Given:
The equation of circle is
[tex](x+3)^2+y^2=9[/tex]
To find:
The polar form of given circle.
Solution:
We have,
[tex](x+3)^2+y^2=9[/tex]
[tex]x^2+2(x)(3)+(3)^2+y^2=9[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex](x^2+y^2)+6x+9=9[/tex]
Subtracting 9 from both sides, we get
[tex](x^2+y^2)+6x=0[/tex]
We know that, [tex]x^2+y^2=r^2[/tex] and [tex]x=r\cos \theta[/tex].
[tex]r^2+6(r\cos \theta)=0[/tex]
[tex]r(r+6\cos \theta)=0[/tex]
[tex]r=0[/tex] and [tex]r+6\cos \theta=0[/tex]
We know that, r is radius it cannot be 0. So,
[tex]r+6\cos \theta=0[/tex]
[tex]r=-6\cos \theta[/tex]
Therefore, the correct option is A.
how to find future value?
Step-by-step explanation:
FV=$1000×(1+0.1)5
try solving with this it might help you and if it did please make me brainliest plzzzzxx
Explain what you would do first to simplify the
expression below. Justify why, and then state the
result of performing this step.
312
1212
2
4+²
Answer:
how do you do this
Step-by-step explanation:
what expression is equivalent to (2.1x+4.3) - (-3x-7)
What is the average rate of change for [-1,2]? I need a answer please!!!!!!!!!
Answer: -2
Hope this helps :)
Answer please, be sure your right or don’t answer at all.
Answer:
y > 1/3x -3
Step-by-step explanation:
Just find the equation of the line, which is y = 1/3x -3, and then determine what the symbol is going to be. Since the line is dotted, it will either be < or >. When the shaded area is on top of the line, it's >. Remember that by saying left on the bottom or right on top.
1. After running, Maggie is 3 miles east of her starting point, and 4 miles north of her starting point. What angle could represent her direction of travel?
Answer:
The angle is 53.13 degrees
Step-by-step explanation:
Here, we want to calculate angle representing the direction of travel
From the question, she is 3 miles east and 4 miles north of her starting point
So the angle that represents her direction of travel will be that which makes a cut with the horizontal (the east direction)
Now, let us picture a right-angled triangle, with 3 miles direction being the adjacent and the 4 miles direction (facing the angle we want to calculate and is the opposite)
the trigonometric identity to use is the Tangent
Tan theta = 4/3
theta = arc tan (4/3)
theta = 53.13 degrees
The graph of f (x) = x + 5 is a vertical translation 5 units
up of the graph of f(x) = x. How can you obtain the graph of
f(x) = x + 5 from the graph of f (x) = x using a horizontal
translation?
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
[tex]\displaystyle f(x)=x[/tex]
To shift vertically n units, we can simply add n to our function. Hence:
[tex]f(x)=x+n[/tex]
So, a vertical shift of 5 units up implies that n=5. So:
[tex]f(x)=x+5[/tex]
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
[tex]f(x-n)=(x-n)[/tex]
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
[tex]f(x-1)=(x-1)[/tex]
Or:
[tex]f(x)=x-1[/tex]
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
The product of a number below - 7/10 is 2/10
what is the number?
-7/20
7/20
- 5/7
5/7
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
This question can be written algebraically as [tex]-\frac{7}{10} x=\frac{1}{2}[/tex]
And the image below shows step-by-step on how to solve it
Hope this helps! :)
Is this true or false? The following graph represents a proportional relationship
A. True
B. False
Answer:
True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
what is an equivalent expression for (6 powered by 4)to -1 powered
Answer:
1/1,296
Step-by-step explanation:
[tex]( {6}^{4} )^{ - 1} = {6}^{ - 4} = \frac{1}{ {6}^{4} } = \frac{1}{1,296} \\ [/tex]
Simplify.
34−4x+12x−12+12x
Enter your answer in the box.
Do not use decimals in your answer.
Answer:
22 - 28x
Step-by-step explanation:
34−4x+12x−12+12x
you wanna combine like terms
34 - 16x + 12 + 12x
34 - 28x + 12
22 - 28x
The dimensions for a rectangular prism are x + 2 for the length, x + 3 for the width, and x for the height. What is the volume of the prism? Enter your answer as a polynomial in standard form. The volume of the prism can be expressed as (_____)
please if you can explain it to me, I want to understand how to do this as well. thank you for your help
Answer:
Step-by-step explanation:
Select all equivalent expressions from the list.
8(7x-6)
•15x-6
•56x-48
•56x-6
•8•7x-8•6
Answer:
It should be 56x-48 and (8*7)x-(8*6)
Step-by-step explanation:
I WILL GIVE BRAINLIEST 50 POINTS
What is the average rate of change for the mold over the 6 days?
Answer:
The average rate of change is 63/6
Step-by-step explanation:
You take the the change from 0 - 6 and 1 - 64 as the changes
the equation is: delta y
delta x
so the average rate is 63/6
I WILL GIVE BRAINLEST!!!!!!
Frank earned x dollars the first week of his new job. He earned 5% more the
second week than the first week. Which expression represents the total amount of
money Frank earned for both weeks?
A. 1.50x
B. 1.05x
C. 2.00x
D. 2.05x
PLSSS SHOW YOUR WORK PLSSSS
-3x + 18 = 6
x = ___
show work please
Answer:
x=4
Step-by-step explanation:
-3x + 18 = 6
First, we have to get x alone. So, we have to subtract 18 from 6.
6 - 18 = -12
-3x = -12
-12/-3 = 4
x=4
I just need help on this please
Answer:
the slope is mx+b so 3
Step-by-step explanation:
mx+b
Paul was making some brownies and cupcakes for his school fundraiser. If the brownies needed 4.8 cups of sugar and the cupcakes needed 5.2 cups, how much sugar would he need altogether?
Answer:
10 cups in total.
Step-by-step explanation:
4.8+5.2= 10.00
add the .2 to the 4.8 you get get 5 then add 5.0+5.0
what is 0.000 002 in standard form
Answer:
[tex] 0.000 002 = 2 \times {10}^{ - 6} [/tex]
Step-by-step explanation:
It is already in standard form and can be expressed in scientific form as:
[tex]0.000 002 = 2 \times {10}^{ - 6} [/tex]
Answer:
0.000 002 in standard form is NaN x 100^0
Step-by-step explanation:
Graph the line with the equation
y=1/2x-6
Answer:
Picture above
Step-by-step explanation:
This was created using Desmos, you can also use this to graph equations! It is online in a browser and a mobile app :)
Step-by-step explanation:
you go down 6 and put a dot there, and then you go up one and to the right 2, and put a dot there too. after, you just keep going up 1 right 2 and putting dots there, and you can also go down 1 to the left 2
That's it, I hope I helped! If I had a graph with me it would be way easier to explain, but I don't
Right answer will get brainlist
Answer:
x = -3
Step-by-step explanation:
System of equations has been given as,
y = 2x + 8
y = [tex]-\frac{2}{3}x[/tex]
Since, solution of the system of equations is the point of intersection on the graph.
Therefore, point of intersection or solution of the system will be,
(x, y) = (-3, 2)
This common point will satisfy both the equations.
And x = -3 will also both the equations.
what is the slope..
Answer:
the slope is 2
Step-by-step explanation:
the x's are increasing by 4 each time and the y's are increasing by 2 each time giving you [tex]\frac{4}{2\\}[/tex] which simplifys to 2
A boat traveled 300 miles in 15 hours. What rate did the boat travel in miles
per hour?
1. 2
2. 20
3. 30
4. 285
Answer:
2.20 ms
Step-by-step explanation:
distance divided by time
300÷15=20
Can someone answer this for me ill give brainliest asap
Glen mixes red bricks with yellow bricks when building sides of a brick house. The ratio is 3 pieces of red brick for every 7 pieces of yellow brick. If there are 28 pieces of yellow brick, how many pieces of red brick will there be?
Answer:
12 red bricks
Step-by-step explanation:
Number the answer like, in the blank type in the answer. Pls help ignore my answers unless correct
1. ____
2____
3______
Answer:
1. 32 2. You got that one correct 3. 1 5/34
Step-by-step explanation:
1. 24 / 3/4
3/4 = .75
24/ .75 = 32
3. Turn into improper fraction
13/4 / 17/6
= 1 5/34
Hope this helps dude
Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: A(3,6) B(11,10)
Line 2: C(-4, 2) D(6, 16)
Parallel, Perpendicular, or Neither:
Answer:
Line 1 : A. Neither B. Parallel__________ Line 2: A. Perpendicular B. Parallel
Step-by-step explanation:
Sorry this was hard to make a picture of it in my head. *Exhausted face* ._.
Why do scientists use models?
A)
Models are unreliable.
B)
Models waste natural resources.
Models predict not just describe events.
Models are based on scientific laws and principals so they are more
reliable than the real thing.
D)
HELP HELP HELP PLEASE
A line has a slope of 1/4. The line passes through the point (4, 6). The line also passes through the point (12, k). What is the value of k?
What is the domain ??
Answer:
[-8, 6]
Step-by-step explanation:
Domain is the x values. Look at the smallet x value, in this case -8, and the largest, in this case 6, and write them like a point using [] not (). You use [ or ] for numbers and ( or ) for infinity signs.