A circle is centered at J(3, 3) and has a radius of 12.
Where does the point F(-6,-5) lie?
Choose 1 answer:
A.- Inside the circle
B.-On the circle
C.- Outside the circle

A Circle Is Centered At J(3, 3) And Has A Radius Of 12.Where Does The Point F(-6,-5) Lie?Choose 1 Answer:A.-

Answers

Answer 1

Answer:

[tex](-6,\, -5)[/tex] is outside the circle of radius of [tex]12[/tex] centered at [tex](3,\, 3)[/tex].

Step-by-step explanation:

Let [tex]J[/tex] and [tex]r[/tex] denote the center and the radius of this circle, respectively. Let [tex]F[/tex] be a point in the plane.

Let [tex]d(J,\, F)[/tex] denote the Euclidean distance between point [tex]J[/tex] and point [tex]F[/tex].

In other words, if [tex]J[/tex] is at [tex](x_j,\, y_j)[/tex] while [tex]F[/tex] is at [tex](x_f,\, y_f)[/tex], then [tex]\displaystyle d(J,\, F) = \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}[/tex].

Point [tex]F[/tex] would be inside this circle if [tex]d(J,\, F) < r[/tex]. (In other words, the distance between [tex]F\![/tex] and the center of this circle is smaller than the radius of this circle.)

Point [tex]F[/tex] would be on this circle if [tex]d(J,\, F) = r[/tex]. (In other words, the distance between [tex]F\![/tex] and the center of this circle is exactly equal to the radius of this circle.)

Point [tex]F[/tex] would be outside this circle if [tex]d(J,\, F) > r[/tex]. (In other words, the distance between [tex]F\![/tex] and the center of this circle exceeds the radius of this circle.)

Calculate the actual distance between [tex]J[/tex] and [tex]F[/tex]:

[tex]\begin{aligned}d(J,\, F) &= \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}\\ &= \sqrt{(3 - (-6))^{2} + (3 - (-5))^{2}} \\ &= \sqrt{145} \end{aligned}[/tex].

On the other hand, notice that the radius of this circle, [tex]r = 12 = \sqrt{144}[/tex], is smaller than [tex]d(J,\, F)[/tex]. Therefore, point [tex]F[/tex] would be outside this circle.

Answer 2

Answer:

outside the circle

Step-by-step explanation:

khan


Related Questions

The graph shown below displays the change in the average temperature of the world over time.
Which statement is the best description of the association between these variables?
Choose 1 answer:
A: As time went by, the average temperature tended to increase.
B: As time went by, the average temperature tended to decrease.
C: There is no clear relationship between time and average temperature.

Answers

Answer:a

Step-by-step explanation: you can clearly see that the points are going up

As time went by, the average temperature tended to increase.

What is scatter plot?

A graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present.

Given is the graph shown below displays the change in the average temperature of the world over time.

The scatterplot has a positive correlation. This means that as time went by, the average temperature tended to increase.

Therefore, as time went by, the average temperature tended to increase.

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A person can pay $33 for a membership to the art museum and then go to the museum for
just $1 per visit. What is the maximum number of visits a member of the art museum can
make for a total cost of $42?

Answers

33 is the starting price. so subtract 42 from 33 and you get 9 visits

Ken ran 2.5 kilometers, 5,250 meters and 75,650 centimeters. how many total meters did Ken run?​

Answers

Answer:

The answer is 2.77 km.

Step-by-step explanation:

8506.5 meters Ken ran

Greatest common factor 20x76 and 8x92

Answers

Answer:

dont know this one my apologies


please i’ve been stuck on this for days i need help

Answers

Answer:

x=12, y=9, z=7, w=3

Step-by-step explanation:

are they cute ? say yes it’s 100 points

Answers

Answer:

they all are super cute.

yes! thanks for free points.

A 98% confidence interval for a proportion is found to be (0.72, 0.78). What is
the sample proportion?

Answers

Answer: 0.75 appex

Step-by-step explanation:

The sample proportion is 0.75 if  98% confidence interval for a proportion is found to be (0.72, 0.78) option (C) is correct.

What is a confidence interval for population standard deviation?

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follows:

[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]

Where s is the standard deviation.

n is the sample size.

[tex]\chi^2_{\alpha/2, \ n-1} and \chi^2_{1-\alpha/2, \ n-1}[/tex] are the constant based on the Chi-Square distribution table:

α is the significance level.

σ is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

 

From the data the margin of error = (0.78 - 0.72)/2

MOE = 0.03

98% Confidence interval for a sample proportion:

n - 0.03 = 0.72

n + 0.03 = 0.78

The interval is (0.72, 0.78)

The sample proportion = 0.75

Thus, the sample proportion is 0.75 if  98% confidence interval for a proportion is found to be (0.72, 0.78) option (C) is correct.

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help plz plz plz

Pentagon ABCDE is similar to pentagon RSTUV . The perimeter of pentagon ABCDE is 36.8 centimeters.


What is the length of ST ?

19.8 cm
18 cm
25.8 cm
15 cm

Answers

Answer:

ST = 15 cm

Step-by-step explanation:

find BC first by adding four other sides and subtracting from 36.8

sum of 4 sides is 30.8, so BC = 6

Now find ST by creating a proportion from corresponding sides:

BC / ST = DE / UV

6 / ST = 13.2 / 33

Cross-multiply:

13.2ST = 198

ST = 198/13.2

ST = 15

Subtract 3x^2+8x3x 2 +8x from -9x^2+3x-8−9x 2 +3x−8.

Answers

Answer:

x =(-8+√-32)/6=(-4+2i√ 2 )/3= -1.3333+0.9428i

Step-by-step explanation:

A coffee shop sells 5 different types of cake and 6 different kind of drinks. Ruby wants to order a cake and a drink. How many different combinations of cake and drink could she choose?

Answers

Answer:

She could choose 30 different combinations of cake and drink

Step-by-step explanation:

A coffee shop sells 5 different types of cake and 6 different kind of drinks.

This means that:

For each type of cake, there are 6 different kind of drink.

At all, there are 5 different types of cake.

So

6*5 = 30

She could choose 30 different combinations of cake and drink

help me please people

Answers

Point Form:
(-1, -10)
Equation Form:
X = -1, y = -10

Evaluate -2x^2y, if x = -3 and y=-1.
-12
18
12
-18

Answers

Answer:

Option A is your answer

Which rational number equals 0 point 2 with bar over 2

Answers

1. 0.2/2 = 1 and one is also rational


Can someone help me find the value of n? For this problem

Answers

Answer:

n = 129

Step-by-step explanation:

Reference angle = 60°

Hypotenuse = n

Adjacent side = 64.5

Apply CAH, which is:

Cos 60 = adj/hyp

Cos 60 = 64.5/n

Multiply both sides by n

n×Cos 60 = 64.5

Divide both sides by cos 60

n = 64.5/Cos 60

n = 64.5/0.5

n = 129

pls this is due soon helopppp

Answers

I believe is 25 minutes and 30 seconds or 25 1/2 minutes
I get 25 mins and 30 sec.

help pls i'll give brainliest, are they inverses or not explain why or why not

Answers

Answer:

no

Step-by-step explain why

because they have to be the same numbers

help please I need help very bad​

Answers

Answer:

(8,2)

Step-by-step explanation:

the third option

Answer:

i guess (8,2)

Step-by-step explanation:

it's where both lines intercept

Diana and Michael, who are taking different classes, are arguing about who did better on their most recent test. Diana received a score of 92 on her History test and Michael received a 688 on his Math test. The mean test score for the History class is 71 with a standard deviation of 15.The mean test score for the Math class is 493 standard deviation of 150. Who did better, relative to other students in the same class? Justify your answer.

Answers

Answer:

Diana's score is better.

Step-by-step explanation:

In Diana case :

Score = 92

Mean score , μ = 71

Standard deviation σ = 15

So,

P( x ≥ 92 ) = 1 - P( x ≤ 92 )

                = 1 - P(z ≤ [tex]\frac{x - u}{\sigma}[/tex] )

                = 1 - P( z ≤ [tex]\frac{92 - 71 }{15}[/tex] )

                = 1 - P( z ≤ 1.4 )

                = 1 - 0.9192

                = 0.0808 = 8.08 %

⇒P( x ≥ 92 ) = 8.08%

∴ we get

Diana score is > 91.92% other students in the class.

In Micheal case :

Score = 688

Mean score , μ = 493

Standard deviation σ = 150

So,

P( x ≥ 688 ) = 1 - P( x ≤ 688 )

                = 1 - P(z ≤ [tex]\frac{x - u}{\sigma}[/tex] )

                = 1 - P( z ≤ [tex]\frac{688 - 493 }{150}[/tex] )

                = 1 - P( z ≤ 1.3 )

                = 1 - 0.9032

                = 0.0968 = 9.68 %

⇒P( x ≥ 688 ) = 9.68%

∴ we get

Micheal score is > 90.32% other students in the class.

From both scores , we can conclude that

Diana's score is better.

Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $224 in interest after 2 years. How much money should he deposit? Can someone help me out I’m kind of struggling

Answers

Answer:

$7000

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 1.6%/100 = 0.016 per year,

then, solving our equation

P = 224 / ( 0.016 × 2 ) = 7000

P = $ 7,000.00

The principal required to

accumulate interest of $ 224.00

on a rate of 1.6% per year for 2 years is $ 7,000.00.

When a card is selected from a deck, find the probability of getting a. A club b. A face card or a heart c. A 6 and a spade d. A king e. A red card

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Number of clubs = 13

Number of face cards = 12

Number of hearts = 13

Number of King's = 4

Number of reds = 26

Number of spade = 13

Number of 6's = 4

Total possible outcomes = total number of cards = 52

Probability = required outcome / Total possible outcomes

1.) P(A club) = 13 / 52

2.) P(face card or heart) =

p(face card) + p(heart)

12 / 52 + 13/52

= (12 + 13) / 52 = 25 /52

3.)

(A 6 and a spade)

4/52 * 13/52

= 52 / 2704

= 1/52

4.) A king

P(king) = 4 /52 = 1/13

5) A red

P(red) = 26 / 52 = 1/2

Find the average rate of change of f(x)=9x^2-2 on the interval of [1,t]

Answers

Answer:

[tex]Rate = 9(t+1)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 9x^2 - 2[/tex]

[tex]Interval = [1,t][/tex]

Required

Determine the average rate of change

This is calculated using:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex][a,b] = [1,t][/tex]

So, we have:

[tex]Rate = \frac{f(t) - f(1)}{t - 1}[/tex]

Solve for f(t) and f(1)

[tex]f(t) = 9t^2 - 2[/tex]

[tex]f(1) = 9*1^2 - 2[/tex]

[tex]f(1) = 9 - 2[/tex]

[tex]f(1) = 7[/tex]

So, we have:

[tex]Rate = \frac{9t^2 - 2 - 7}{t - 1}[/tex]

[tex]Rate = \frac{9t^2 - 9}{t - 1}[/tex]

Factorize:

[tex]Rate = \frac{9(t^2 - 1)}{t - 1}[/tex]

Apply difference of two squares

[tex]Rate = \frac{9(t- 1)(t+1)}{t - 1}[/tex]

[tex]Rate = 9(t+1)[/tex]

Help me out here ✏️ Mathematics

Answers

Answer:

it's definitely F .. Your welcome

What's the correct formula for this function? ​

Answers

Answer:

Option C. y = -2x + 3

Step-by-step explanation:

When we look at this function we see that it has a negative slope and the y-intercept is equal to (0,3).  From this we know that the function we are looking for will be looking like...

y = mx + 3

And as I said earlier since the slope is negative, the only right option is this case will be Option C

Answer:

The correct anwer is (C) : y = - 2x + 3

4.
The probability that I will go sailing today AND the fair six-sided die will come up even on the next roll is .3.
these events are independent, what is the probability that I will go sailing today?

Answers

Answer:

Step-by-step explanation:

Let us consider P(A) to be the probability for the fact that I will go for sailing today

Likewise, P(B) will be the probability of a die to come up on an even number in the next roll.

Now, according to the question,

P(A and B) = 0.3

It is known to us that the probability of a die to land with an even number on its side up =  

Moreover, we are given with the fact that both P(A) and P(B) are independent.

∴ P(A and B) = P(A) × P(B)

⇒ 0.3 = P(A) × 0.5

⇒ P(A) =  = 0.6

29 cm
10 cm
8 cm
34 cm
26 cm
39 cm
Find the area.

Answers

Answer:

1246 sq cm

Step-by-step explanation:

First, you find the area of the rectangle without the part cut out of it. Then, you find the area of the part cut out. Finally, you subtract the two.

34 x 39 = 1326

10 x 8 = 80

1326 - 80 = 1246

Given the following triangle, determine the measure of angle B to the nearest
degree

Answers

The answer is 12, Good luck!

Algebraic expressions can have a variable, operational symbols, and numbers?
true or flase

Answers

This is true variables is a x in the equation, operational symbols are the plus sign (➕ ), and numbers are 1 2 3 etc...

Solve for x. + 9 = 30 x = 18 x = 24 x = 34 x = 44

Answers

Answer: 11 = x

Step-by-step explanation:

What is the product of 3.6 x 4.2

How did you find it.

Answers

Answer:

15.12

Step-by-step explanation:

3.6 x 4.2

first aline the decmials like you would regularly do to multiply.

Then multiply 2 x 6=12 and then 2 x 3=6 and put them down were you would already do noramly multiplying.

and then muliply 4x6=24 and 4x3=12 and do the same thing as you would do normaly and then add 72 and 144 to get 1512 and then count your decmail placing. which is 2 placeing in total which makes 1512 into 15.12

and now you done!

Example of how it should look...

       3   . 6

×       4   . 2

+       7   . 2

+   1 4 4  

=  1 5 1 2

Grayson is going to invest $710 and leave it in an account for 17 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Grayson to end up
with $920?

Answers

Answer:

1.52%

Step-by-step explanation:

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