound = 10 total servings

find two consecutive even integers such that twice the smaller is 16 more than the larger

Answers

Define x:
Let one of the numbers be x.
The other number is x + 2

Construct equation:
twice the smaller is 16 more than the larger
⇒2x = x + 2 - 16

Solve x:
2x = x + 2 - 16
x = -14

Find the two numbers:
Smaller number = x = -14
Larger number = x + 2 = -12

Answer: The two numbers are -14 and -12

Let's make an equation. X will be the smaller number while y is the bigger.
x+2=y; since they're consecutive even numbers. We will use that equation to represent y.
Twice the smaller; 2x
16 more than the larger; 16+x+2
2x=16+x+2; let's add like terms.
2x=18+x
Let's subtract x from both sides.
x=18
If the smaller number is 18, the bigger number is 20.

The two numbers are 18 and 20.

Suppose you want to organize a community watch, one from each street. you have 5 volunteers from maple street and 3 volunteers from elm street. how many permutations do you get?

Answers

There would be 15 different options for the community watch.

One one side there are 5 volunteers and on the other side there are 3 volunteers. You just have to multiply 5 by 3 and you get 15 different options.

If 6 is 30% of a value,
a.what is 70% of that value? b8 is omlwhat is 10%of the value?

Answers

70% is 14. And 10% is 2

so if 6 is 30% of a value we know that the value let's say x multiplied by .3 is 6. so we can write an equation to solve for the value x
[tex].3x = 6 \\ x = \frac{6}{.3} \\ x = 6 \times \frac{10}{3} = 20[/tex]

so our value is 20 and as 10% of 20 is 2 we see 30% of 20 is 2×3=6

now we want to find 70% of 20 and 10% of 20. we already know 10% of 20 is 20 because to find 10% we take the value 20.0 and move the decimal 1 place to the left which gives us 2.0. To find 70% we can multiply 20 by .7 or since we know 10% just multiply that by 7 because 10% ×7 =70% so 2×7=14 so 14 is 70% of 20. solving the other way we get
[tex]20 \times .7 = 20 \times \frac{7}{10} = \frac{20}{10} \times 7 = 2 \times 7 \\ = 14[/tex]
so we can see we are correct!

if you like my answer please rate as brainliest! thx

Nearly 90 percent of the people of indonesia are _______.

Answers

Answer: Muslims

Total Muslims in Indonesia is approximately 207.2 million or 87.2 (90%) of the total population. Other religions recognized by the Indonesian government aside from Islam are Protestant, Catholic, Hindu, Buddhism, and Confucian which accounts for 6.9,2.9,1.7,.7 and .05% of the total population, respectively.

Religion is a mandatory personal data to the Indonesians.

Answer:

MUSLIMS

Step-by-step explanation:

Find the absolute maximum value of the function

Answers

The answer to this question is 1. If we differentiate each piece, we get
                       f'(x) = {2,          -2 < x < 0
                                  { -2x,       x>0
The critical number is x = 0. We can also see that f(x) is decreasing on x>0.
We check the end points and critical numbers for the absolute maximum. One end point at
                                   f(-2) = 2(-2) + 1 = -3
The critical number checked gives
                                    f(0) = -0^2 + 1 = 1
The absolute maximum value is 1.

A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is the theoretical probability of rolling a 4?

A. 47/120; 1/30
B. 47/120; 1/6 ******
C. 4/47; 1/6
D. 1/6; 47/120

Am I Correct?

Answers

Yes you are.
(Your answer is B, right?)

A number cube is rolled 120 times. The number 4 comes up 47 times.

We have to determine the experimental probability of rolling a 4.

The formula to evaluate probability of an event is given by:

Probability = [tex] \frac{Favourable outcomes}{Total outcomes} [/tex]

So, Probability of rolling a 4 = [tex] \frac{ Total number of times when 4 appears}{Total number of times number cube rolled} [/tex]

= [tex] \frac{47}{120} [/tex]

Now, we have to find the theoretical probability of rolling a 4.

Total number of outcomes of number cube = {1,2,3,4,5,6}

Probability of rolling a 4 = [tex] \frac{1}{6} [/tex]

So, Option B is the correct answer.

Anyone know the answer?

Answers

Hi there your answer would be d

The answer is D. 77.

HELP PLEASE Simplify the rational expression. State any excluded values. x^2-12x+35/x^2-3x-10

Answers

[tex]\frac{{x}^{2} - 12x + 35 }{ {x}^{2} - 3x - 10 } [/tex]
Factorise both the term by splitting the mid term and you'll get

[tex] \frac{ {x}^{2} - 5x - 7x + 35}{ {x}^{2} - 5x + 2x - 10 } \\ = \frac{x(x - 5) - 7(x - 5)}{x(x - 5) + 2(x - 5)} \\ = \frac{(x - 7)(x - 5)}{(x + 2)(x - 5)} \\ = \frac{x - 7}{x + 2} [/tex]

Will give brainliest! pts to the correct answer! Are quadratic equations already in rectangular form? I'm asked to eliminate the parameter t from these two questions to get it into the rectangular equation with x and y. Is it possible?
x(t) = 0.5t^2+0.4t-87.30
y(t)= 0.4t^2+0.1t +29.44

Answers

[tex]\bf x(t)=0.5t^2+0.4t-87.30\implies x(t)=\cfrac{1}{2}t^2+\cfrac{2}{5}t-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left( t^2+\cfrac{4}{5}t+\boxed{?}^2 \right)-\cfrac{873}{10}[/tex]

so, as you already know, we'll borrow from our good friend Mr Zero, 0, to get that missing value for the perfect square trinomial,

[tex]\bf x=\cfrac{1}{2}\left[ t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2-\left( \cfrac{2}{5} \right)^2 \right]-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\cfrac{4}{25}-\cfrac{4}{25} \right]-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2\right]-\cfrac{2}{25}-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2\right]-\cfrac{4369}{50}[/tex]

[tex]\bf x=\cfrac{1}{2}\left( t+\frac{2}{5} \right)^2-\cfrac{4369}{50}\implies x+\cfrac{4369}{50}=\cfrac{1}{2}\left( t+\frac{2}{5} \right)^2 \\\\\\ 2x+\cfrac{4369}{25}=\left( t+\frac{2}{5} \right)^2\implies \sqrt{2x+\cfrac{4369}{25}}=t+\cfrac{2}{5} \\\\\\ \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5}=t[/tex]

[tex]\bf -------------------------------\\\\ y(t)=0.4t^2+0.1t+29.44\implies y=\cfrac{2}{5}t^2+\cfrac{1}{10}t+\cfrac{736}{25} \\\\\\ y=\cfrac{2}{5}\left( \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5} \right)^2+\cfrac{1}{10}\left( \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5} \right)+\cfrac{736}{25}[/tex]

When i am divided into 22, the remained is one. when i am added to 5, the answer is an even number. what number am i? * 5 7 9 10 4 2/5?

Answers

Working with the given answers we can find the correct answer. Indeed, it is a comfortable and cozy way to solve this problem. We have given 5, 7, 9, 10, 4 and 0.4. Among these numbers, if we take 7 we can see that when 22 is divided into that, 1 is remaining and when we sum up 7 and 5, the result is 12, which is an even number. The correct answer is 7

Answer:

Number is 23.

Step-by-step explanation:

We have been given the information when a number is divided by 22 the remainder is 1.

And when it is added to 5 it will give us an even number.

So, the number 23 if we take when divided by 22 it will give the remainder 1.

And when added to 5 it will give 23+5=28 which is an even number.

So, the number is 23.

I would appreciate it if someone could please check my work on this calculus problem! My steps/answers are in green.

Answers

A. Correct.
B. Some error in evaluation. The result should be near 2.10592505299.
C. Your final answer should have ln(2) in the denominator. The evaluation should be near 1.354326176.
D. Need ln(4) in the denominator everywhere. The evaluation should be near 79.408765453.

XXXXHELPXXXX
Choose the equation that represents the graph below:

Answers:

y = −2x − 6
y = 2/3x + 6
y = −2/3x + 6
y = 2x + 6

Answers

y= -2/3x+6 is the answer.

you got this fam????????????????????????????????

A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.

What is the vertical clearance 7 m from the edge of the tunnel?

Answers

Answer: 15.75 m

Explanation:

1) Since the vertex is at the origin, i.e point (0,0), and the simmetry axis is paralell to the vertical axis, you know that the canonical equation of the parabola is:

y = -4px², where p is the focal distance.

You can also use y = ax², where a = -4p.

2) Using y = ax², you can find a from the fact that at x = 8 (one edge of the tunnel), y = - 16 ( negative value of the height).

Substitute those values (8,16) in the equation y = ax², and you get:

- 16 = a (8²) ⇒ a = - 16 / 64 = - 1/4

Therefore, the equation of the parabola is: y = (-1/4)x².

3) To find the vertical clearance at 7 m from the edge of the tunnel, you must realize that the x-coordinate is x = 8 - 7 = 1.

Then, find y for x = 1:

y = (-1/4)(1²) = - 1/4 = - 0.25

That is the y-coordinate; the clearance is the 16m - 0.25m = 15.75m

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