MATHEMATICS HIGH SCHOOL

30 points and BRAINLIEST! Write the general equation for the circle that passes through the points: (1, 7) (8, 6) (7, -1)

Answers

Answer 1

Answer:

Answer:

(x − 4)² + (y − 3)² = 25

Step-by-step explanation:

The equation of a circle is:

(x − h)² + (y − k)² = r²

Given three points on the circle, we can write three equations:

(1 − h)² + (7 − k)² = r²

(8 − h)² + (6 − k)² = r²

(7 − h)² + (-1 − k)² = r²

Expanding:

1 − 2h + h² + 49 − 14k + k² = r²

64 − 16h + h² + 36 − 12k + k² = r²

49 − 14h + h² + 1 + 2k + k² = r²

Simplifying:

50 − 2h + h² − 14k + k² = r²

100 − 16h + h² − 12k + k² = r²

50 − 14h + h² + 2k + k² = r²

Subtracting the first equation from the second and third equations:

50 − 14h + 2k = 0

-12h + 16k = 0

Solving the system of equations, first reduce:

25 − 7h + k = 0

-3h + 4k = 0

Solve with substitution or elimination. Using substitution, solve for k in the first equation and substitute into the second.

k = 7h − 25

-3h + 4(7h − 25) = 0

-3h + 28h − 100 = 0

25h = 100

h = 4

k = 7h −25

k = 7(4) − 25

k = 3

Now plug these into any of the original three equations to find r.

(1 − h)² + (7 − k)² = r²

(1 − 4)² + (7 − 3)² = r²

9 + 16 = r²

25 = r²

The equation of the circle is:

(x − 4)² + (y − 3)² = 25

Graph: desmos.com/calculator/ctoljeqhnp

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PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

Answers

Answer:

2/1 or 2

Step-by-step explanation:

m(slope)= y2-y1/ x2-x1

i hope this helps

ALGEBRA 1, SEMESTER 2What is the average rate of change of the function over the interval x = 0 to x = 8?

f(x)=2x+3/3x−3
Enter your answer, as a fraction

Answers

Replace X with 0 and solve the equation, then replace x with 8 and solve the equation again.

Then find the difference between the 2 answers and divide that by the difference in the 2 X values.:

f(0) = 2(0) + 33(0) -3 = -3

f(8) = 2(8) +33(8) - 3 = 16 + 264 - 3 = 280-3 = 277

Difference: 277 - (-3) = 277+3 = 280

Difference between the X values 8 - 0 = 8

Average rate of change: 280 / 8 = 35

A bouncy ball is dropped such that the height of its first bounce is 2.75 feet and eachsuccessive bounce is 69% of the previous bounce's height. Write a recursive formula
to represent the height of the nth bounce of the ball.

Answers

The value 2.75 goes in the first box, since it's the first term.

The expression $0.69*a_(n-1)$ goes in the second box. The second line says "to get the nth term, we multiply the previous term by 0.69"

So the distance of a aircraft flies a proportional relationship whith its number of hours inflight. The table shows the number of miles flown for a number of hours in flight. Find the constant of proportionality. How long will the jet take to travel 5,880.

Answers

The constant of proportionality is k = 490 and the equation is y = 490x where x is the number of hours and y is the total number of miles

The time required is 12 hours

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the distance of the aircraft be = x

Let the total time taken by the aircraft be = y

Let the constant of proportionality be k

when x = 1 ,

y = 490

So , the equation will be y = kx

Substituting the values in the equation , we get

y = 490x

when x = 2

y = 490 ( 2 )

y = 980

Now , the time taken by aircraft to travel 5,880 miles is

Substitute the value of y as 5880 in the equation , we get

5880 = 490x

Divide by 490 on both sides of the equation , we get

x = 5880 / 490

x = 12

Therefore , the time taken is 12 hours

Hence , the constant of proportionality is 490

To learn more about proportion click :

brainly.com/question/7096655

#SPJ2

Answer:

The constant of proportionality is 490

The jet will take 12 hours to travel 5,880 miles

Step-by-step explanation: The miles multiply by 490 each time.

490 x 12 is 5,880

A ball is thrown horizontally from the top ofa building 110 m high. The ball strikes the
ground 61 m horizontally from the point of
release.
What is the speed of the ball just before it
strikes the ground?
Answer in units of m/s