Step-by-step explanation:
r − r cos θ = 6
r = r cos θ + 6
r² = (r cos θ + 6)²
x² + y² = (x + 6)²
x² + y² = x² + 12x + 36
y² = 12x + 36
The rectangular form of the polar equation is x² + y² = 2x + y - 2.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To convert a polar equation to rectangular form, you can use the following relationships between polar and rectangular coordinates:
x = r x cos(theta)
y = r x sin(theta)
where r is the distance from the origin to the point in polar coordinates, and theta is the angle between the positive x-axis and the line connecting the origin and the point.
Now,
So, if you have a polar equation in the form of r = f(theta), you can substitute these expressions for x and y into the equation to obtain a rectangular equation in terms of x and y.
The resulting equation will typically be a function of x and y, rather than just one variable as in the polar form.
For example,
If you have the polar equation r = 2 + sin(Ф), you can substitute x = rcos(Ф) and y = rsin(Ф) to get:
x = (2 + sin(Ф)) x cos(Ф)
y = (2 + sin(Ф)) x sin(Ф)
Simplifying these expressions using trigonometric identities, you can get the rectangular form of the polar equation:
x² + y² = 2x + y - 2
Thus,
The rectangular form of the polar equation is x² + y² = 2x + y - 2.
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Factor the algebraic expression 21a + 9
Answer:
21a + 9
Simplifying
21a + 9
Reorder the terms:
9 + 21a
Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 7a)
Final result:
3(3 + 7a)
HOPE THIS HELP
Answer:
[tex]3(7a+3)[/tex]
Step-by-step explanation:
What is the slope of the line described by the equation below?
y-5 = 6(x-4)
Answer:
6
Step-by-step explanation:
To solve this, you need to have your equation in slope-intercept form. This is y=mx+b, where m is the slope and b is the y-intercept.
y - 5 = 6(x - 4)
y - 5 = 6x - 24
y = 6x - 19
The slope, m, is equal to 6.
The floor of a living room is 7m by 5m. How many 50cm square tiles are required?
Answer
7m x 5m = 35, then multiply by 100, so then the answer is 3,500
Step-by-step explanation:
The number of tiles that can fit in the living room is 7000.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
As per the given dimension of the living room,
7m by 5m
Area = 7 x 5 = 35 m²
Area of one tile = 50 cm² = 0.005m²
With this surface area the number of tiles that can be fit,
35/0.005 = 35000/5 = 7000
Hence "The number of tiles that can fit in the living room is 7000".
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How many ways can you pick a President, Vice President, Secretary and Treasurer from a group of 12 people?
479,001,600
19,958,400
20,736
11, 880
Answer: 20,736
Step-by-step explanation:
There are 12 people total in the room, so the base of the exponent will be 12.
Sine there are 4 possible positions, the exponent will be 4.
# of possibilities = 12^4
12^4 = 12 * 12 * 12 *12 = 20,736
A prism has a length of 15 inches, height of 5 inches, and width of 4 inches. The formula for volume of a rectangular prism is V = lwh. The length of the prism is in. The width of the prism is in. The height of the prism is in. The volume of the prism is in.3.
Answer:
it is 300
Step-by-step explanation:
you must multiply 15 by 4 by 4
The volume of the prism is 300 in³.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The length of the prism is 15 inches.
The width of the prism is 4 inches.
The height of the prism is 5 inches.
To find the volume of the prism, we use the formula.
V = l w h
V = (15)(4)(5)
V = 300 cubic inches.
Therefore,
The volume of the prism is 300 in³.
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rosa pays a monthly membership fee at a gym. She also pays $5 for each cycling class she takes. in May, she took 4 cycling classes and her total cost for the month was $55. in June, Rosas total cost was equal to twice the membership fee. How many cycling classes did she take?
Answer:
14 classes
Step-by-step explanation:
if she pays $5 per cycling class than in May she payed $20. $55 - $20 = 35. If in June the cost was double the membership fee than 35 x 2 = 70. Than you do 70 / 5 = 14.
f(x) = x
g(x) = 1
What is the domain of
(g/f)(x)
Answer: x≠0
Step-by-step explanation:
Makes the equation undefined
The temperature at dawn is -6°F but by noon it is 22°F. What is the difference in
temperatures?
O -16°F
O-28°F
O 16°F
O 28°F
Answer: 28 degrees farenheit
Step-by-step explanation: add 22 and 6 for the total of how many degrees -6 is from 22.
If the temperature at dawn is -6°F but by noon it is 22°F.Then 28°F is the difference in temperatures
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The temperature at dawn is -6°F
The temperature at dawn in afternoon is 22°F.
We need to find the difference in temperatures.
Difference is nothing but subtracting one number with another number.
Now subtract -6°F from 22°F.
22°F-(-6°F)
Twenty two degree fahrenheit plus six degree fahrenheit
22°F+6°F
28°F
Hence there is 28°F in temperatures. Option D is correct.
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ANSWER QUICK. I NEED ANSWER IN 5 MINUTES.
Answer:
yes. it is correct.
Answer:
Yes
Step-by-step explanation:
because the plus two just move all the points up two so the vertex would be (0,2) which is what the vertex is
Find two numbers a and b whose sum a+b is −3, and whose difference a−b is −7.Your answer is
Answer:
a = -5
b = 2
Step-by-step explanation:
a+b=-3
a-b= -7 +
2a = -10
a = -10/2
a = -5
a + b = -3
-5 + b = -3
b = -3 + 5
b = 2
URGENT PLEASE
Rhonda kept track of the cats at a shelter where she volunteers. She measured how many times per day each cat ate, and she also ranked their activity level on a scale from 1 to 10 each day. She found the line of best fit for the data has the equation y=0.23x+4.1, where x represents the activity level and y represents the number of meals eaten.
If a cat had an activity level of about 9, then it's likely to have eaten about _[blank]_ meals.
Enter the value that correctly fills in the blank.
Round to the nearest whole number, if necessary, like this: 42
If a cat had an activity level of about 9, then it's likely to have eaten about 6 meals.
What is a linear equation?A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the intial value of y.
Let x represents the activity level and y represents the number of meals eaten. Given that:
y = 0.23x + 4.1
For an activity level of 9 (x = 9):
y = 0.23(9) + 4.1 = 6.17
If a cat had an activity level of about 9, then it's likely to have eaten about 6 meals.
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Answer:
answer is 6
Step-by-step explanation:
i took the work
Which three programs or services are supported by taxes?
fire departments
Medicare
public education
shopping malls
theaters
Answer: A,B,C
fire department, medicare, public education
Step-by-step explanation: Plato answer
The three programs or services are supported by taxes are fire departments, Medicare and public education
What is Tax?A tax is a sum of money that people pay to the government for the services provided by the government.
The three programs or services that are supported by taxes are:
Fire departments: Taxes are used to fund fire departments that provide emergency services such as firefighting, rescue, and medical assistance.
Medicare: Taxes are used to fund Medicare, a federal health insurance program for people who are 65 or older, certain younger people with disabilities, and people with End-Stage Renal Disease.
Public education: Taxes are used to fund public education, including elementary, middle, and high schools, as well as public colleges and universities.
Shopping malls and theaters are not typically supported by taxes.
They are usually privately owned and funded by their owners.
Hence, the three programs or services are supported by taxes are fire departments, Medicare and public education
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I need help. It's kinda hard for me. We have to use decimal numbers
Answer: 2.4 + 7.6 = 10
Step-by-step explanation:
Hope this helps
Currently, there are $350$ students in the seventh grade at Winchester Heights Middle School. For the upcoming school year, they are planning to increase the number of seventh graders by $10\%$ .
How many seventh-grade students does Winchester Heights Middle School plan to have in the upcoming school year?
Answer: 385 students
Step-by-step explanation:
Answer:
Current number of students : 350
The number of students after increasing 10% N:
N = 350 + 10% of 350 = 350 + 350 x 10/100 = 350 + 35 = 385 students
Hope this helps!
:)
What is the initial value of the sequence?
The points shown on the graph represent the numbers in a
geometric sequence.
1
2
3
8
Answer:
B) 2
Step-by-step explanation:
the initial value would be the first point and on this graph that first point is (1,2). and you should look at the x-value meaning your answer is 2
Answer:
It's 2
Step-by-step explanation: hope it helps ^w^
Which expression is equivalent to 9 – 8x?
A. -8x – 9
B. -8x + 9
O c. 8x - 9
D. 8x + 9
Answer:
option B -8x+9
Step-by-step explanation:
If you switch position around, - 8x will go in front and +9 will go at the back
*remember that the signs in front of a number is for the number and number without signs their signs are automatically +
The expression is 9 - 8x is equivalent to the -8x + 9.
What is expression?
An expression is statement which is "combination of numbers, variables and functions".
According to the question,
The expression is 9 - 8x is equivalent to the -8x + 9.
The signs in front of a number is for the number and number without signs their signs are automatically +.
Hence, the expression is 9 - 8x is equivalent to the -8x + 9.
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I AM GIVING OUT BRAINLIEST One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?
-x^2 + 18x + 81
3x^2 - 3x - 168
x^2 - 4x - 4
25x^2 - 30x + 9
x^2 - 14x + 24
Answer:
3/5
Step-by-step explanation:
First one 18^2 - 4(-1)(81) > 0 so no repeated root
Second one (-3)^2 - 4(3) (-168) > 0 so no repeated root
Third one (-4) - (4) (1) (-4) > 0 so no repeated root
Fourth one (-30)^2 - 4(25) (9) = 900 - 100(9) = 0 repeated root
Note this factors as (5x - 3)^2
(5x - 3)^2 = 0 take both roots
5x - 3 = 0
5x = 3
x = 3/5 = repeated root
The quadratic expression [tex]25x^{2} -30x+9[/tex] has repeated root and the repeated root is 3/5
How to know a quadratic has repeated root ?Let, [tex]ax^{2} +bx+c=0[/tex] is a quadratic.
Then the expression ([tex]b^{2}-4ac[/tex]) is called the discriminant of the quadratic.
If [tex]b^{2}-4ac[/tex] = 0 then we can say that the quadratic has a repeated real root.
Which quadratic has repeated root ?The discriminant of [tex]-x^{2} +18x+81[/tex] is,
[tex]b^{2}-4ac[/tex] = [tex]18^{2}-4(-1)(81)[/tex] = 324+324=648 > 0
So, This quadratic has no repeated root.
The discriminant of [tex]3x^{2} -3x-168[/tex] is,
[tex]b^{2}-4ac[/tex] = [tex](-3)^{2}-4(3)(-168)[/tex] = 9+2016 = 2025 > 0
So, This quadratic has no repeated root.
The discriminant of [tex]x^{2} -4x-4[/tex] is,
[tex]b^{2}-4ac[/tex] = [tex](-4)^{2}-4(1)(-4)[/tex] = 16+16 = 32 > 0
So, This quadratic has no repeated root.
The discriminant of [tex]25x^{2} -30x+9[/tex] is,
[tex]b^{2}-4ac[/tex] = [tex](-30)^{2} -4(25)(9)[/tex] = 900-900 = 0
So, This quadratic has repeated root.
The discriminant of [tex]x^{2} -14x+24[/tex] is,
[tex]b^{2}-4ac[/tex] = [tex](-14)^{2}-4(1)(24)[/tex] = 196-96 = 100 > 0
So, This quadratic has no repeated root.
What is the repeated root ?The equation [tex]25x^{2} -30x+9[/tex] = 0 has repeated root.
Simplifying the equation we get,
[tex]25x^{2} -30x+9[/tex] = 0
⇒ [tex](5x)^{2}-2(5x)(3)+3^{2}[/tex] = 0
⇒ [tex](5x-3)^{2}[/tex] = 0
⇒ 5x-3 = 0
⇒ 5x = 3
⇒ x = 3/5
The repeated root is 3/5.
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What is the circumference and area of a circle with a radius of 4 meters? Round your answer to the nearest tenth.
Answer:
50.27 for the area
25.13 for the circumference
Step-by-step explanation:
A=πr2=π·42≈50.26548
C=2πr=2·π·4≈25.13274
help plz geometry !!!!
Answer:
27 ) x = 15°,
28 ) x = 18°
Step-by-step explanation:
27 ) We are given angle measures of 85 degrees, consecutively 6x + 5, each forming a linear pair;
85 + ( 6x + 5 ) = 180 ⇒ by definition of linear pair we have two measures of angles that add to 180°,
85 + ( 6x + 5 ) = 180 ⇒ take out ( ),
85 + 6x + 5 = 180 ⇒ combine like terms,
90 + 6x = 180 ⇒ subtract 90 from either side of equation,
6x = 90 ⇒ divide 6 on either side of equation,
Solution; x = 15°
28 ) We are given angle measures of 110 degrees, consecutively 3x + 16, each forming a linear pair;
110 + ( 3x + 16 ) = 180 ⇒ by definition of linear pair we have two measures of angles that add to 180°,
110 + ( 3x + 16 ) = 180 ⇒ take out ( ),
110 + 3x + 16 = 180 ⇒ combine like terms,
126 + 3x = 180 ⇒ subtract 126 from either side of equation,
3x = 54 ⇒ divide 6 on either side of equation,
Solution; x = 18°
can y'all help me plz anyone
Answer:
y=2x+2
Step-by-step explanation:
2 is the slope and 2 is also the y intercept. So your equation would be y=2x+2. It is correct because 14=2(6)+2 is true.
The first equation is 3x + 2y = 17 and the second equation is -2x - y = -12. What would I have to multiply the second equation by so I could add andeliminate the y's.
3
2
-2
0
Answer:
Multiply the second equation by 2
Step-by-step explanation:
If you do that you will get 2y in the first equation and -2y in the second equation. then, you can add the 2 equations to get rid of y.
Answer:
2
Step-by-step explanation:
For elimination problems, you have to have the variables that you want to cancel out equal in value but opposite in sign.
Since you are trying to cancel out y and you are changing the second equation, look at the first equation.
The y variable is +2y. This means that the second equation with a y variable of -2y.
Since the the second equation's y variable is -y, multiply it by 2.
-y x 2 = -2y
What is the solution to the equation x + 4.7 = 6.3?
a. x = 11.0
b. x = 6.3
c. x = 2.4
d. x = 1.6
The value of X is 1.6
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
[tex]x = 1.6[/tex]
Step-by-step explanation:
[tex]x + 4.7 = 6.3 \\ x = 6.3 - 4.7 \\ x = 1.6[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Help I made it maxed points
Answer:
B
Step-by-step explanation:
66/4=99/6=330/20=16.5
Since there is a constant ratio between these values, the function is a line, and the equation of that line is w=16.5m, or choice B. Hope this helps!
Answer:
w=16.5
Step-by-step explanation:
All you have to do is divide the number of gallons of water by the number of minutes and you will get your answer.
66/4=16.5
99/6=16.5
330/20=16.5
I hope I've helped.
HELP PLZ I NEED HELP QUICK!!!! ILL GIVE U 20 POINTS
Answer:
B) Z
Step-by-step explanation:
Solve for a in the problem:
-3(9a+2)=129
Answer: a = -5
Step-by-step explanation:
-3 (9a+2)=129
-27a -6 = 129
-27a = 129+6
-27a = 135
a = -135/27
Answer:
a= -5
Step-by-step explanation:
To solve the equation, we want to find out what a is. In order to do this, we have to get a by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
-3(9a+2)=129
-3 is being multiplied by 9a+2. The opposite of multiplication is division, so divide both sides by -3.
-3(9a+2)/-3=129/-3
9a+2=129/-3
9a+2=-43
2 is being added on to 9a. The opposite of addition is subtraction, so subtract 2 from both sides.
9a+2-2= -43-2
9a= -43-2
9a= -45
a is being multiplied by 9. The opposite of multiplication is division, so divide both sides by 9.
9a/9= -45/9
a= -45/9
a=-5
The surface area of a sphere is 452.15 cm squared. Find the length of the radius and use 3.14 for pie
Answer:
Step-by-step explanation:
6cm approximately
Colin rolls a fair dice 18 times.
How many times would Colin expect to roll a number greater than 3?
Answer:
8 or 1/2
Step-by-step explanation:
The requried probability that colin expects to roll a number greater than 3 is 1/2.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Colin rolls a fair die 18 times.
The total outcome of 1 die = 6
So, for 18 die total outcome = 6 × 18
Now,
Favorable outcome = 4, 5, 6 = 3
A total favorable outcome for 18 dice = 3 × 18
Probability, many times would Colin expect to roll a number greater than 3.
= 3 × 18 / 6 × 18
= 1 / 2
Thus, the requried probability that colin expects to roll a number greater than 3 is 1/2.
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PLEASE ANSWER ASAP!!!!!!!!!!
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
The formula of volume of any prism is Bh
B=Area of the base
h=height
So just multiply them together:
So as a mixed fraction you get 14 2/3
Improper fraction: 44/3
Hope this helps!
In the United States, federal tax rates are based on the amount of income an individual or family earns. What do you think happens to the tax rate as the amount of income earned goes up?
Answer: The tax rate would get higher the more money you make
4a + 2 < 2- 4a helpppp ppppp
Answer:
a ≤0 but without the line
Step-by-step explanation: