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 product of (1.1x + 2.7y) (1.1x - 2.7y)
Answers
Step-by-step explanation:
Please refer to the attachment
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.
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:
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:
please i need help with it
3(x−2)+5x=26
Answers
Answer:
x=4
Step-by-step explanation:
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
- 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
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
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.
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
Answer to this question?
Answers
Answer:
First Answer is correct
Step-by-step explanation:
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!
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
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
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
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
1/4 + 1/8= ????????????
Answers
Answer:
3/8!! hope i helped :))
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
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.
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:
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:
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♀️
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
Simplify. 6(23x–5)−7x−8
Answers
The diagonal of a rhombus are 14cmand 10 cm find the area of
rhombus.
Answers
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
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
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
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
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: