Part 2: Identify key features and graph a circle from general form.
Answer the following questions to determine the key features of the circle whose equation is shown
and then graph it.
x2 + y2 + 12x-2y - 12 = 0
a) Write the equation of the circle in standard form. (3 points)
b) What is the center of the circle? (1 point)
c) What is the radius of the circle? (1 points)
d) Sketch a graph of the circle and label the center and the endpoints of the horizontal and
vertical diameter. (4 points)
Answers
Answer:
Subtract
12
from both sides of the equation.
x
2
+
y
2
−
12
x
+
2
y
=
−
12
Complete the square for
x
2
−
12
x
.
Tap for more steps...
(
x
−
6
)
2
−
36
Substitute
(
x
−
6
)
2
−
36
for
x
2
−
12
x
in the equation
x
2
+
y
2
−
12
x
+
2
y
=
−
12
.
(
x
−
6
)
2
−
36+y2+2y=−12
Move
−36
to the right side of the equation by adding
36
to both sides.
(x−6)2+y2+2y=−12+36
Complete the square for
y2+2y.
Tap for more steps...
(y+1)2−1
Substitute
(y+1)2−1
for
y2+2y
in the equation
x2+y2−12x+2y=−12.
(x−6)2+(y+1)2−1=−12+36
Move
−1
to the right side of the equation by adding
1
to both sides.
(x−6)2+(y+1)2=−12+36+1
Simplify
−12+36+1.
Tap for more steps...
(x−6)2+(y+1)2=25
This is the form of a circle. Use this form to determine the center and radius of the circle.
(x−h)2+(y−k)2=r2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r=5 h=6 k=−1
The center of the circle is found at
(h,k).
Center:
(6,−1)
These values represent the important values for graphing and analyzing a circle.
Center: (6,−1)
Radius:
5
image of graph
Step-by-step explanation:
Answer:
A) (x+6)^2 + (y-1)^2 =49
B) (-6, 1)
C) Radius of 7
D) I’ll try to add picture
Step-by-step explanation:
hotomath
Related Questions
-4x - 18 = 46
need help
Answers
Answer:
x=−16
Step-by-step explanation:
−4x−18=46
Add 18 to both sides
−4x−18+18=46+18
−4x=64
Divide both sides by -4
-4x/4=64/-4
x=−16
Answer:
x= -16
Step-by-step explanation:
Let's solve your equation step-by-step.
−4x − 18 = 46
Step 1: Add 18 to both sides.
−4x − 18 + 18 = 46 + 18
−4x = 64
Step 2: Divide both sides by -4.
−4x / −4 = 64 / -4
x=−16
Hope it helps T-T
Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken a mean of 5.4 sick days. This year, the firm introduces telecommuting. Management chooses a simple random sample of 80 employees to follow in detail, and at the end of the year, these employees average 4.5 sick days with a standard deviation of 2.7 days.
a) Describe the population in the context of this problem
b) Describe the parameter u in the context of this problem.
c) Describe the sample in the context of this problem.
d) Describe the statistic in the context of this problem
e) The firm would like to know if there is evidence that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced. State the hypotheses. Use ?-0.10.
f) Check the assumptions. If you don't know if an assumption is satisfied based on the information provided, then state "We must assume
g) Calculate the test statistic
h) Find the p-value.
i) Make a decision.
j) State the conclusion in terms of the problem.
Answers
Answer:
A.) Population : All employees at a firm
B.) μ = 5.4
C.) Sample : 80 employees at a firm
D.) Sample mean, x bar = 4.5
Step-by-step explanation:
From the question :
E.)
H0: μ ≥ 5.4
H1 : μ < 5.4
F.)
If Pvalue < α ; Reject H0
G.)
Test statistic :
(xbar - μ) ÷ (s/sqrt(n))
(4.5 - 5.4) ÷ (2.7/sqrt(80))
-0.9 ÷ 0.3018691
= - 2.98
H.)
Pvalue fro Zscore calculator, α = 0.10 = 0.002882
I.)
Decision :
0.002882 < 0.10
Since, Pvalue < α ; We reject the Null
J.)
We Can conclude that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced
&50+ E3 857=6180 150 #130 GELD Four girls have $5.00 to share equally. How much money will each girl get? Explain. What if four girls want to share $5.52 equally? Hov vill each
girl get? Explain.
answer is 5.00/4=1.25
Answers
Answer:
Step-by-step explanation:
(5 dollars)/(4 girls) = (5/4 dollars)/girl = (1.25 dollars)/girl
:::::
(5.52 dollars)/(4 girls) = (5.52/4 dollars)/girl = (1.38 dollars)/girl
find the area simplify your answer
Answers
Answer:
6x^2-8x-64
Step-by-step explanation:
the answer for solving a quadrilateral
is base times height
so the base is 2x-8 and the height is 3x+8
(2x-8)(3x+8)
expand
6x^2-8x-64
Hope that helps :)
Please give brainliest
The diagram below shows a circular pizza with a diameter of 16 inches. The pizza is in a square box with side lengths of 18 inches. In square inches, how much of the box is empty?Use π = 3.14 and round your answer to the nearest hundredth.
Answers
Answer:
pls do mark my answer as the brainliest..........
Step-by-step explanation:
portion of square empty = 256 - 153.86 = 102.14cm^2
Can someone please answer this question? It is from RSM. The first to answer will be marked brainliest
Answers
Answer:
16/20=0.8
Step-by-step explanation:
hope this helps
Answer:
I think it's the second one
Find the perimeter and area of the figure
Answers
Answer:
C.
Step-by-step explanation:
C. is the only answer option with the correct perimeter of 18u
area is correct too
Answer:C
Step-by-step explanation: If you look at the graph it shows that the triangle is 18.u as a perimeter and 20.5 as area.
What percent of 125 is 90? Write your answers in the blanks.
Answers
Answer:
72
Step-by-step explanation:
Answer:
The percent of 125 to give 90 is 72%
PLEASEEEEEEE HELP ME! WILL GIVE 20 POINTS AND BRAINLIEST
Answers
Answer:
a - 50/100
b - 9/4
c - 27/8
Step-by-step explanation:
Scale: 50/100
Ratio: 36/16 = 18/8 = 9/4
Ratio: 216/64 = 108/32 = 54/16 = 27/8
Here are five statements.
For each statement, say whether it is TRUE or FALSE.
The first one has been done for you.
Note: Please make sure you follow the format of the answers, e.g.
2) ....
3) ...
Answers
Answer:
Step-by-step explanation:
2) False.
3) True. It could be 50°-65°-65°.
4) True. It could be 35°-35°-110°.
5) True. It could be 40°-50°-90°.
Who can help me with this please
Answers
Answer:
I cant see the full question, what is it ?
Step-by-step explanation:
having trouble with this problem, pls help :/ I know the answer, just not how to get there. (ap calc ab, integrals)
Answers
Answer: D) 101
Step-by-step explanation:
By linearity, we can break it up into 2 integrals. The integral and derivative of f easily cancel out
[tex]\int\limits^{10}_{-1} {(2x+0.5f'(x))} \, dx =\int\limits^{10}_{-1} {2x} \, dx +0.5\int\limits^{10}_{-1} {f'(x)} \, dx =x^2|^{^{10}}_{_{-1}}+0.5f(x)|^{^{10}}_{_{-1}}\\=(100-1)+0.5(f(10)-f(-1))=99+0.5(8-4))=101[/tex]
I used the table for values of f(x) at 10 and -1. Wouldn't be surprised if this was part of a series of questions about f because I really can't see how you could use the hypothesis that f is twice differentiable on R. Same for the other table values. I'm curious about how you found the answer. Was it a different way?
what is the volume of a rectangular prism wi the the dimensions base 5/8 cm, height 2/3 cm, and length 3/4 cm?
Answers
Answer:
5/16 cm³Step-by-step explanation:
Given that:
Width (W) = 5/8 cmHeight (H) = 2/3 cmLength (L) = 3/4 cmFind the volume of the cuboid!
Volume equation =
W × H × L =
5/8 × 2/3 × 3/4 =
(5×2×3)/(8×3×4) =
30/96 =
5/16 cm³The volume = 5/16 cubic centimetres
____________________
#IndonesianPride - kexcvi
the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence
Answers
Given:
In an arithmetic sequence,
[tex]a_1=2[/tex]
[tex]a_i=a_{i-1}-3[/tex]
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
[tex]a_i=a_{i-1}+d[/tex] ...(i)
Where, d is the common difference.
We have,
[tex]a_i=a_{i-1}-3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]d=-3[/tex]
The sum of first i terms of an arithmetic sequence is:
[tex]S_i=\dfrac{i}{2}[2a+(i-1)d][/tex]
Putting [tex]i=335,a=2,d=-3[/tex], we get
[tex]S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)][/tex]
[tex]S_{335}=\dfrac{335}{2}[4+(334)(-3)][/tex]
[tex]S_{335}=\dfrac{335}{2}[4-1002][/tex]
[tex]S_{335}=\dfrac{335}{2}(-998)[/tex]
On further simplification, we get
[tex]S_{335}=335\times (-499)[/tex]
[tex]S_{335}=-167165[/tex]
Therefore, the sum of the first 335 terms in the given sequence is -167165.
write the fraction 4/9 as an equivalent fraction with the given denominator 45
Answers
Answer:
answer is in the picture
What is another possible solution to the inequality -2x > 6?
Answers
Answer:
Step-by-step explanation:
Answer:
x<−3
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2x>6
Step 1: Divide both sides by -2.
−2x/−2 > 6/−2
Answer:
x<−3
HOPE THIS HELPS
Branliest pls?
The television show 50 Minutes has been successful for many years. That show recently had a share of 15, which means, that among the TV sets in use, 15% were tuned to 50 Minutes. An advertiser wants to verify that 15% share value by conducting its own survey, and a pilot survey begins with 15 households have TV sets in use at the time of a 50 Minutes broadcast.
Required:
a. Find the probability that none of the households are tuned to Lindsay and Tobias. (Round to three decimal places as needed)
b. Find the probability that at least one household is tuned to Lindsay and Tobias.
c. Find the probability that at most one household is tuned to Lindsay and Tobias.
d. If a most one household is tuned to Linday and Tobias, does it appear that the 15% share value is wrong? Why or wh not?
Answers
Answer- b
Step-by-step explanation:
its b
In ………………………………… areas, the annula temperatures is often below Freezing point
Answers
Answer:
Tundra
Step-by-step explanation:
In Tundra (or arctic) areas, the annula temperatures is often below Freezing point
Let event A = The animal is a bird
Let event B = The animal can fly.
Which outcomes are in A and B?
A. {penguin, robin, sparrow, pelican, bat)
OB. {robin, sparrow, pelican}
O C. (penguin, robin, sparrow, pelican}
O D. (robin, sparrow, pelican, bat)
Answers
Answer:
B. {robin, sparrow, pelican}
Step-by-step explanation:
hope it helps you...
The outcomes are in A and B is,
⇒ {robin, sparrow, pelican}
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Let event A = The animal is a bird
Let event B = The animal can fly.
Hence, We get;
The outcomes are in A and B in which animal is a bird and also can fly.
Thus, The outcomes are in A and B is,
⇒ {robin, sparrow, pelican}
Hence, The outcomes are in A and B is,
⇒ {robin, sparrow, pelican}
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ7
In this fraction, which number is the denominator? 1/15
A.
1
B.
15
Answers
Answer: B. 15
Step-by-step explanation: The number on the bottom of the fraction is always the denominator, therefore 15 is the denominator in the fraction.
help me? please?????????
Answers
Answer:
[tex]\huge\boxed{\tt{\frac{8}{63} }}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{8}{9} * \frac{1}{7} \\\\= \frac{8*1}{9*7} \\\\= \frac{8}{63} \\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807This my lil sis work help her
Answers
Answer:
Option D is your answer
answer:
d
step-by-step explanation:
here i will show you how to convert the improper fraction 18/15 to a mixed number (aka mixed fraction). we start by setting up the fraction below.
[tex]\frac{18}{15}[/tex]
step 1 - find the whole number
calculate out how many times the denominator goes into the numerator. to do that, divide 18 by 15 and keep only what is to the left of the decimal point:
18 / 15 = 1.2000 = 1
step 2 - find the new numerator
multiply the answer from step 1 by the denominator and deduct that from the original numerator.
18 - (15 x 1) = 3
step 3 - put it together
keep the original denominator and use the answers from step 1 and step 2 to get this:
1 [tex]\frac{3}{15}[/tex]
good luck :)
i hope this helps
have a nice day !
find the perimeter of following figure. 2 yd ,2yd ,5yd and 4 yd.
Answers
Answer:
13yd
Step-by-step explanation:
Perimeter is all the side lengths added
Lauren brings brownies to class and gives 3/5 of them to Peter, Wendy, and Michael. If she gave them 21 brownies, how many did she bring to class?
Answers
Answer:
If 3/5 of all the brownies is 21, then 5/3 of 21 is the number of the brownies that Lauren brought in.
That probably sounded super confusing. When multiplying a number by a reciprocal of a fraction (a fraction where the numerator and denominator is reversed), the previous fraction multiplication is reversed.
Multiplying 21 with 5/3 will give us the original number of brownies.
Lauren originally brought 35 brownies.
Step-by-step explanation:
plz mark brainlyest it really helps
Each question is worth 10 pts, I will do brainliest for the person who does both and follow pls help.
1. One scoop of ice cream weighs about 3 ounces. Last Thursday the ice-cream parlor used 18 pounds of ice cream. About how many scoops of ice cream were served last Thursday?
2. Doris's bill at the ice-cream parlor comes to $2.54. She realizes that she doesn't have any dollar bills, so she is paying with coins. She has 24 coins including quarters, dimes, nickels, and pennies. She has the same number of nickels as quarters and twice as many dimes as quarters. If she has 5 nickels, how many quarters, dimes, and pennies does she have?
Answers
Answer:
1. 6
2.
pennies = 9
nickels = 5
quaters = 5
dimes = 10
Step-by-step explanation:
1.
18/3 = 6
as we know that there are 18 scoops, and 3 per icecream, we can divide the two to get the number of ice creams
2.
5n
#n = #q; #q = 2#d, this is a simple ratio, you just plug in the variables to get
5n = 5q = 10d = 15 coins
24 - 15 = 9 pennies
pennies = 9
nickels = 5
quaters = 5
dimes = 10
An artist is painting a flower pot that each require 1/34 gallons of paint what is the maximum numbers of flowerpots the artist can paint with 3/4 gallons of paint.
A.12
B.16
C.24
D.32
E.42
Answers
Answer:
C
Step-by-step explanation:
Hello There!
We can easily calculate the amount of flower pots he can paint by dividing the amount of paint he has by how much paint each flower pot requires
[tex]\frac{.75}{\frac{1}{34} } =25.5[/tex]
The closest number is 24 therefore your answer is C
The sum of 15 and p is equal to 27.
Write the equation that represents the description.
Answers
Please help!!! Rachael deposits $1,500 into a retirement fund each year. The fund earns 8.2% annual interest, compounded monthly. If she opened her account when she was 19 years old, how much will she have by the time she is 55? How much of that amount will be interest earned?
Answers
Answer:$82,500
Step-by-step explanation:
what is 4x + 8 = 10
Answers
4x+8=10 1. Subtract 8 from both sides
-8 -8
——————
4x=2 2. Divide each side by 4
/4 /4
—————— 3. Simplify fraction
x=1/2
9 and 11 need help
Mark brainlist
Answers
I will do 9 only. You can do 11.
Question 9
sin(60) = x/8
sin(60)(8) = x
4•sqrt{3} = x
x^2 + y^2 = 8^2
(4•sqrt{3})^2 + y^2 = 64
16(3) + y^2 = 64
48 + y^2 = 64
y^2 = 64 - 48
y^2 = 16
sqrt{y^2} = sqrt{16}
y = 4
Do 11 the same way.