Mathematics College

1.Show that the points (5,5),(6,4),(-2,4) and (7,1) are concyclic .Also find the equation ,centre and radius of the circle on which they lie.​

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

This is how I solved it.

Plotted the given points. See the attached.

Identified two pairs to connect, the two chords.

(5. 5) with (7, 1) and (6,4) with (-2, 4).

Determined the equation of both lines:

y -5 = [( 1 - 5)/(7-5)](x - 5) ⇒  y - 5 = -2(x - 5)y = -2x + 15

and

y = 4 (horizontal line)

Identified perpendicular bisectors of those two chords, they both pass through the center of circle.

Midpoints of the chords:

[(5 + 7)/2, (5 + 1)/2] = (6, 3)

and

(6 - 2)/ 2 = 2

The equations:

y - 3 = 1/2(x - 6) ⇒ y = 1/2x x = 2 (perpendicular to y = 4 and passing through x = 2)

Solving the system found the intersecting of those, the center.

Found the center:

(2, 1)

Found the distance from the center to one of the points (7, 1):

7 - 2 = 5, this is the radius

The equation of circle:

(x - 2)² + (y - 1)² = 25

Verified all the other points are on same circle, confirmed.

1.Show That The Points (5,5),(6,4),(-2,4) And (7,1) Are Concyclic .Also Find The Equation ,centre And

Related Questions

How do you solve the equation 3 1/5 +n=9?

Answers

Answer:

n = [tex]5\frac{4}{5}[/tex]

Step-by-step explanation:

You obviously have to solve for n

What is the measure of remote angle, ∠A?

Answers

Answer:

40

Step-by-step explanation:

Inscribed Angle =  1/2 Intercepted Arc

<A = 1/2 (80)

<A = 40

A boy is flying two kites at the same time. He has 450 ft of line out to one kite and 390 ft to the other. He estimates the angle between the two lines to be 34 degrees. Approximate the distance between the kites.

Answers

Answer:

[tex]C=252.2ft[/tex]

Step-by-step explanation:

From the question we are told that:

First Kite Distance [tex]A=450ft[/tex]

Second Kite Distance [tex]B=390ft[/tex]

Angle [tex]\theta=34\textdegree[/tex]

Generally the equation for Distance X between the kites is mathematically given by

Using Cosine Rule

 [tex]C^2=A^2+B^2-2abCos \theta[/tex]

Therefore

 [tex]C^2=(450)^2+(390)^2-2(450)(390)Cos 34[/tex]

 [tex]C^2=63607.81[/tex]

 [tex]C=\sqrt(63607.81)[/tex]

 [tex]C=252.2ft[/tex]

The track team has 12 more boys than girls. There are a total of 142 team members. How many boys and girls are on the team?

Answers

Answer:

77 boys, 65 girls

Step-by-step explanation:

x as the variable to represent amount of girls, and there are 12 more boys than girls (x+12). So the equation would be:

x + x + 12 = 142

2x + 12 = 142

x = 65

65 girls

then 65+ 12 = 77 boys

Assume the total cost of a college education will be $200,000 when your child enters college in 16 years. You presently have $55,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?

Answers

Answer:

8.4%

Step-by-step explanation:

let x = interest rate

55,000(1 + x)^16 = 200,000

divide both sides by 55,000

(1 + x)^16 = 3.636

find the invese of 16

1 + x = 1.084

x = 0.084

x = 8.4

Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor.

PLEASE ANSWER
The drop down selections are is is not for the first part and the second are is can/cannot
also, if there is a scalefactor please tell me what it is!

Answers

Answer:

Is can

Is can

1 is the answer

Step-by-step explanation:

But what’s the name of that topic?

Answer:

Is can

Is can

1 is the answer

Step-by-step explanation:

Plz help me well mark brainliest if correct..??

Answers

Answer:

C/5

Step-by-step explanation:

This is because there are 2 people in the 3| part, and 3 people under 6 in the 4| part.

What is the volume of the cone below?
O A. 396pie units 3
O B. 132 units 3
O C. 792pie units3
O D. 264pie units 3

Answers

Answer:

D. 264π units³

Step-by-step explanation:

1/3(πr²h)

1/3(π•6²•22)

1/3(π•36•22)

1/3(π•792)

264π

Kim took a 3,000 mile trip in 4 days.

1st day - 850 miles

2nd day - 745 miles

3rd day - 660 miles

How many miles did she travel the 4th day?

O A. 2265 miles

B. 745 miles

C. 855 miles

O D. 265 miles

E 755 miles

Answers

Answer:

B. 745 miles

Step-by-step explanation:

Given that

Kim took 3000 miles trip in 4 days

And,

1st day - 850 miles

2nd day - 745 miles

3rd day - 660 miles

We need to find out that how much she travel in the 4th day

So, it is

= 3000 miles - 850 miles - 745 miles - 660 miles

= 745 miles

Hence, the option b is correct

What is the exact measurement of the line segment?

Answers

It looks like it’s 3.25 or 3 and 1/4

Solve
4x > 16
..............​

Answers

Answer:

256. fffddddddssddddd

1. 4x > 16 = x > 4.

hope i could help

what is the length of the hypotenuse?

please help!

Answers

Answer:

34

Step-by-step explanation:

Hypotenuse is the longest side

I hope this helped have a great day

Find the degree measure 7pi/4 radians

Answers

The degree for 7pi/4 is : 315°

Wat is the average number between 1,000, 2300,1000,2600

Answers

Answer:

here summation x = sum of all number

Help with 5+5-3 please

Answers

Step-by-step explanation:

5+5-3= 7

!!!!!!!!!!!!!!!!!

Answer:

answer is 7 please give a brainliest please

Step-by-step explanation:

Find the area of the composite figure

Answers

Answer:

area of semicircle=76.969 inches

triangle is=10 in so 20 since there is 2 triangles made

rectangle=140 in

236.969 inches is the total

hope this helps

have a good day :)

Step-by-step explanation:

can someone please help me with this​

Answers

Answer:

Surface Area = 139.4 (rounded to nearest tenth)

A letter is randomly chosen from the word CANDLESTICK. Find the probability that
you chose an Nor S.

Answers

Answer:

The probability of you choosing S would be a 1/11 chance or a 0.0909090909 chance.

Answer:

1 / 11

Step-by-step explanation:

there are 11 letters in candlesick so 11 possibilities and 1 S which is 1 out of 11 or 1 / 11.

Hope this helps ( :

maths question 11 divided by 4 please give me the answer in decimal as fast as u can

Answers

2.75

Step-by-step explanation:

[tex]\sf\purple{2.75}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{11}{4} \\ = 2.75[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.ඞ}}}}}[/tex]

A screening test for a disease shows a positive result in 91% of all cases when the disease is actually present and in 7% of all cases when it is not. Assume that the prevalence of the disease is 1 in 650. If the test is administered to a randomly chosen individual, what is the probability that the result is positive

Answers

Answer:

0.0713 = 7.13% probability that the result is positive.

Step-by-step explanation:

Probability of a positive test:

91% of 1/650(has the disease).

7% of 1 - 1/650 = 649/650(does not have the disease). So

[tex]p = 0.91\frac{1}{650} + 0.07\frac{649}{650} = \frac{0.91 + 0.07*649}{650} = 0.0713[/tex]

0.0713 = 7.13% probability that the result is positive.

Need the answer ASAP!! 20 points

Answers

Answer:

I think C. is it

Step-by-step explanation:

If 1=3
2=3
3=5
4=4
5=4, then 6=?

Answers

Answer:

six equal to eight?????

7th grade math help :)​

Answers

70

One McDonald’s drink is $10
The burger is $5
The fries are $2
5+2 = 7x10 = 70
If the drinks time 3 equal 30 they equal 10 individually then is you put the drink plus the burgers the burgers equal 5 individually then the burger plus fries together equal 9 so the fries equal 2 individually so 10+5+2 is our formula and the answer is 17!

A fair coin is flipped three times. Events A and B are defined as: A: there are at least two consecutive heads somewhere in the sequence B: at least one flip comes up tails What is p(A | B)?

Answers

Answer:

2 / 7

Step-by-step explanation:

Coin flipped 3 times has following outcomes, of heads 'H' & Tails 'T'

HHH , TTT , HTT, THT , TTH , THH , HTH , HHT  = total outcomes

P (A) = 2 consecutive heads , P (B) = atleast one tail

P (A) = 2 outcomes ( HHH , HHT , THH ) / total 8 outcomes = 3 / 8

P (B) = 7 outcomes (all except HHH) / total 8 outcomes = 7 / 8

P (A | B) = P ( A ∩ B ) / P (B)

P ( A ∩ B ) = P ( 2 consecutive heads & atleast one tail) / Total outcomes =   2 outcomes ( HHT , THH ) / total 8 outcomes = 2 / 8

So, P (A | B) = ( 2 / 8 ) /  ( 7 / 8 ) = 2 / 7

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity:

Answers

Answer:

[tex]\begin{array}{cc}{Stem} & {Leaves} & {4} & {7} & {5} & {2, 7, 8, 8} & {6} & {1, 6, 6, 8, 8} & {7} & {0, 2, 2, 3, 3, 5, 6, 7} & {8} & {4, 4, 4, 5, 6, 6, 7, 9} & {9} & {0, 1, 1, 2, 3, 7} \ \end{array}[/tex]

Step-by-step explanation:

Given

See comment for complete part of the question

Required

Make a stem and leaf plot

We have:

[tex]58, 52, 68, 86, 72, 66, 97, 89, 84, 91[/tex]

[tex]91, 92, 66, 68, 87, 86, 73, 61, 70, 75, 72, 73[/tex]

[tex]85, 84, 90, 57, 77, 76, 84, 93, 58, 47[/tex]

Categorize the dataset according to tens

[tex]47[/tex]

[tex]52, 57, 58, 58[/tex]

[tex]61, 66, 66, 68, 68[/tex]

[tex]70, 72, 72, 73, 73, 75, 76, 77[/tex]

[tex]84, 84, 84, 85, 86, 86, 87, 89[/tex]

[tex]90, 91, 91, 92, 93, 97[/tex]

So, the stem and leaf plot is:

[tex]\begin{array}{cc}{Stem} & {Leaves} & {4} & {7} & {5} & {2, 7, 8, 8} & {6} & {1, 6, 6, 8, 8} & {7} & {0, 2, 2, 3, 3, 5, 6, 7} & {8} & {4, 4, 4, 5, 6, 6, 7, 9} & {9} & {0, 1, 1, 2, 3, 7} \ \end{array}[/tex]

Please help me with simplifying this equation? (-5)^5/ (-5)^-6
Thanks

Answers

I think so that the answer is -48828125

help needed with math​

Answers

Answer:

angle y = 49°

Step-by-step explanation:

If AB = AD and BC = DC, then the two triangles are isosceles triangles. The altitude from the top to the base divides the top angle into two equal angles, with 90° angles at the base. If angle C is divided into two equal angles (41°) and at the base is a 90° angle, that makes angle CBD 49°. On an isosceles triangle, the two angles opposite to the equal sides are identical. So angle y is identical to angle CBD.

Y=49 degree angle! Because I when you do the math you get that

What is its equation in slope-intercept form ?

Answers

Answer:

Candice

Step-by-step explanation:

What is the inverse operation of multiply by 12? A. add 12 B. subtract 12 C. multiply by 12 D. divide by 12​

Answers

Answer:

D. divide by 12​

Step-by-step explanation:

→ When you :

- Multiply, the inverse is divide

- Divide, the inverse is multiply

- Add, the inverse is minus

- Minus, the inverse is add

IM LOW ON TIME AND NEED YOUR HELP 30 PST

Answers

Answer:

12.56

Step-by-step explanation:

First of all, pi = 3.14

Diameter=4

Radius=2

3.14×[tex]2^{2}[/tex]

So,

3.14 × 4 =

12.56

Hope this helps!! (Hope I did this in time!!)

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