2. Given the equation of a circle in standard form, identify the center, radius, and graph the circle.
(x + 1)2 + (y - 2)2 = 36
Center:
Radius:
Answers
Answer:
Center: ( -1 , 2 )
Radius: 6
Step-by-step explanation:
The equation for a circle is given as follow:
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
Where,
the Center is: ( h , k ) (note that the signs of the number are different)
and the radius is: r
So if we compare the original circle equation to the equation in the question we can see that:
[tex](x+1)^{2} +(y-2)^{2} =36[/tex]
the Center is: (-1,2)
and the radius is: [tex]\sqrt{36}[/tex] = 6
2. To draw the graph find points that lay on the circle, it's better to take the values of x and y from the Center:
first sub y=2 in the equation to find the values for x:
[tex](x+1)^{2} +(y-2)^{2} =36[/tex]
[tex](x+1)^{2} +(2-2)^{2} =36[/tex]
[tex](x+1)^{2} +(0)^{2} =36[/tex]
[tex](x+1)^{2} =36[/tex]
[tex]x+1 =±\sqrt{36}[/tex]
[tex]x=6-1[/tex] AND [tex]x=-6-1[/tex]
[tex]x=5[/tex] AND [tex]x=-7[/tex]
The points are A(5,2) and B(-7,2)second sub x= -1 in the equation to find the values for y:
[tex](x+1)^{2} +(y-2)^{2} =36[/tex]
[tex](-1+1)^{2} +(y-2)^{2} =36[/tex]
[tex](0)^{2} +(y-2)^{2} =36[/tex]
[tex](y-2)^{2} =36[/tex]
[tex]y-2=±\sqrt{36}[/tex]
[tex]y=6+2[/tex] AND [tex]y=-6+2[/tex]
[tex]y=8[/tex] AND [tex]y=-4[/tex]
The points are D(-1,8) and E(-1,-4)After finding the points write them in the graph and match them together to get the like the circle in the picture below:
Related Questions
Find the measure of the indicated angle
Answers
Answer:
x = 7
angle (7x + 8) = 57 degrees
Step-by-step explanation:
all triangles interior angles add up to 180 degrees.
(7x+8) + 90 + 33 = 180
7x+8 = 57
7x = 49
x = 7
(7x + 8) = 57
Answer:
57 degrees
Step-by-step explanation:
7x+8+33=90
7x=90-8-33
=90-41
7x=49
x=7
PLz Welp.............................
Answers
9514 1404 393
Answer:
No
Step-by-step explanation:
If the relationship were proportional, the ratio of y to x would be a constant.
y/x = 3/1 ≠ 7/3
x and y are not proportional.
handing out brainliest!! first one to answer!❤️
Answers
Answer:
should be a hope it helps
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
90/1=90
140/2=70
190/3=63.3333333
240/4=60
so the first hour cost more than the others, hope this helps!
prove it please
answer only if you know
Answers
Part (c)
We'll use this identity
[tex]\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\[/tex]
to say
[tex]\sin(A+45) = \sin(A)\cos(45) + \cos(A)\sin(45)\\\\\sin(A+45) = \sin(A)\frac{\sqrt{2}}{2} + \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\[/tex]
Similarly,
[tex]\sin(A-45) = \sin(A + (-45))\\\\\sin(A-45) = \sin(A)\cos(-45) + \cos(A)\sin(-45)\\\\\sin(A-45) = \sin(A)\cos(45) - \cos(A)\sin(45)\\\\\sin(A-45) = \sin(A)\frac{\sqrt{2}}{2} - \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\[/tex]
-------------------------
The key takeaways here are that
[tex]\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\[/tex]
Therefore,
[tex]2\sin(A+45)*\sin(A-45) = 2*\frac{\sqrt{2}}{2}(\sin(A)+\cos(A))*\frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\2\sin(A+45)*\sin(A-45) = 2*\left(\frac{\sqrt{2}}{2}\right)^2\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = 2*\frac{2}{4}\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = \sin^2(A)-\cos^2(A)\\\\[/tex]
The identity is confirmed.
==========================================================
Part (d)
[tex]\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\\sin(45+A) = \sin(45)\cos(A) + \cos(45)\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}\cos(A) + \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\[/tex]
Similarly,
[tex]\sin(45-A) = \sin(45 + (-A))\\\\\sin(45-A) = \sin(45)\cos(-A) + \cos(45)\sin(-A)\\\\\sin(45-A) = \sin(45)\cos(A) - \cos(45)\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}\cos(A) - \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\[/tex]
-----------------
We'll square each equation
[tex]\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\\sin^2(45+A) = \left(\frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\right)^2\\\\\sin^2(45+A) = \frac{1}{2}\left(\cos^2(A)+2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]
and
[tex]\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\\sin^2(45-A) = \left(\frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\right)^2\\\\\sin^2(45-A) = \frac{1}{2}\left(\cos^2(A)-2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]
--------------------
Let's compare the results we got.
[tex]\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]
Now if we add the terms straight down, we end up with [tex]\sin^2(45+A)+\sin^2(45-A)[/tex] on the left side
As for the right side, the sin(A)cos(A) terms cancel out since they add to 0.
Also note how [tex]\frac{1}{2}\cos^2(A)+\frac{1}{2}\cos^2(A) = \cos^2(A)[/tex] and similarly for the sin^2 terms as well.
The right hand side becomes [tex]\cos^2(A)+\sin^2(A)[/tex] but that's always equal to 1 (pythagorean trig identity)
This confirms that [tex]\sin^2(45+A)+\sin^2(45-A) = 1[/tex] is an identity
You start at point A and walk north for 12 meters. You turn right and walk for 8 additional meeters. Finally, you turn south and walk 3 meters. How far away are you from your original position. Leave your answer as a simplified radical.
Answers
Answer:
28m
Step-by-step explanation:
Simplify. 6(23x–5)−7x−8
Answers
Which equation represents a proportional relationship? A. y=x/8. B. y=8/x. C. y=x/8+8. D. y=8/x+8.
Answers
Answer:
c and d have a proportial relationship.
Step-by-step explanation:
hope this helps
Answer to this question?
Answers
Answer:
First Answer is correct
Step-by-step explanation:
Which of the following shapes is concave?
OA)
OB)
OC)
OD)
Answers
Answer:
A is a concave polygon,....,.
Answer:
the answer will be A.
Step-by-step explanation:
Jerry was trying out for the cross country team. He has to be able to run an 8.5 min mile. If he ran 5 mi in 45 mins last weekend, will this rate be good enough to make the team.
Answers
Answer:no he misses the rate he needs to run by 30m seconds
Step-by-step explanation:
45/5=9
Answer: No because in 5 miles he needs to run for 42.5 minutes or less
I need help with this one please and can yall explain this because I try to do but I can't just figure it out
Answers
Answer:
9
Step-by-step explanation:
because the FIM and LAK are similar, then
FI/LA=IM/AK=MF/KL
MF/KL=2/3
The diagonal of a rhombus are 14cmand 10 cm find the area of
rhombus.
Answers
PLEASE HELP 20 POINTS One day, River writes down the numbers $1,$ $2,$ $\dots,$ $999.$ What is the sum of all the digits that River wrote down?
Answers
Question isn't well formatted :
Actual question :
One day, River writes down the numbers 1,2,...,999. What is the sum of all the digits that River wrote down?
Answer:
499500
Step-by-step explanation:
Number written :
1, 2,...., 999
The interpretation of the number written is 1 up to 999
Hence, the sum of the number written is the addition of all the numbers from 1 up to 999
Using the python program :
sum = 0
for i in range(1000):
sum += i
print (sum)
Output = 499500
Answer:
13500
Step-by-step explanation:
Notice how it says the sum of all of the DIGITs. We have to add together the sum of the digits. We can do this by:
300(1 + 2 + 3 + 4.... + 9) = 300*45 = 13500
A little help?!? Pleaseee
Answers
Answer:
I think no. Because degree is the sum all variables in first equation degree. Is14 but second equation degree not 14.
Ron works 8 hours a day, 5 days a week, $15 dollars an hour, for 12 weeks.
What is his gross pay?
Answers
Answer:
If Ron works 8 hours a day and get's paid $15 an hour
for 5 days a week and works for 12 weeks
1 hour = $15
8 hours = $120
So Ron get's paid $120 a day
So if he works 5 days a week then
120 x 5 = $600
Ron get's paid $600 a week
So if Ron works for 12 weeks then
600 x 12 = $7,200
Ron's gross pay is $7,200
Step-by-step explanation:
1/4 + 1/8= ????????????
Answers
Answer:
3/8!! hope i helped :))
How many pieces of ribbon can you cut from 10 meters, if each piece is 4
cm long?
Answers
Answer:
answer:250 pieces
1 metre=100cm so
10metres =100*10 =1000cm
each piece is 4 CM long, so.,
no. of pieces=1000/4
by dividing by 2....
=500/4
again by dividing by2...
=250/1=250 pieces
so 250 pieces of ribbon can be cuttted from 10 metre long ribbon.
- 2x + 4 for x = - 3, 0 , and 3.
Answers
Answer:
when x=-3 y=10
when x=0 y=4
when x=3 y=-2
Step-by-step explanation:
all you have to do is plug in -3 0 and 3 for x
-2(-3)=6
6+4=10 so when x=-3 y=10
-2(0)=0
0+4=4
so when x=0 y=4
-2(3)=-6
-6+4=-2
so when x=3 y=-2
What digit is missing from the quotient?
Answers
Answer:
1
Step-by-step explanation:
Answer:
1 is missing
Step-by-step explanation:
As 4285 ÷ 7 = Quotient- 612 , Remainder - 1
please i need help with it
3(x−2)+5x=26
Answers
Answer:
x=4
Step-by-step explanation:
Frederick's brother is going on a hike. He has his backpack filled with supplies. His backpack weighs 400 ounces. How many pounds is Frederick's backpack? Note: 1 pound = 16 ounces
Answers
Answer:
25
Step-by-step explanation:
Do 400 divided by 16 to convert to pounds
400/16=25
Hope this helped :)
Answer:
25 pounds
Step-by-step explanation:
1 Pound=16 ounces
? Pounds=400 ounces
400 divided by 16=25
25 pounds=400 ounces
Which algebraic expression represents “Marcus practiced the trumpet twice as long this week”?
2 + p
2p
p minus 2
StartFraction p Over 2 EndFraction
Please Help!
Answers
Answer:
2p should be the correct answer!
Answer:
2p is the answer
Step-by-step explanation:
I took the answer edg2021
In each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained. C
Answers
What is the answer?
here is the image
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
What is dilation?Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image.
From the diagram:
Scale factor = A'B' / AB = 6/3 = 2
Center = (6, -6)
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
Find out more on dilation at: https://brainly.com/question/10253650
This means that each point where the two lines intersect is a
Answers
Answer: When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.
I think this the answer♀️
which statement shows the correct reasoning for finding 12divided by 3/8
A. multiply 12 by 8,then divide by 3
B. multiply 12 by 3 than divide by 8
C. multiply 3 by 8,then divide by 12
D. multiply 12 by 1/8, then multiply by 3
Answers
12×8/3
=
12×8
---------
3
96
------
3
32
so option A is correct
Answer:
Option A is the right one
Givereasons
a) The image gives all the details of an object.
b) The shadow of a translucent material is not clear.
Answers
Answer:
a
Step-by-step explanation:
Help me ASAP!!!!!!!!!
See picture attached.
WINNER GETS BRAINLIEST, A STAR RATING OF EXCELLENT AND THANKS!!!!!!!!!!! Good luck!
Answers
Answer:
Step-by-step explanation:
A)8
A) 8
B) 64
Find the product of (1.1x + 2.7y) (1.1x - 2.7y)
Answers
Step-by-step explanation:
Please refer to the attachment
A rectangular prism has a volume of 360 in3. If the height measures 6in. which base measurements could the prism have?
Answers
Answer:
Both sides that are parallel ( 6 inches I believe ) would be 12 in total for both sides. Then the top and bottom would be 3 inches ( I believe ) which would be 6. I think you need to do 6 times 12 until you get 360 and then see how many times you multiplied it and that is your answer. But I am not FULLY sure. Hope this helps somehow!
Step-by-step explanation:
if y varies directly as x and y=32 when x=4. find the constant of variation
Answers
Answer:
k = 8
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 32 when x = 4, then
32 = 4k ( divide both sides by 4 )
8 = k
