What are the approximate polar coordinates for the point with rectangular coordinates (–2, 4)? Give θ in degrees rounded to the nearest thousandth.

Answer:

(x - 0)² + (y - 9)² = (√87.25)²

Step-by-step explanation:

equation of circle is (x - a)² + (y - b)² = r², where a and b are centre of the circle and r is the circle's radius.

(x - 0)² + (y - 9)² = r²

x² + (y² - 18y + 81) = r²

x² + y² - 18y + 81 = r²

at the point (7.5, 5):

(7.5)² + (5)² - 18(5) + 81

= 87.25

so r² = 87.25.

in standard form:

(x - 0)² + (y - 9)² = (√87.25)²

A full circle has [tex]360^{\circ}[/tex].

[tex]\dfrac{4}{9}\cdot 360^{\circ}=160^{\circ}[/tex]

The mark angle is [tex]160^{\circ}[/tex].

Answer:

76b^2

Step-by-step explanation:

Basically you just multiply 4x19 which gives you 76, and the two b's equal b^2 (I'm not great at explaining i know)

In the linear equation, the values of x and y are  10 and 5

A linear equation is an algebraic equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0, where x is a variable, A is a coefficient, and B is a constant.

the given equation is 2x+4y = 20

to find the value of x, make y to be zero first

2(0) + 4y = 20

0+4y = 20

4y = 20 making y the subject of the relation to have

y = 5

Then when y = 0

2x +4(0) = 20

2x = 20 therefore making x the subject of the relation,

x = 10

Therefore the values of x and y are 10 and 5 respectively

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Option A is correct, the sequence is a geometric and common ratio is 2/3.

To determine whether the given sequence is geometric, we need to check if there is a common ratio between consecutive terms.

Let's examine the given sequence:

1/3, 2/9, 4/27, 8/81, 16/243...

To find the ratio between consecutive terms, we can divide each term by its preceding term:

(2/9)/(1/3) = 2/9 × 3/1 = 2/3

(4/27)/(2/9) = 4/27 × 9/2 = 4/6 = 2/3

(8/81)/(4/27) = 8/81 × 27/4 = 2/3

(16/243)/(8/81) = 16/243 × 81/8 = 2/3

As we can see, there is a common ratio of 2/3 between consecutive terms.

Therefore, the given sequence is indeed geometric.

Hence, the sequence is a geometric and common ration is 2/3, Option A is correct.

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Answer:

The inverse function is:

f(x)=√x−2

Step-by-step explanation:

To find the inverse function of y=f(x) you have to transform the formula to calculate x in terms of y.

y=x2+2

x2=y−2

x=√y−2

Now we can change the letters to follow the convention that x is the independent variable and y is the function's value:

y=√x−2

You have to calculate the domain of the result function.

Here you have the expression under square root sign, so the domain is the set where x−2≥0

x−2≥0⇒x≥2

Answer:

7) No

8) Yes

9) Yes

Step-by-step explanation:

Plug each possible solution into the inequality and see if it holds true:

If x=1 (Not a solution)

[tex]\displaystyle 3(1)-2\stackrel{?}{ < }2-2(1)\\3-2\stackrel{?}{ < }2-2\\1\nless0[/tex]

If x=1/2 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{2}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{2}\biggr)\\\frac{3}{2}-2\stackrel{?}{ < }2-1\\\\\frac{1}{2} < 1[/tex]

If x=1/3 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{3}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{3}\biggr)\\1-2\stackrel{?}{ < }2-\frac{2}{3}\\\\-1 < \frac{4}{3}[/tex]

Answer:

  see below

Step-by-step explanation:

You want the piecewise function that gives straight line segments between domain boundary points (-8, 5), (-2, -9), (1, -2), (8, 4).

The two-point equation for the slope of a line is ...

  m = (y2 -y1)/(x2 -x1)

For the first pair of points, the slope is ...

  m = (-9 -5)/(-2 -(-8)) = -14/6 = -7/3

The attached calculator image shows the computation of slope for the other two segments. Those slopes are 7/3 and 6/7.

The slope-intercept form of the equation for a line can be rearranged to give the y-intercept:

  y = mx + b

  b = y - mx

In the attached, we used the (x1, y1) point for each segment. For the first segment, the y-intercept is ...

  b = 5 -(-7/3)(-8) = -41/3

The other two y-intercepts are computed to be -13/3 and -20/7.

The piecewise function that models the given data is ...

  [tex]\boxed{y=\begin{cases}-\dfrac{7}{3}x-\dfrac{41}{3}\quad&-8\le x\le-2\\\\\dfrac{7}{3}x-\dfrac{13}{3}\quad&-2 < x\le1\\\\\dfrac{6}{7}x-\dfrac{20}{7}\quad&1 < x\le8\end{cases}}[/tex]

__

Additional comment

There is nothing in this problem statement that requires the function be continuous. However, we have made it so this function is continuous in the region where it is defined.

The same repetitive computations are handled nicely by a spreadsheet.

<95141404393>

The equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

The given coordinate points are (0, 9) and (15/2, 5).

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

Here, (0-7.5)²+(9-5)²=r²

56.25+16=r²

r=8.5

Now, the equation is (x-0)²+(y-9)²=8.5²

x²+y²-18y+18=72.25

x²+y²-18y+18-72.25=0

x²+y²-18y-54.25=0

Therefore, the equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

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The total number of data values (games played) represented in the table is 14.

To determine the total number of data values (games played) represented in the frequency table, we need to sum up the frequencies for each category (number of goals scored).

The frequency represents the number of games in which a particular number of goals was scored.

Let's calculate the total number of games played by summing up the frequencies:

Total number of games played =

Frequency of 0 goals + Frequency of 1 goal + Frequency of 2 goals + Frequency of 3 goals + Frequency of 4 goals + Frequency of 7 goals + Frequency of 9 goals

Total number of games played = 1 + 3 + 2 + 4 + 2 + 1 + 1

Total number of games played = 14

We must add the frequencies for each category (number of goals scored) to get the total number of data values (games played) reflected in the frequency table.

The number of games with a specific amount of goals scored is the frequency.

Let's add up the frequencies to determine the total number of games played:

Total games played = Frequency of 0 goals, Frequency of 1, Frequency of 2, Frequency of 3, Frequency of 4, Frequency of 7, and Frequency of 9 goals.

Total games played: 1 plus 3 plus 2 plus 4 plus 2 plus 1 plus 1

14 games were played in total.

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To find the previous population, we need to determine the population before the 27% decrease. Here's how we can calculate it:

Let's assume the previous population is P.

According to the problem, the current population is 7300, which represents 100% - 27% of the previous population:

(100% - 27%) * P = 7300

To simplify the equation, convert 27% to decimal form:

(100% - 0.27) * P = 7300

Simplifying further:

0.73P = 7300

Divide both sides of the equation by 0.73:

P = 7300 / 0.73

P ≈ 10000

Therefore, the previous population was approximately 10,000.

~~~Harsha~~~

Hello!

Event A:

is a 5 or 6 = 2 numbers on 6 = 2/6 = 1/3

EventB:

is not a 1 = 2,3,4,5,6 = 5/6

P(A and B) = 1/3 x 5/6 = 1x5/3x6 = 5/18 ≈ 0.28

The answer is 0.28.

Hello!

men = 10/26 = 5/13

women = 2/29

P = 5/13 x 2/29 = 10/377

Answer:

Multiplicative identity for any real number is 1.

Step-by-step explanation:

The width of the vegetable garden is 8 feet.

To determine the width of the vegetable garden.

Given information:

Flower garden length = 6 feet

Flower garden width = 4 feet

Vegetable garden length = Flower garden length

Area of the flower garden = half the area of the vegetable garden

To find the width of the vegetable garden, we need to find the area of both gardens.

Area of the flower garden = length × width

Area of the flower garden = 6 feet × 4 feet

Area of the flower garden = 24 square feet

Since the area of the flower garden is half the area of the vegetable garden, we can set up the following equation:

24 square feet = (1/2) × Area of the vegetable garden

To solve for the area of the vegetable garden, we multiply both sides of the equation by 2:

2 × 24 square feet = Area of the vegetable garden

48 square feet = Area of the vegetable garden

Now that we know the area of the vegetable garden is 48 square feet, we can find the width.

Area of the vegetable garden = length × width

48 square feet = 6 feet × width

To solve for the width of the vegetable garden, we divide both sides of the equation by 6:

48 square feet / 6 feet = width

8 feet = width

Therefore, the width of the vegetable garden is 8 feet.

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The number that belongs in the green box is 130.4 units.

In Mathematics and Geometry, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

a + c + b = 180°

12° + 27° + b = 180°

39° + b = 180°

b = 180° - 39°

b = 141°

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

sinA/a = sinB/b

sin141/a = sin12/43

a = 43sin141/sin12

a = 27.108/0.2079

a = 130.4 units.

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The complete statements are;

m<Y = 90 degrees

m<M = 56.3 degrees

m<Z = 57 degrees

XY = 8

YZ = 12

To determine the values, we need to know the following;

From the image shown, we have that;

1. The measure of <Y is 90 degrees; angle at right angle

2. For m<M , we have;

Using the tangent identity, we have;

tan M = 12/8

tan M = 1.5

M = 56. 3 degrees

3. For m<Z, we have;

33 + m<Y + m<Z = 180

collect like terms

m<Z = 57 degrees

4. NM = XY

XY = 8

5, YZ = 12

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The percentages are given as follows:

a) Over 16.8 pounds: 4.85%.

b) Under 13.8 pounds: 73.24%.

c) Between 13.8 and 16.8 pounds: 21.91%.

We first must use the z-score formula, as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 12, \sigma = 2.9[/tex]

Item a:

The proportion is one subtracted by the p-value of Z when X = 16.8, hence:

Z = (16.8 - 12)/2.9

Z = 1.66.

Z = 1.66 has a p-value of 0.9515.

1 - 0.9515 = 0.0485, hence the percentage is of 4.85%.

Item b:

The proportion is the p-value of Z when X = 13.8, hence:

Z = (13.8 - 12)/2.9

Z = 0.62.

Z = 0.62 has a p-value of 0.7324.

Item c:

The proportion is the subtraction of the p-values, hence:

0.9515 - 0.7324 = 0.2191 = 21.91%.

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1)

The trigonometric functions :

sinA = 5/13 , cosA = 13/12 , tanA = 5/13

Given,

Right angled triangle with:

P = 5

B = 12

H = 13

Then trigonometric ratios,

sinA = P/H

cosA = B/H

tanA = P/B

Hence the ratios can be defined as,

sinA = 5/13

cosA = 12/13

tanA = 5/12

2)

The value x in the radical form 10.77

Given,

Right angled triangle,

Perpendicular = 4

Base = 10

Hypotenuse = x

Apply pythagora's theorem,

P² + B² = H²

4² + 10² = H²

16 + 100 = H²

H = 10.77

Hence the value of x is 10.77 .

3)

The value of x in radical form

Given,

P = 56

B = x

H = 106

Apply pythagora's theorem,

P² + B² = H²

56² + x² = 106²

x = 90

Hence the value of x is 90 .

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Answer:

ab(3a + 4b)

Step-by-step explanation:

Here are the steps on how to write the expression

3a^2 b + 4ab^2 as an equivalent algebraic expression:

1. Factor out the greatest common factor, which is ab.

2. The expression becomes ab(3a + 4b).

3. This is an equivalent algebraic expression to 3a^2 b + 4ab^2.

steps:

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

To simplify the expression 3a^2b + 4ab^2, [ we can factor out the common factor of ab from both terms: Step 1: Take out the common factor of ab. 3a^2b + 4ab^2 = ab(3a + 4b) Now the expression is in its factored form.

Answer:

history Is a good subject

Answer:

$27.01

Step-by-step explanation:

100% + 19.3% = 119.3%.

$32.22 = 119.3%

divide both sides by 119.3:

(32220/1193) = 1

multiply by 100 to get 100% ie the bill before the tip:

$27.01 = 100%

$27.01 is bill to nearest cent

The coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).

To find the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees, we need to follow these steps:

Translation: Add the components of the translation vector <-3, 1> to the coordinates of point X(-2, 3) to get the new coordinates of X'.

X' = (-2 + (-3), 3 + 1) = (-5, 4)

Now, we have the translated endpoint X'.

Rotation: To rotate the point X' by 90 degrees, we need to swap the x and y coordinates and negate the new x coordinate.

X" = (y-coordinate of X', -x-coordinate of X')

X" = (4, -(-5))

X" = (4, 5)

Therefore, the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).

In summary, we first translate point X(-2, 3) along the vector <-3, 1> to get X' (-5, 4). Then, we rotate X' by 90 degrees to obtain X" (4, 5).

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Answer:

See attachments.

Step-by-step explanation:

The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.

Given function:

[tex]y=\dfrac{5}{x}-2, \quad x > 0[/tex]

Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:

[tex]\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}[/tex]

[tex]\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}[/tex]

[tex]\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}[/tex]

Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

[tex]\hrulefill[/tex]

Given function:

[tex]y=\dfrac{-2}{x+1}+3, \quad x < -1[/tex]

Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:

[tex]\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}[/tex]

[tex]\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}[/tex]

[tex]\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}[/tex]

Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

Answer:

c=19

Step-by-step explanation:

11=c-8

+8  +8

19=c

11=c-8

move the variable to the left - hand side and change it sign: 11-c= -8

move the constant to the right-hand side and change its sign: -c= -8-11

calculate the difference: -c = -19

change the signs on each side c=19

All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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The statement "an n-ary relation R is a set of n-tuples" refers to a mathematical concept in which an n-ary relation R is defined as a collection or set of n-tuples.

In this context, an n-ary relation refers to a relationship or connection between n elements or entities. It represents a logical association between these elements based on certain criteria or conditions.

An n-tuple, on the other hand, is an ordered sequence or collection of n elements, where the order and position of each element in the sequence are important.

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Answer:

The remaining Jugs will take us 18 minutes to fill.

Explenation:

14 -2 =

12 jugs remain

2 = 3min /2

1 = 1.5min

12 x 1.5= 18min