Convert the given Cartesian equation into a polar equation.
x2+y2=2y

The equation that shows the total number of miles Jill walked, w, on Tuesday and Wednesday is w = 3 + 2

From the question, we have the following parameters that can be used in our computation:

Tuesday = 3 miles

Wednesday = 1 less than Tuesday

This means that

Wednesday = 3 miles - 1 mile

Evaluating the like terms, we have

Wednesday = 2 miles

The equation shows the total number of miles Jill walked, w, on Tuesday and Wednesday is represented as

w = Tuesday + Wednesday

Substitute the known values in the above equation, so, we have the following representation

w = 3 + 2

Evaluate

w = 5

Hence, the equation is w = 3 + 2 and the number of miles s 5

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The volume of the file cabinet in this problem is given as follows:

V = 8 and 7/10 cu ft.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

2.167 ft, 1.5 ft and 2.67 ft.

Hence the volume of the prism is given as follows:

V = 2.167 x 1.5 x 2.67

V = 8.7 ft³.

As a mixed number, the volume is given as follows:

V = 8 and 7/10 cu ft.

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The Greatest common Factor of 16 and 32 is 16

Greatest common factor is the largest factor that all the numbers share. For example, 12, and 18 have three common factors: 2, 3and 6 the greatest is 6.

Similarly the factors of 16 and 32 are shown below;

factors of 16 are : 2,4,8,16

factors of 32 are : 2,4,8,16,32

The common factors are: 2,4,8,16

and the largest number among the common factors is 16

Therefore the greatest common factor of 16 and 32 is 16

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Answer:

Rice:Water = 1:2

Step-by-step explanation:

The rules for the two graphs above are: A. first graph: y = 3 + x; second graph : y = 6 + x.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of graph 1;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 3)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (0, 3) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 1(x - 0)  

y = x + 3

Next, we would determine the slope of graph 2;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (7 - 6)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (0, 6) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 1(x - 0)  

y = x + 6

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B

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular.

An equilateral triangle can never be obtuse. 

A linear equation in slope intercept form for each of this line are as follows;

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (2, 7) and a slope of -7, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 7 = -7(x - 2)  

y - 7 = -7x + 14

y = -7x + 21

y = 5x - 6

At data point (-1, -7) and a slope of 1, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - (-7) = 1(x - (-1))  

y + 7 = x + 1

y = x - 8

At data point (6, 7) and a slope of 1/2, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 7 = 1/2(x - 6)  

y - 7 = x/2 - 3

y = x/2 + 4

At data point (9, 0) and a slope of -2/3, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 0 = -2/3(x - 9)  

y - 0 = -2x/3 + 6

y = -2x/3 + 6

At data point (5, 19) and a slope of 5, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:

y - 19 = 5(x - 5)  

y - 19 = 5x - 25

y = 5x - 6

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The solution to the system of linear equations, would be :

We can rewrite the system of linear equations to be:

x + 0 y + z = - 1

0 x + y + 4 z = - 4

0x + 0y + 0z = 0

The simple version is:

x + z = -1

y + 4z = -4

0 = 0

Therefore, the solution can be written as:

x = -1 - z

y = -4 - 4z

z = z

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The unknown measure in the line segment is as follows:

∠x = 141 degrees

When line segment intersect, angle relationships are formed such as vertical angles, adjacent angles etc.

Therefore, let's find the angle x in the line intersection as follows:

Therefore, the angle x comprises of angle 90 degrees and angle 50 degrees.

The sum of angle 90 degrees and 50 degrees is equals to angle x

Hence,

x = 51 + 90

x = 141 degrees

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The function value of f(f(7)) is -13.

We have,

x     9   -11    7   11      -6   -13

f(x)  11    4   -6   -1    -15    -5

From the table,

Using the given table, we can see that:

f(93) is not in the list of x values, so we cannot find its inverse.

Therefore,

We cannot evaluate [tex]f^{-1}(f(93)).[/tex]

f(7) is in the list of x values, and its corresponding function value is f(7) = -6. Therefore,

We can evaluate f(f(7)) by finding the function value corresponding to -6.

i.e

f(-6) = -13

Now,

The function value of f(f(7)).

= f(-6)

= -13

Thus,

The function value of f(f(7)) is -13.

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The area of the desktop is 307.72 square inches.

Remember that the area of a semicircle of radius R is given by the formula:

A = (pi/2)*R²

Where pi = 3.14

Here we know that the diameter is 28 inches, then the radius is:

R = 28in/2 = 14 inches

Replacing that in the formula for the area we will get:

A=  (3.14/2)*(14 in)²

A = 307.72 in²

That is the area of the desktop.

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The measure of angle A in triangle ABC is approximately 113.8 degrees.

To find the measure of angle A (LA) in triangle ABC, we can use the Law of Cosines:

c² = a² + b² - 2ab*cos(C)

where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.

In this case, we want to find LA, which is opposite to side a (BC). So we can rewrite the Law of Cosines as:

cos(A) = (b² + c² - a²) / 2bc

Plugging in the values we have:

cos(A) = (24.1² + 15.7² - 25.3²) / (2 * 24.1 * 15.7)

cos(A) = -0.3694

Now we need to find the inverse cosine (cos⁻¹) of -0.3694 to get the measure of angle A:

A = cos⁻¹(-0.3694)

Using a calculator, we get:

A ≈ 113.8 degrees

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Answer:

k = 1

Step-by-step explanation:

given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0

here the polynomial is divided by (x + 1)

then substitute x = - 1 into the polynomial and equate to zero

k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0

- k + 1 + 5 - 5 = 0

- k + 1 = 0 ( subtract 1 from both sides )

- k = - 1 ( multiply both sides by - 1 )

k = 1

Triangle GHI is similar to triangle SQR. Therefore, option A and E are correct answers.

Given that, in triangle GHI, ∠G=104°, ∠H=45° and ∠I=31°.

In triangle QRS, ∠Q=45°, ∠R=31° and ∠S=104°.

In triangle XYZ, ∠X=104°, ∠Y=45° and ∠Z=31°.

Consider triangle GHI and triangle QRS

∠G=∠S=104°

∠H=∠Q=45°

∠I=∠R=31°

ΔGHI is similar to ΔSQR

Consider triangle XYZ and triangle QRS

∠X=∠S=104°

∠Z=∠Q=45°

∠Y=∠R=31°

ΔXYZ is similar to ΔSRQ

Consider triangle XYZ and triangle GHI

∠X=∠G=104°

∠Z=∠H=45°

∠Y=∠I=31°

ΔXYZ is similar to ΔGIH

Therefore, option A and E are correct answers.

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An expression that represents the amount of canned food collected so far by the three friends is 8x² + 2xy - 4.

An expression that represents the number of cans the friends still need to collect to meet their goal is 4x² - 4xy + 2.

From the information provided above, we can logically deduce the following number of canned food collection expressions for each friend:

Jessa; 3x²

Tyree: 5x² - 8

Ben: 2xy + 4

Canned food collection goal: 12x² - 2xy - 2

Therefore, an expression that represents the total amount of canned food collected so far by the three friends can be calculated and written as follows;

Total amount collected so far = 3x² + 5x² - 8 + 2xy + 4

Total amount collected so far = 8x² + 2xy - 4

In order to meet the goal, they need to collect this amount:

Remaining canned foods = 12x² - 2xy - 2 - (8x² + 2xy - 4)

Remaining canned foods = 12x² - 2xy - 2 - 8x² - 2xy + 4

Remaining canned foods = 4x² - 4xy + 2

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The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

Based on the information, dy/dx + 3y = 2x³ e^(-3x)

The integrating factor is e^(∫3 dx) = e^(3x),

e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)

d/dx (e^(3x) y) = 2x^3

e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C

C is an arbitrary constant of integration.

y = (1/2) x^4 e^(-3x) + C e^(-3x)

The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

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Answer:

câu này là 500 nhen

Answer:

[tex] - 8(45) + 482 = - 360 + 482 = 122[/tex]

The percentage of saline solution in brand B is 3%.

Let x be Percentage of saline solution in brand B

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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The values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.

The figure is a cyclic quadrilateral since it four side vertices lie on the circumference of the circle. The sum of the interior angles of a cyclic quadrilateral is also 360°. Also opposite angles of a cyclic quadrilateral add up to 180°

Thus;

11x + 8 + 8x + 1 = 180° {opposite angles of a cyclic quadrilateral}

19x + 9 = 180°

19x = 180° - 9 {collect like terms}

19x = 171

x = 171/19

x = 9

Also;

6y - 4 + 5y - 3 = 180°

11y - 7 = 180°

11y = 180 + 7

11y = 187

y = 187/11

y = 17

Therefore, the values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.

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The number of article sold for Rupees 20 to gain a profit of 20% is equal to 4.

Number of article sold for Rupees 20 = 6

Percent of loss in selling 6 article for Rupees 20 = 20%

Let us start by finding the cost price of one article.

We know that if 6 articles are sold for 20 rupees,

then the selling price of one article is equal to,

Selling price of 1 article = 20/6

⇒ Selling price of 1 article = 3.33 rupees

There was a loss of 20% when 6 articles were sold for 20 rupees.

This means that the cost price of 6 articles is equal to,

Cost price of 6 articles

= Selling price of 6 articles / (1 - Loss%)

= 20 / ( 1 - 20% )

= 20 / (1 - 0.2)    

= 25 rupees

To gain 20% profit, the selling price of the articles should be equal to,

Profit% is 20% = 0.2

Selling price of 6 articles

= Cost price of 6 articles × (1 + Profit%)

= 25 × (1 + 0.2)  

= 30 rupees

Now , the selling price of one article to calculate how many articles can be sold for 20 rupees,

Selling price of 1 article

= Selling price of 6 articles / 6

= 30 / 6

= 5 rupees

This implies,

The number of articles that can be sold for 20 rupees to gain a 20% profit is equal to,

Number of articles

= 20 / 5

= 4 articles

Therefore,  4 articles must be sold for 20 rupees to gain a 20% profit.

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Answer:

events at A and B are independent because P(A)(B)≠P(A)

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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One of the stages in Cooley's looking-glass self theory is A. We imagine how we look to other people.

As per Cooley's theory, our self-concept is shaped through a social interchange in which we envision how others perceive us, evaluate that perception and then deliberate on how those assessments influence our self-esteem.

All these components are part of the "looking-glass self" process, consisting of three stages: 1) fantasising about how one appears to others 2) pondering over the judgments made based on appearance and 3) evolution of the self-image influenced by such judgements. Notably, imagining one's outward persona forms an integral element of this psychological principle.

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