Determine the equation of the circle with center (8,5) containing the point (-4,21)
Answers
Answer:
(x-8)² + (y-5)² = 400
Step-by-step explanation:
general equation of a circle : (x-h)² + (y-k)² = r²
where (h,k) is at center and r = radius
here we are given the center as well as a point on the circle
first we will need to identify the radius by finding the distance between the center and the point on the circle using using the distance formula ( we know this is the radius because the radius is a line that goes on the center of the circle to any point on the circle )
Identifying the radius using the distance formula
Distance formula : [tex]d=\sqrt{(x_2-x1)^2+(y_2-y_1)^2}[/tex]
where the x and y values are derived from the two given points
Given points are (8,5) and (-4,21)
Assigning variables we get (x1,y1) = (8,5) , so x1 = 8 and y1 = 5
and (x2,y2) = (-4,21) so x2 = -4 and y2 = 21
Plugging this into the formula we get
[tex]d=\sqrt{(-4-8)^2+(21-5)^2}[/tex]
==> subtract values inside of parenthesis
[tex]d=\sqrt{(-12)^2+(16)^2}[/tex]
==> evaluate exponents
[tex]d = \sqrt{144+256}[/tex]
==> add 144 and 256
[tex]d=\sqrt{400}[/tex]
==> take the square root of 400
[tex]d=20[/tex]
so the radius is 400
Finding the equation of the circle
again we have the general equation of a circle as (x-h)² + (y-k)² = r²
where (h,k) is at center and r = radius
here the center is at (8,5) and the radius is 20
so (h,k) = (8,5) so h = 8 and k = 5 and radius is 20 so r = 20
plugging these values into the general equation of a circle we get
(x-8)² + (y-5)² = 20²
==> evaluate exponent
(x-8)² + (y-5)² = 400
and we are done!
For more validation check the attached image :)
Related Questions
PLEASE HELP ME, I GIVE 69 POINTS FOR CORRECT ANSWER
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
A: Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
B: Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
C: Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
D: Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
(PS: If you choose C, you're wrong.)
Answers
Answer:
D
Step-by-step explanation:
I hope this helps! If it does, please mark me Brainliest! Thanks in advance!
Tell whether the system has one solution, infinitely many solutions, or no solution.
Answers
Answer:
Has infinite solutions
Explanation:
-x + 5y = -3..... eq1
2x - 10y = 6 .... eq2
===============
make x the subject in equation 1
-x + 5y = -3
-x = -3 - 5y
x = 5y + 3
========= insert this in equation 2
2(5y + 3) - 10y = 6
10y + 6 -10y = 6
6 = 6
So, Has infinite solutions as L.H.S = R.H.S
liam has 12 red ballons and 14 blue ballons he puts all of his ballons into 2 equal groups how many ballons are in each group
Answers
Answer: 6 red and 7 blue
Step-by-step explanation:
Cut in half the amount of each balloon
Then he divided 26 into 2 equal groups so divide 26 by 2 which is 13
13 is your answer :)
Many counties in Florida missed many school days in the fall of 2004 due to hurricanes that year. To make up those days, they added time to each school day for a portion of the year. It was decided that in order to make up a 6 hour school day, 10 minutes would be added to each day. How many extended days would be needed to make up 3 school days?
Answers
Answer:
if 10 minutes was added each day 30 minutes is how long it would extend in 3 days
11.75 in fraction form
Answers
Answer:
47/4 but you can simplify it to 11 3/4
Step-by-step explanation:
11 is the whole number and 75 is 3/4ths of 1 or another whole number.
Write down the exact value of tan 60
Answers
Answer:
[tex] \sqrt{3} [/tex]
Goodluck
Answer:
[tex]\sqrt 3[/tex]
Step-by-step explanation:
[tex]\tan 60^{\circ} = \dfrac{\sin 60^{\circ}}{\cos 60^{\circ}} = \dfrac{\tfrac{\sqrt 3}2}{\tfrac 12} = \dfrac{\sqrt 3}2 \cdot 2 = \sqrt 3[/tex]
please help thank you
Jack and Marcy are at an amusement park. Jack is standing 75 meters from a hot air balloon ride. He is recording Marcy with his cell phone as she gets into the basket of the balloon and the hot air balloon begins to rise.
Answers
Tan65°=h/75m
2.1445 × 75 = h
h = 160.83
Step-by-step explanation:
This is very very simple
if you have 10 goldfish and 3 die how many are left
Answers
Answer:
7 goldfish
Step-by-step explanation:
10-3=7
Answer:
10-3=8
i think
What value of x makes this equation true? -80= -120 + X
Answers
Answer:
x = 40
Step-by-step explanation:
Preform the opposite opposite operation to get x by itself.
-80 = -120 + x
+ 120 +120
40 = x
Answer:
answer
Step-by-step explanation:
Answer is, 40
Do the ratios 21:45 and 7:15 form a proportion?
Answers
Answer:
yes, it form a proportion...
Pls help me and show work! Thank you <3
Answers
Answer: 23
Step-by-step explanation:
By the alternate exterior angles theorem, [tex]4x-11=x+58 \longrightarrow x=\boxed{23}[/tex]
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
294 inches squred
Step-by-step explanation:
3 x 10 = 30
3 x 9 = 27
10 x 9 = 90
2(30) + 2(27) + 2(90) = 294
What is the volume of a cube with sides measuring 1.5 inches
Answers
Answer:
A cube with a side length of 3 inches has a volume of 27 cubic inches.
Step-by-step explanation:
yes
This question is worth 20 points if someone answers it!
Answers
The maximum number of tourists in the third week will be maximum in the numberville city.The solution of f(x)=h(x) will be x(5,2).
What are equations?The equation is actually a relationship between the numbers and the variables.
To calculate the number of the tourists in the third week we will put the value 3 in every function:
[tex]f(x)=x^2+5x+10=(3)^2+(3\times 3)+10=29\\\\\\g(x)=3^x=3^3=27\\\\\\h(x)=10x=10\times 3=30[/tex]
So we can see that the function third h(x) numberville city is having a maximum number of tourists.
The solution of f(x)=h(x) will be calculated as:
[tex]x^2-3x+10=10x\\\\\\x^2-7x+10=0\\\\\\x^2-5x-2x+10=0\\\\\\x(x-5)-2(x-5)=0\\\\\\x=5,2[/tex]
Hence the solution of f(x)=h(x) will be x(5,2).
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A bottle of laundry detergent is 7/10
full. Jamie uses
3/10
of the bottle to
do her laundry. What fraction of the
bottle of laundry detergent is left?
Explain.
Answers
Answer:4/10 =2/5
Step-by-step explanation:
you subtract the numerator but the denominator stays the same. I then found a number that could be divided into both numbers and got 2/5.
How much dollars is 92¢?
Answers
Its 0.92
Sure hope this helsp you :D
You wish to buy a new set of strings for your guitar. You phone five different
music shops and obtain a quote for a set of strings from each of them. The
average price charged by the five music shops is R225,00. If the first two music
shops both charge R180,00 for the strings, while the third and fourth shops
respectively charge R280,00 and R270,00, how much did the fifth music shop
charge for the strings?
Answers
Answer:
215,00.
Step-by-step explanation:
Average price = 22500
18000*2 + 28000 + 27000 + x = 22500*5
91000 + x = 112500
X = 21500
Answer:
R215,00
Step-by-step explanation:
Let x = amount the 5th music shop charges for the strings
[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
[tex]\implies \sf 225=\dfrac{180+180+280+270+x}{5}[/tex]
[tex]\implies \sf 225\cdot 5=910+x[/tex]
[tex]\implies \sf 1125=910+x[/tex]
[tex]\implies \sf x=1125-910[/tex]
[tex]\implies \sf x=215[/tex]
Therefore, the fifth music shop charged R215,00 for the strings.
Please help I need it quick!!!! Please
Answers
Answer:
Question 1
Cost per 10,000 Popsicle sticks = $725.20
⇒ Single Popsicle stick = 725.20 ÷ 10000 = $0.07 (nearest cent)
Question 2
Cost per 1,000 motherboards = $8,730
⇒ Cost of Single motherboard = 8730 ÷ 1000 = $8.73
Cost per 10 motherboards = $100
⇒ Cost of Single motherboard = 100 ÷ 10 = $10
Difference = 10 - 8.73 = $1.27
Question 3
Create a table with the cost per 1 unit:
[tex]\begin{array}{| c | c | c | c |}\cline{1-4} \sf PART & \sf COST\:PER\:1\:of\:10 & \sf COST\:PER\:1\:of\:1000 & \sf COST\:PER\:1\:of\:10000\\\cline{1-4} \sf Motherboard & \$10.00 & \$8.73 & \$7.04 \\\cline{1-4} \sf Processor & \$5.00 & \$1.25 & \$0.63 \\\cline{1-4} \sf Popsicle & \$0.10 & \$0.09 & \$0.07 \\\cline{1-4} \sf Motor & \$4.50 & \$0.18 & \$0.04 \\\cline{1-4} \sf Sensor & \$6.30 & \$4.54 & \$3.18 \\\cline{1-4} \sf Small\:gear & \$1.00 & \$0.80 & \$0.70 \\\cline{1-4} \end{array}[/tex]
From inspection of the table, the Motor saves the most money per unit when 10,000 is bought, since the difference between the cost of 1 unit is the greatest for this part.
Question 4
Cost of 1100 motherboards
= cost of 1000 + cost of 10 x 10
= 8730 + 100 x 10
= 8730 + 1000
= $9,730
Question 5
Cost of 12050 sensors
= cost of 10000 + cost of 1000 x 2 + cost of 10 x 5
= 31752 + 4536 x 2 + 63 x 5
= 31752 + 9072 + 315
= $41,139
PLEASE HELP ILL MARK AS BRAINLEST
Which statement describes the speed of the remote-control car over time? O The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mili for the last 5 seconds. O The speed of the car increases from 4 mi h to 2 mih in the first 3 seconds, decreases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds. O The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 6 mi/h in the next second, and then remains at 6 mi/h for the last 6 seconds. O The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mih in the next 5 seconds, and then remains at 5 mi/h for the last 10 seconds,
Answers
Answer:
Step-by-step explanation:
The explanation of the problem is shown in the attached figure.
AS shown in the graph:
At t = 0 the speed = 4 miles/h then decrease to the speed = 2 miles/h during the first 3 seconds then increased to 5 miles/h during the next 2 seconds, then it became constant at 5 miles/h for the last 5 seconds.
So, the correct option is:
A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
The function h is defined as follows.
Screenshot shows the question.
Answers
[tex]\sf Simplified[/tex] ⇒ -2h
_______________________
[tex]\sf Given~h(-2)[/tex][tex]\sf Simply~move~2~to~the~left.[/tex]_______________________
Part A
Which expression can be used for the missing side length of the rectangle?
Part B
Find the length of the missing side when x = 3. Round answer to the nearest tenth.
Length = in.
Answers
Answer:
d
Step-by-step explanation:
(8x)^2 = (2x)^2 + y^2
64x^2 - 4x^2 = y^2
60x^2 = y^2
y = 2x√15
Please select the correct answer!
Answers
Answer:
the value of x must be -2 . ie option b
Answer:
x-1=-x²+2x+5
-x²+(2x-x)+(5+1)=0
-x²+x+6=0
(x-3)(x+2)
x=3 or x=-2
Evaluate: 2 • [(6 + 1)2 + 1]
Answers
Answer:
20
Step-by-step explanation:
2•[(6+1)2+1]
2•[(7)3]
2•10
• means times
2×10
20 answer
Answer:
p
Step-by-step explanation:
2 • [(6 + 1)2 + 1]
First The Brackets :
[(6 + 1)
->>> 6 + 1
= 7
But there's a bracket around 6 + 1 so now we multiply
-->>> [(7)2 + 1]
->>> 7 x 2
= 14
So now we add :
-->>> 14 + 1
= 15
And now we multiply:
->>> 15 • 2
--->>> 30
Hope it helps :))))
Pls help me, this is due by tonight. What is the volume
Hopefully easy for some of you. :)
Answers
Answer:
115.86
Step-by-step explanation:
Select the correct answer.
Factor completely
5x² - 45
OA (5x + 9)(x - 5)
O.B. 5(x - 45)
OC. 5(x-9)(x+ 9)
OD. 5(x+3)(x - 3)
Reset
Next
Answers
Answer:
D. 5(x + 3)(x - 3)
Step-by-step explanation:
Both terms are perfect squares, therefore we will factor using the difference of squares formula;a² - b² = (a + b) (a - b)
5(x + 3)(x - 3)
5(x² - 9)
(5x² - 45)
5x² - 45
Option D is correct, the factored form of the expression 5x² - 45 is 5(x+3)(x - 3)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 5x² - 45
Five times of x square minus forty five
x is the variable and minus is the operator
Let us take 5 common from the expression to find the factor form
5(x² - 9)
5(x² - 3²)
Now we know that a² - b² = (a+b)(a-b)
5(x+3)(x-3)
Hence, the factored form of the expression 5x² - 45 is 5(x+3)(x - 3)
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For what values of a can you solve the linear system az + 3y = 2 and 4x + 5y = 6 by elimination without
multiplying first?
The values
and
Answers
Answer:
4, -4
Step-by-step explanation:
I think the first equation is ax + 3y = 2, not az + 3y = 2.
ax + 3y = 2
4x + 5y = 6
To use elimination, you need the coefficients of a to either add to zero, or to have a difference of zero if you subtract them.
a + 4 = 0
a = -4
a - 4 = 0
a = 4
Answer: a must be 4 or -4.
Answer:
-4 and 4
Step-by-step explanation:
Given linear system:
[tex]ax+3y=2[/tex]
[tex]4x+5y=6[/tex]
In order to solve the given linear system by elimination without multiplying first, [tex]a[/tex] must be either -4 or 4. That way, when you add or subtract the equations, the variable [tex]x[/tex] will be eliminated.
when [tex]a = -4[/tex]:
[tex]\large\begin{array}{ l r c c l r}& -4x & + & 3y & = & 2\\+ & 4x & + & 5y & = & 6\\\cline{1-6}& & & 8y & = & 8\\\cline{1-6}\end{array}[/tex]
when [tex]a = 4[/tex]:
[tex]\large\begin{array}{ l r c c l r}& 4x & + & 3y & = & 2\\- & 4x & + & 5y & = & 6\\\cline{1-6}& & & -2y & = & -4\\\cline{1-6}\end{array}[/tex]
How can I get 9th grade to add up to 500? You can only change summer and fall. Thank you
Answers
Answer:
8th fall- 203 9th fall-95
Step-by-step explanation:
the 9th total is 500
8th fall is 203
9th fall is 95
3x+5y= -9
Y= 2x-7
Use substitution to solve the system
Answers
Answer:
x = 2
Step-by-step explanation:
3x + 5y = -9 ___(1)
y = 2x - 7
Substituting y's value in (1) ..
3x + 5( 2x - 7) = -9
3x + 10x -35 = -9
13x = -9 + 35
13x = 26
x = 26/13
x = 2
what is the product ?
Answers
Explanation:
(5x+1) (5x-1)
(5x)^2 - 1^2
25x^2 - 1^2
Answer:
b) 25x² - 1
Step-by-step explanation:
→ (5x + 1)(5x - 1)
→ 25x² + 5x - 5x - 1
→ 25x² - 1
Thus, option (b) is the answer.
please help will give brainliest
