Help please!!! :')
Given a diameter of a circle at endpoints (8,-7) and (4,5), algebraically find the equation of the circle.
thank you smm <3
Answers
Answer:
(x-6)^2 + (y+1)^2=40
Step-by-step explanation:
see image. Use Midpoint Formula to find the center. Then use Distance Formula to find the diameter. Cut the diameter in half to find the radius. Use the circle formula to insert (h,k) the center and r, the radius to find the equation. See image.
Answer: [tex](x - 6)^2 + (y + 1)^2 = 40[/tex]
=========================================================
Explanation:
The x coordinates of the given endpoints are x = 8 and x = 4. Apply the midpoint to them to get [tex]\frac{x_1+x_2}{2} = \frac{8+4}{2} = \frac{12}{2} = 6[/tex] which is the x coordinate of the midpoint. I added them up and divided by 2.
Similar steps will have the y coordinate of the midpoint be
[tex]\frac{y_1+y_2}{2} = \frac{-7+5}{2} = \frac{-2}{2} = -1[/tex]
Overall, the midpoint of those given points is (6, -1)
This is the center of the circle because the two endpoints are part of a diameter.
-------------------------------------------------
Now turn to the template
[tex](x - h)^2 + (y -k )^2 = r^2[/tex]
We will plug in the center (h,k) = (6, -1) and one of the endpoints for (x,y). Let's say we go for (x,y) = (4,5)
This leads us to the following:
[tex](x - h)^2 + (y -k )^2 = r^2\\\\(4 - 6)^2 + (5 - (-1) )^2 = r^2\\\\(4 - 6)^2 + (5 + 1 )^2 = r^2\\\\(-2)^2 + (6 )^2 = r^2\\\\4 + 36 = r^2\\\\r^2 = 40\\\\[/tex]
We don't need to isolate r itself. If you wanted, you could take the square root of both sides to see that the radius is [tex]r = \sqrt{40} \approx 6.3246[/tex]. However, again we don't need to solve for r entirely when forming the circle's equation.
With that [tex]r^2[/tex] value in mind, and the h & k values as well, we go from this template
[tex](x - h)^2 + (y -k )^2 = r^2[/tex]
to this final answer
[tex](x - 6)^2 + (y + 1)^2 = 40[/tex]
Related Questions
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
Answers
Answer:
Step-by-step explanation:
Both lines have same slope so the graph of both equation will be same and hence it will overlap each other that is why the Henry could only see one line.
Step-by-step explanation:
Given : A system of linear equation 3x - 2y = 4 and 9x - 6y = 12
We have to show whey when Henry graphed the equations 3x-2y=4 and 9x-6y=12 he could only see one line.
Consider the given system of linear equation
3x - 2y = 4 ................(1)
9x - 6y = 12 ..................(2)
Since,
Equation (2) is multiple of equation (1),
3 × ( 3x - 2y = 4) = 9x - 6y = 12
Also the slope of given equations are same
For equation (1),
Differentiate with respect to x, we get,
3-2dy/dx = 0
dy/dx = 3/2
Also for equation (2),
Differentiate with respect to x, we get,
9 - 6dy/dx = 0
dy/dx = 9/6 = 3/2
Since, both lines have same slope so the graph of both equation will be same and hence it will overlap each other.
That is why the Henry could only see one line.
How many terms are in the following expression? x2+7x-13
Answers
Answer:
There are 3 terms
Step-by-step explanation:
Write 23/12 as a mixed number.
Answers
Hey there!
23/12
= 23/1 ÷ 12/1
= 23/1 × 1/12
= 23(1) × 1(12)
= 23/12
≈ 1 11/12
Those steps above are somewhat easier to solving your given equation!
Anyways, your answer is: 1 11/12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
the answer is 1 11/12
Step-by-step explanation:
we know that 23 can fit once into 12,
so we can subtract 23 by 12 to get 11
now, we have 1 11/12
1 11/12
5 < -5(3x-7) Solve the inequality.
Answers
Answer:
x<2
Step-by-step explanation:
5<-5(3x-7)
divide by 5
1<-3x+7
3x<7-1
3x<6
x<2
Santa seated his guests so that X number of people sat at each of Y number of tables. Mrs. Claus placed Y number of people at each table, but she had X number of tables. Compare the number of guests Santa and Mrs. Claus were able to seat.
Answers
Answer:
they are the same
Step-by-step explanation:
The number of guests seated were, in each case, ...
(guests per table) × (number of tables)
__
For Santa, this product is ...
X × Y
For Mrs. Claus, this product is ...
Y × X
The commutative property of multiplication tells you that ...
XY = YX
The numbers of guests were the same.
Betty's bedroom is 18ft
long and 25 ft wide. She
wants to install the
hardwood flooring. The
cost is $6.00 per square
foot. How much is the
total cost for room
flooring?
Answers
Answer:
You'll need to find the area first.
18ft x 25ft= 450ft
Area is 450ft.
Area divided by $6.00 = 75
The total cost is $75 dollar for the whole room flooring.
Tell which value of the variable is the solution of the equation.
30 = 6w
w = 3, 5, 6, 8
Answers
Answer:
w = 5
Step-by-step explanation:
6w/6 = 30/6
= 5
what are the features of the function f(x) = 2^x -1 graphed below
Answers
I believe it's right two down one
Find the area of the shaded region
Answers
Answer:
1390
Step-by-step explanation:
(35*44)-((44-(17*2))*(35-(10*2)))
= 1390
please explain thourougly thanks!
Answers
Answer:
There are 2 x-intercepts
Step-by-step explanation:
The equation has 2 x variables, so the graph would have 2 x -intercepts.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use the discriminant method, we have to find discriminant of the given quadratic function, if discriminant is greater than 0, then it has two intercepts, if it is equal to 0, then it has 1 intercepts and if it is smaller than 0, then it has no x intercepts.
[tex]\qquad \sf \dashrightarrow \:D = {b}^{2} - 4ac[/tex]
where, a, b and c are coefficients of x², x and constant term. D = discriminant
[tex]\qquad \sf \dashrightarrow \:D = {( - 30)}^{2} - 4(22 \times 1)[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 900 - 4(22 )[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 900 - 88[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 812[/tex]
Discriminant is greater than 0, hence it has two x - intercepts.
Consider the line 3x+8y= 1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answers
Answer:
slope of a line parallel to this line= -3/8
slope of a line perpendicular to this line= 8/3
Step-by-step explanation:
The general equation of a line in terms of a and b is:
y=ax+b where a=slope
in order to get the slope of the line we have to write its equation as the form shown above:
3x+8y=1
8y= -3x+1
y= (-3/8)x+(1/8)
so slope= -3/8
Parallel lines have equal slopes
⇒ slope of parallel line= -3/8
The slope of the line perpendicular to another line is the opposite reciprocal of the original line's slope. This means that we have to exchange the numerater by the denomenator and multiply the obtained number by a negative sign:
⇒ slope of perpendicular line= -(-8/3) = 8/3
HELPPPPP LOOK AT PICTURES. I'LL GIVE BRAINLIEST!!!!
Answers
[tex](D)\ d(r)=7\times (0,75)^2[/tex]
Step-by-step explanation:[tex]r=0.75\ \ \ \ \ d_1=7\times 0.75\ \ \ \ \ d_2=0.75d_1=7\times 0.75^2[/tex]
[tex]so\ at\ 1\le r\le 7[/tex]
[tex]d(y)=7x(0,75)^2[/tex]
I hope this helps you
:)
The smith family wants to fence their yard. the yard is 96 meters and 52 meters wide. how much fencing will they need?
Answers
The radius of a circle can be found by dividing the circumference of the circle by 6. 28 What is the radius of a circle that has a circumference of 17. 27 feet
Answers
Answer:
2.75 feet
Step-by-step explanation:
I did the problem with the given instructions, but it really should be 2.74 feet. Instead of dividing the circumference by 6.28, you should divide the circumference by pi, then by two.
Hope this helps! :)
Find the volume of the figure below.
Answers
Answer:
a
Step-by-step explanation:
Volume = πr2h
= π×3.52×5
= 61.25π
= 192.42255003237 centimeters3
and
Volume = 7×5×12 = 420 feet3
so,
192.4+420= 612.4 cm^3
- Chris deposited $435 in a new account at his bank.
• The bank pays 1.7% interest compounded annually on this account.
• Chris makes no additional deposits or withdrawals.
How much interest will the account have earned at the end of 10 years?
Answers
Answer:
END OF EACH YEAR
-1 442.395
-2 449.91
-3 457.56
-4 465.34
-5 473.25
-6 481.29
-7 489.481
-8 497.80
-9 506.26
-10 514.87
however, how much INTEREST
514.87-435=
79.8
Jeffrey is looking at a map of his town to help him get from his school to the library. If 1 inch is equal to 9 miles, and the distance on the map is 1/4
inch, how far is it to the library?
Answers
Answer:
2.25 miles
Step-by-step explanation:
1/4 of 9 is 2.25
Answer:
2.25 miles away
Step-by-step explanation:
first make 1/4 a percent
second set up a proportion
then solve the proportion and then you get 2.25 and add a label
Please help me soon, been stuck for a while!
Answers
Answer:
Step-by-step explanation:
Answer:
3p + 2s = 27.5
3p + 2s = 27.54p + 3s = 37.5
Multiplies first equation by 4 and second equation by -3
12p + 8s = 110
12p + 8s = 110-12p + -9s = -112.5
12p + 8s = 110-12p + -9s = -112.5Adding them together-s = -2.5s = 2.5
12p + 8s = 110-12p + -9s = -112.5Adding them together-s = -2.5s = 2.53p + 2(2.5) = 27.5
12p + 8s = 110-12p + -9s = -112.5Adding them together-s = -2.5s = 2.53p + 2(2.5) = 27.53p +5 = 27.53p = 22.5p = 7.5
pumpkins weigh 7.5 pounds and squash weighs 2.5 pounds
hope it helps
pls mark as brainliest answer
follow me on brainly
Answer:
the blank is 10 lbs
Step by step:
3p + 2s = 27.5
3p + 2s = 27.54p + 3s = 37.5
Multiplies first equation by 4 and second equation by -3
12p + 8s = 110
12p + 8s = 110-12p + -9s = -112.5
12p + 8s = 110-12p + -9s = -112.5Adding them together-s = -2.5s = 2.5
12p + 8s = 110-12p + -9s = -112.5Adding them together-s = -2.5s = 2.53p + 2(2.5) = 27.5
12p + 8s = 110-12p + -9s = -112.5Adding them together-s = -2.5s = 2.53p + 2(2.5) = 27.53p +5 = 27.53p = 22.5p = 7.5
Answer 2:
pumpkins weigh 7.5 pounds and squash weighs 2.5 pounds
A punch bowl contained 2 liters of soda, 1 liter of orange juice
Answers
$9,000 is invested in a stock that loses 3%/yr on average. What is its worth after 6 years? Value:
Answers
please help me if you can tysm! :))))
Answers
Answer:
9.9
Is the answer to the question
Prove: An even times an even is
an even.
Answers
Answer: 4
Step-by-step explanation:
i just guessed and it was right, sorry i don't have a better explanation than that
I NEED HELP ASAP !!!!!!!
Answers
Answer:
$42,782.40
Step-by-step explanation:
You want to know how much more Glados paid than Shaq on a 30-year mortgage if their monthly payments were $755.99 and $637.15, respectively.
Added amountEach month, Glados paid this amount more:
$755.99 -637.15 = $118.84
Over the 360-month life of the 30-year loan, this excess amount adds up to ...
360 × $118.84 = $42,782.40
Glados pays $42,782.40 more than Shaq for the same loan amount.
<95141404393>
What is the product of -1−1 and-8−8?
Answers
Answer:
32
Step-by-step explanation:
Evaluate −30 ÷ −6. ghvfhv
Answers
Answer:
5
Step-by-step explanation:
used a cal
Answer:
5
Step-by-step explanation:
-30 / -6 = 5
-6 * x = -30
(drop the negatives)
30 / 6 = 5
-6 * 5 = -30
Write a congruence statement for the pair of triangles shown.
Answers
Answer:
Triangle UTS is congruent to Triangle RST.
Step-by-step explanation:
When stating congruence, the corresponding angles and sides must be listed in order. In triangle uts, based on the points, the angle is U, and the side is US. This means that for the other triangle, the first point needs to be the angle, and the last one needs to be the other point for the side. This gives us Triangle UTS is congruent to triangle RST. Hope this helps!
A small movie theater sells children's tickets for $4 each and adult tickets for $10 each for an animated
movie. The theater sells a total of $388 in ticket sales.
(a) If c represents the number of children's (b) Show that c= 52 and a =18 is a solution to
tickets sold and a represents the number of
this equation (not system).
adult tickets sold, write an equation that
models the information shown above.
C) Show that after multiplying both sides of the
equation in (a) by 2, c=52 and a=18 is
still a solution to this equation.
(d) How can you interpret multiplying both sides
of the equation by 2 in letter (a) in terms of
ticket prices and total ticket sales?
Answers
Answer:
b) Show that c= 52 and a =18 is a solution to
tickets sold and a represents the number of
this equation (not system).
Linear equation that models the given equation is 4c + 10a = 388 where c is the number of children ticket sold and a is the number of adult ticket sold. c = 52 and a = 18 is a solution to the linear equation. Multiplying a constant on both sides of the equation won't affect its solutions.
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
Let number of children ticket sold be c.
Let number of adult ticket sold be a.
Cost of one children ticket = $4.
Cost of one adult ticket = $10.
Total sales = $388
Linear equation that models the above equation: 4c + 10a = 388
Checking if a = 18 and c = 52 is a solution of the equation. It can be done by substituting the values.
LHS: 4c + 10a = 4*52 + 10*18 = 388
RHS: 388
Hence, c = 52 and a = 18 is a solution to the linear equation.
Multiplying 2 to both sides of the equation:
2(4c + 10a) = 2(388)
8c + 20a = 776
Substituting c = 52 and a = 18.
8(52) + 20(18) = 776
c = 52 and a = 18 is still a solution to the linear equation.
Learn more about linear equation here
https://brainly.com/question/11897796
#SPJ2
Answer Choices (Multiple Choice)-
A. 6240+t<=8000
B. 8000>=6240t
C. 6240+5t<=8000
D. 8000+6240<=5t
E. 8000-6240>=5t
Answers
Answer:
c,e, d
Step-by-step explanation:
c,e,d is the correct to me
Please help me with this!
What is the distance between ( − 2 , − 4 ) and ( 5 , 7 ) ? Use the distance formula, d = √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .
4.24
6.32
10.25
13.03
Answers
Answer:
13.03
Step-by-step explanation:
Suppose ( x₁ , y₁ ) = ( − 2 , − 4 ) and (x₂ , y₂ ) = (5 , 7)
In the formula : d = √ [( x₂− x₁ )² + ( y₂ − y₁ )²]
Just replace x₁ by -2
replace y₁ by -4
replace x₂ by 5
replace y₂ by 7
We get ,
d = √ [( 5− (-2) )² + ( 7 − (-4) )²]
Then
d = √ [(7 )² + ( 11 )²]
d = √ [49 + 121]
d = √ [170]
≈ 13.03
Line A is perpendicular to Line B.
If the slope of Line A is 3
what is the slope of Line B?
Answers
Answer:
- 1/3
Step-by-step explanation:
m = slope of a line
Perpindicular slope = - 1/m
= - 1/3
Let slope of that line be m
We know product of slopes of two perpendicular line=-1
3m=-1m=-1/3