Answers
We are given with a equation of Circle and we need to find it's radius and it's equation in standard form . But , let's recall , the standard equation of a circle is [tex]{\bf (x-h)^{2}+(y-k)^{2}=r^{2}}[/tex] where (h,k) is the centre of the circle and radius is r . Proceeding further ;
[tex]{:\implies \quad \sf x^{2}+12y+22x+y^{2}-167=0}[/tex]
Collecting x terms , y terms and transposing the constant to RHS ;
[tex]{:\implies \quad \sf (x^{2}+22x)+(y^{2}+12y)=167}[/tex]
Now , as in standard equation their is a whole square , so we need to develop a whole square in LHS , for which we will use completing the square method , as coefficient of x² and y² is 1 , so adding 121 and 36 to LHS and RHS .
[tex]{:\implies \quad \sf (x^{2}+22x+121)+(y^{2}+12y+36)=167+121+36}[/tex]
[tex]{:\implies \quad \sf (x+11)^{2}+(y+6)^{2}=324\quad \qquad \{\because a^{2}+2ab+b^{2}=(a+b)^{2}\}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\{x-(-11)\}^{2}+\{y-(-6)\}^{2}=(18)^{2}}}}[/tex]
On comparing this with the standard equation , we got our centre at (-11,-6) and radius is 18 units
Related Questions
Can I please help me with this math question
Answers
Answer:
y =
-4
-3
-2
-1
0
Fill in the blank so that the ordered pair is a solution of y=9x - 9.
( ), 63
Answers
Answer:
(8, 63)
Step-by-step explanation:
The ordered pair is a solution to the equation when substituting the values for x and y make the equation a true statement.
If we let x represent the first number of the ordered pair, it will be a solution when ...
63 = 9x -9
7 = x -1 . . . . . . . divide by 9
8 = x . . . . . . . add 1
The blank gets filled with 8, so the ordered pair is (8, 63).
If the exterior angle of a regular
polygon measures 12°, how
many sides does the polygon
have?
Answers
Work Shown:
E = exterior angle = 12 degrees
n = number of sides
n = 360/E
n = 360/12
n = 30
This regular polygon has 30 sides.
m∠BAC=43 and BA=9 What is the length of arc BDC? Round to the nearest tenth.
Answers
Answer: 224.1
Step-by-step explanation:
:
The ratio of Amber's age to her brother Zach's age is 1 : 2. Find the
missing age.
6. Amber is 10; Zach is ?
7. Zach is 26; Amber is?
Answers
7. If Zach is 26, Amber is 13.
Basically, the ratio of Amber’s and Zach’s ages, which is 2:1, means that Amber is half Zach’s age/Zach is twice Amber’s age.
I hope this helps!
Hey I could use some help with this asap. Thank you. Will be marked.
Answers
Answer:
top left
Step-by-step explanation:
2.5=2 1/2=5/2
2 over 5 up
top left
What is the answer to 11 > b + 4 > -6
Answers
[tex]11 > b+4 > -6\\11 - 4 > b > -6-4\\7 > b > -10[/tex]
Hope that helps!
1 over 11 time what equals 1
Answers
1/11 x 11 = 1
^^^ This is basically
1. 11. 11
— x — = — = 1
11. 1. 11
The 11 also crosses itself out because of cross multiplication so it could be 1/1
The “what” is 11
Evaluate S5 for 600 300 150 … and select the correct answer below. 1,162. 5 581. 25 37. 5 18,0600.
Answers
Answer:
The answer is 1,162.5
a
In a survey of 450 people, 74% admitted that
they hate brussels sprouts. How many people in
this survey hate this vegetable?
Answers
Answer:
333 people
Step-by-step explanation:
74% of 450 = 0.74
0.74 × 450 = 333
Have a great day! :D
There are 333 peoples in this survey hate this vegetable.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
In a survey of 450 people, 74% admitted that they hate brussels sprouts.
Hence, Number of peoples in this survey hate this vegetable is,
⇒ 74% of 450
⇒ 74/100 × 450
⇒ 333
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ2
Where in real-life will we come across something that is more than 100%, e. G. 135%? Give three examples
Answers
Real life situations can be represented using mathematical statements
Examples of real life situations of things more than 100% are:
Markup pricesEnlarging the area of a gardenIncrease in savingsHow to determine the real life scenariosWhen something is greater than 100%, then there is an increment in the thing.
Take for instance, a unit of apple that was sold at $4 is not $10.
The percentage change is 150%
Other possible scenarios are when the area of a garden is enlarged and when you increase your weekly savings by more than 100%
Read more about percentage change at:
https://brainly.com/question/11360390
Find the area of the composite figure below.
Answers
Answer:
15
Step-by-step explanation:
To find area, you must add.
10×10^-11
[tex]10 \times 10 to \: the \: power \: of \: - 11[/tex]
10×10^-11
Answers
Answer:
[tex] {10}^{ - 10} [/tex]
Step-by-step explanation:
since the base is the same you have to add +1 to -11 which equals to -10
The radius of a circle is 10 meters. What is the length of a 135° arc?
Answers
Answer:
Step-by-step explanation:
The total circumference of the circle is: C = 2*pi*radius = 2*(3.14159)*(6) = 37.7 m The total circle has 365o. Your arc has only 135o. Hence: 135o x------- = -------------365o 37.7 m where x is the length of the 135o arc. Solve for x.
use the following function to find f(2) f(x) = 11x + 2
Answers
Answer:
123
Step-by-step explanation:
insert 2 everywhere you see an x
11^2 +2 = 121+2 = 123
HOPE THIS HELPS!!!
plssssssssssssssssssssss helpppp
Answers
Solve for X (Trigonometry)
Answers
Answer:
7.0
Step-by-step explanation:
When doing trigonometry, remember SOH-CAH-TOA...
Sine : Opposite/Hypotenuse
Cosine : Adjacent/Hypotenuse
Tangent : Opposite/Adjacent
In this figure, we are given the measure of a 23° angle, and two sides that are opposite of the angle, and the hypotenuse.
This means we need to use sine:
[tex]sin(23)=\frac{x}{18}[/tex]
Multiply both sides by 18:
[tex]18sin(23)=x[/tex]
[tex]18(0.391)=x\\x=7.038\\x\approx7.0[/tex]
80 points help meez In the diagram, ΔUVW~ΔXYW. Use similarity criteria for triangles to determine determine the height of the tree. Then fill in the blank:
h = _____ ft (Answer with numbers only.)
Answers
Answer:
look at the picture i have sent
By what percent will a fraction increase if its numerator is decreased by 30%
а
and its denominator is decreased by 50%?
Answers
Answer:
40%
Step-by-step explanation:
Let x = numerator
Let y = denominator
[tex]\implies \dfrac{x}{y}[/tex]
Decreased by 30% = 100% - 30% = 70% = 70/100 = 0.7
Decreased by 50% = 100% - 50% = 50% = 50/100 = 0.5
[tex]\implies \dfrac{0.7x}{0.5y}[/tex]
[tex]\implies \dfrac{0.7}{0.5}=1.4[/tex]
[tex]\implies 1.4 \ \dfrac{x}{y}[/tex]
1.4 as a percentage = 1.4 x 100 = 140%
Therefore, the percentage increase is 140 - 100 = 40%
A dozen cupcakes cost $36. What is the rate, and the unit rate?
Answers
Answer:
A unit rate has a denominator of 1 unit when the rate is written as a fraction. To write a rate as a unit rate: divide the numerator and the denominator of the rate by the denominator. Example #1: A rate compares two quantities of different units. Each part of the rate must be labeled!
Step-by-step explanation:
Sana maka tulong
What is the value of n?
Answers
Answer:
4x6=3*n
Step-by-step explanation:
just got it off the web enjoy might not be right
A prism is dilated by a factor of 1. 5. How many times larger is the volume of the resulting prism than the volume of the original prism? Enter your answer as a decimal in the box.
Answers
The volume of the resulting prism is 3.375 times of original volume.
What is a dilation or scale factor?The factor by which the dimensions of an object are enlarged is called the scale factor.
Let us take the base area of Prizm = a²
Height of the prism = h
Enlarged area = (scale factor)² * previous area
Enlarged area = 1.5²*a² = 2.25a²
Enlarged height = 1.5h
So, enlarged volume = enlarged area* enlarged height
Enlarged volume= 2.25a²*1.5h = 3.375a²h
Enlarged area/previous area = 3.375a²/a² = 3.375
Therefore, the volume of the resulting prism is 3.375 times of original volume.
To get more about dilation visit to:
https://brainly.com/question/10253650
Can someone help with this challenging graph
Answers
Answer:
(a) (-∞, -8) (-6, -4) (-2, ∞)
(b) -6, -2
(c) negative
(d) 5
Step-by-step explanation:
(a) A function is "decreasing" when the y-value decreases as the x-value increases.
⇒ the function is decreasing over these intervals : (-∞, -8) (-6, -4) (-2, ∞)
(b) Local maxima are the points on the function where it reaches a maximum.
⇒ maxima at x = -6 and x = -2
(c) negative
(d) 5
help.
4x^7y^6 + 9x^3y x 2x^4y^5
Answers
Answer:
9x9y6+4x7y^6
Step-by-step explanation:
4x^7y^6+9x^3yx2x^4y^5
=4x^7y^6+9x^9y^6
=9x^9y^6+4x^7y^6
Answer:
4x^7y^6 + 18x^6y^6
4 feet wide and 8 feet tall a manufactur wants to use a scale factor of 1.5 to englarge a window. what will the area of the window be after it is enlarged
Answers
Answer:
72 square feet
Step-by-step explanation:
[tex]4*1.5=6[/tex]
[tex]8*1.5=12[/tex]
[tex]6*12=72[/tex]
find the area 8ft. 7ft. 14ft. ( EXPLAIN)
Answers
Answer:
The area is 77 ft.
Step-by-step explanation:
The formula for area of a trapezoid is 1/2 (base1 + base2) x height.
So, 1/2 (14+8) x 7 = 77.
Answer:
77Ft
if we were to ignore the extra "space" or area, and just do the area of the square we would get 8x7, but you probably want to know how I figured the area of both triangles, well this is simple the triangle has a height of 7 while it has a base(bottom) of 3 since 14-8(top)=6 and there are two triangles and they are the same lenght, when there is a triangle we do the base x height then divide by 2 since it's half a square so we do in this situation 3x7=21 and since there is another triangle we do it one more 3x7=21 add them together 3x7x2=42 then divide this by 2 and we get 21, we then add this to 56 which is the area of the square and get our result 77ft
Last week, Kip went to the fair. It costs $4.95 to enter the fair and $0.50 per ticket. In the equation below, x represents the number of tickets Kip bought, and y represents the total amount Kip spent.
y = $0.50x + $4.95
If Kip spent $12.45 at the fair, how many tickets did he buy?
Group of answer choices
8
15
25
35
Answers
Answer:
x = 15
Step-by-step explanation:
[tex]12.45=4.95+0.5\timesx[/tex]×x
Solve the equation
[tex]12.45=4.95+0.5x[/tex]
Rearrange variables to the left side of the equation
[tex]-0.5x=4.95-12.45[/tex]
Calculate the sum or difference
[tex]-0.5x=-7.5[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]x=\frac{-7.5}{-0.5}[/tex]
Determine the sign for multiplication or division
[tex]x=\frac{7.5}{0.5}[/tex]
Multiply both the numerator and denominator with the same integer
[tex]x=\frac{75}{5}[/tex]
Cross out the common factor
[tex]x=15[/tex]
I hope this helps you
:)
the angles of a triangle are(x+10), (x+40) and (2x-30). Find the measure of all angles and name the type of triangle
Answers
Answer:
x=40
Step-by-step explanation:
(x+10)+(x+40)+(2x-30)=180
(x+x+2x)+(10+40-30)=180
4x+20=180 step 1: -20 on both sides
4x=160 step 2: /4 on both sides
x=40
Select from the drop-down menu to correctly complete the statement.
The product of 5 and 7/8 is
Choose...
A. greater than 5
B. less than 5
C. equal to 5
because 7/8 is less than 1.
Answers
Answer:
c
Step-by-step explanation:
hope it helps u have a good day
Answer:
correct answer is A ..because it passed 5 and about to reach 6 ..only 1/8 left to be 6
in an isosceles right triangle ABC, the right angle is at B, which is the hypotenuse?
A. AB
B. BC
C. AC
D. BA
Answers
Answer: c
AC is the hypotenuse
