The provided function, f(x)=(.8)^x, has a 20% rate of decay.
What is the Rate of decay or growth?
A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
given, a function f(x)=(.8)^x. To calculate the decay rate of this function.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a (1 - r)x is the general form.
Where
a = the initial amount
1-r is the decay factor
x = time span
from the given expression,
Decay factor = 0.8
That is also equal to 1 - r
1 - r = 0.8
r =0.2
Thus, rate of decay = r * 100%
rate of decay = 0.2 * 100 = 20%
therefore, The rate of the of the given function f(x)=(.8)^x is 20%.
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What is the value of 3 in tan?
The value of tan 3° is 0.0524.
tangent is the trigonometric ratio.
we can find out the value of tangent by taking perpendicular of the triangle divided by base of the triangle.
tan Q = perpendicular of the triangle /base of the triangle.
sine theta divided by cos theta gives the value of tan theta.
tan Q = sin Q/ cos Q.
some formula of the tan Q are as follows,
1- tan Q = sin Q/cos Q
2- tan Q= 1 /cot Q
3-tan^2 Q =sec^2 Q -1
4- tan(90 - Q)=cot Q
5- tan (Q+π) = tan Q
6- tan (π-Q) = -tan Q
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You use a technical support company for your computer. The company bills you at a rate of $10 per month and $35 per hour for phone support.
a. Identify the fixed cost (the constant).
b. Identify the independent variable (x).
c. Identify the dependent variable (y).
d. Write an equation that describes the situation above.
e. If you were billed $97.50 for last month, how many hours of phone support did you need? Show all work.
Answer:fixed cost=10
Independent variable=months paid
Dependent=hours on support
month=x,h=hour,10x+35h=total cost
97.50=10+35h
87.50=35h
h=2.5 hours
Step-by-step explanation:
showed work
Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16
Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.
As per the given data the given equation is:
[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]
The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]
Your hyperbola opens left/right, because it is of form x - y.
Comparing terms, we find that
h = -4, k = 5, a = 3, y = 4
In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].
Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).
The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]
[tex]c^2=9+16=25$[/tex], so c = 5.
The coordinates of the foci are (-9, 5) and (-1, 5).
The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)
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2 diagonals of a regular nonagon (a 9-sided polygon) are chosen. What is the probability that their intersection lies inside the nonagon
The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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How many terms are there in the expression 7x2 5x?
There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.
Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.
An algebraic expression with three terms is called a trinomial.
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solvve for z: (1st answer or nice and detailed answer brainliest)
1/2z+5=57
[tex]\dfrac{1}{2} z+5=57[/tex]
Subtract 5 from both sides:
[tex]\dfrac{1}{2} z+5-5=57-5[/tex]
[tex]\dfrac{1}{2} z=52[/tex]
Multiply both sides by 2:
[tex]2\times(\dfrac{1}{2} z)=2\times(52)[/tex]
[tex]\fbox{z = 104}[/tex]
Answer:
z=104
Step-by-step explanation:
1/2z=57-5
1/2z=52
1/2z*2=52*2
1z=104
1/1z=104/1
z=104
how does the value of A determine the range for f(x) = a|x|
HELP PLEASE ASAP
Answer:
It will either invert the graph or stretch/compress the horizontal
Step-by-step explanation:
When a is negative It will invert the graph, and reflect it over the x-axis
By plugging in a=1 you get a normal absolute value function of x ( a V on the graph)
If a>1 then your graph will compress
If a<1 then your graph will stretch
I’m doing math homework and is about functions they said f(x)= x-3 and g(x)= √x-2
After I set them up I have this
am I supposed to just add the numbers or is there something else to do?
√ (x-3)-2
Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.
To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.
For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:
h(5) = √(5-3) - 2
= √2 - 2
= 1.4 - 2
= -0.6
Therefore, the value of h(x) for x = 5 is -0.6.
You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.
Step-by-step explanation:
Answer:
g[f(x)]
Step-by-step explanation:
Given functions:
[tex]f(x)=x-3[/tex]
[tex]g(x)=\sqrt{x}-2[/tex]
Composite functions are when the output of one function is used as the input of another.
Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):
[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]
Work out the size of angle x
Answer:
x = 13
Step-by-step explanation:
There is more than one 98-degree angle since they are all corresponding interior angles.
The supplementary angle to the 98-degree angle next to the triangle is:
180 - 98 = 82 degrees
In addition, another angle inside the triangle is an 85-degree angle. This is because this 85-degree angle is opposite adjacent to the other 85-degree angle.
Hence, the angles inside the triangle are: x, 85, and 82
x + 85 + 82 = 180 ==> Triangles add up to 180 degrees
x + 167 = 180 ==> simplify
x = 13 degrees ==> subtract 167 on both sides
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In store the ratio of blue shirts to red shirts is 2:5. If there is 100 red shirts in the store, how many blue shirts are there?
The ratio of blue shirts to red shirts is 2:5, so for every five red shirts, there are two blue shirts.
What is ratio?Ratio is a mathematical term used to compare two different values. It is a way of expressing one quantity in relation to another. Ratios can be written as fractions, decimals, or percentages. Ratios are used in many different areas, such as finance, economics, science, and engineering. Ratios are also used to compare the size, speed, or cost of different items. Ratios can be used to compare parts of a whole, or to compare different items within a group.
Since there are 100 red shirts in the store, there are 40 blue shirts in the store (100 / 5 x 2 = 40).
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What if Aya and Sakura could only afford a monthly payment of $1800?
What would be the maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
a) The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same = $369,181.93.
b) The total amount that would be paid to the lender over 25 years = $540000
To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.
Here, future value = 0
number of periods = 25 years
= 25 × 12 months per year
= 300
payment amount = -1800 dollars
interest rate = 4.25% per year
= 0.3542% per month
the maximum mortgage amount they could afford = $369,181.93.
And the total payments would be equal to 300 × 1800 = 540000
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The complete question is:
Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.
What if Aya and Harumi could only afford a monthly payment of $2,000?
What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
please help quickly
These polygons are similar. x=?
The value of x in the similar polygons is 7.
How to find the side of similar polygon?Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion.
Therefore, the polygons WXY and STU are similar.
Hence, using proportion, let's find the value of x
3 / 9 = 4 / x + 5
cross multiply
3(x + 5) = 9 × 4
3x + 15 = 36
subtract 15 from both sides of the equation
3x + 15 - 15 = 36 - 15
3x = 21
divide both sides by 3
x = 21 / 3
x = 7
Therefore,
x = 7
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WASTE Suppose the waste generated by nonrecycled paper and cardboard products in tons y after x days can be approximated by the function y=1000(2)0.3x.
a. Identify key features.
y-intercept: , 1 of 8.
domain: , 2 of 8.
range: , 3 of 8.
b. Identify the relevant domain and range.
Because time , 4 of 8. , the relevant domain is , 5 of 8. .
Because the amount of recycled paper and cardboard , 6 of 8. , and the amount when x=0
is , 7 of 8.tons, the relevant range is , 8 of 8. .
a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:
y-intercept: y = 100.Domain: all real values.Range: y ≥ 1000.b. The relevant domain and range are given as follows:
Domain: x ≥ 0.Range: y ≥ 1000.What are the features of the exponential function?The exponential function for this problem is modeled as follows:
y = 1000(2)^(0.3x).
The features are given as follows:
Initial value, when x = 0, of y = 1000, representing the y-intercept.Rate of change of 2 for each period of 0.3 units.The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.
However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.
The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.
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How do you find the third side of an isosceles triangle when given the angle?
The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.
First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.
We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.
[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]
To calculate 'c', we can first calculate 'a' by using the formula:
a = c * sin(A)
Then we plug 'a' into the equation for 'c':
c = sqrt(2*(c * sin(A))^2)
c = sqrt(2)*c*sin(A)
Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
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The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past 171717 years.
The stem represents the tens place and the leaves represent the unit place of each data point, allowing for easy visualization of the distribution of the data.
A stem-and-leaf plot is a type of graph used to display the distribution of a set of data. It is a way to show the frequency of different values in a dataset. In this case, it is showing the number of days of snowfall at a winter sports resort for each of the past 171717 years.
Continuous and discrete data distributions are the two main forms found in statistics. Continuous data is information having a wide range of possible values. When measuring this kind of information, such weight or temperature, a scale is frequently used. A histogram is another tool for representing continuous data.
The complete question will be :
The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past years. represents a year with days of snowfall. Here is the five-number summary for these data Five-number summary According to the - IQR rule for outliers, how many high outliers are there in the data set?
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Answer:
0
Step-by-step explanation:
3y+2=2y-5x into y=mx+b form
3y + 2 = 2y - 5x
3y - 2y = -5x -2
y = -5x - 2
The length of the base of an isosceles triangle is x. The length of a leg is 5x -2. The perimeter of the triangle is 106. Find x. X =
Answer:
x = 10
Step-by-step explanation:
the legs of an isosceles triangle are congruent.
the perimeter is the sum of the 3 sides of the triangle
sum the 3 sides and equate to 106
x + 5x - 2 + 5x - 2 = 106
11x - 4 = 106 ( add 4 to both sides )
11x = 110 ( divide both sides by 11 )
x = 10
A line passes through the points (-2,8) and (5,-20)
The linear equation that passes through these two points is:
y = -4x
How to find the equation for the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (-2, 8) and (5, -20), so the slope is:
a = (-20 - 8)/(5 + 2) = -28/7 = -4
So the line is:
y = -4*x + b
To find the value of b, we can replace the values of the point (-2, 8), so we will get:
8 = -4*(-2) + b
Now we can solve this for b.
8 = -4*(-2) + b
8 = 4*2 + b
8 = 8 + b
8 - 8 = b
0 = b
Then the linear equation is:
y = -4*x
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What is the degree of 3x³?
Answer:
3x³ is a polynomial of degree
The degree of the polynomial 3x³ is 3
Can someone help me!!!!!!
The y - intercept of the graph, given the formula of 2 y - 5x = 16, is y - intercept : ( 0, 8)
How to find the y - intercept ?To find the y - intercept, use the slope - intercept form of the equation of a line which is:
y = mx + b
m = slope
b = y - intercept
So first rewrite the formula given to look like the slope - intercept :
2 y - 5x = 16
2 y = 5x + 16
( 2 y = 5x + 16 ) / 2
y = 5/ 2 x + 8
The y- intercept is therefore 8. As a point on the graph, this is ( 0, 8 )
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The table shows the number of students going on a field trip one chaperone is needed for every 12 students
Answer:
I'm not sure what equation is needed here. Could you share the table?
Either way, you can take the number of students there are and multiply that to the number of chaperones needed per group of 12- basically see how many groups of 12 you can fit in the overall group of students
i need help plsss help meee
Corresponding angle pairs - (1,5) , (2,6) , (3,7) and (4,8)
What are the intervals of 5?
The set of numbers x such that 0 ≤ x ≤ 5 is an interval containing 0, 5, and all numbers between 0 and 5.
Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers.
In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing 0, 1, and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).
Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.
Complete Question:
What is the interval of 0,5 ?
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the survey is a research method in which: group of answer choices individuals are carefully observed in their natural environments. a representative, random sample of individuals are questioned regarding their attitudes or behaviors. an individual is studied in great depth. an investigator determines the extent to which two variables influence each other.
The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.
B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.
C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.
D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.
Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
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7. A triangle has sides with lengths 7, 24, and 25. (Lesson 4-5)
a. Verify this is a Pythagorean triple.
b. Approximate the acute angles in this triangle.
A triangle has sides of 7, 24, and 25 cm. The length of the hypotenuse is equal to 25 cm if the triangle is a right triangle.
What are the angles of a 7/ 24/ 25 triangle?The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious.
49, 576, and 625 are the results of squaring the lengths of the side of the.
49 + 576 = 625\s(7)2 + (24)2 = (25)2
As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.
the hypotenuse is 25 cm long.
Angles of 16.26 degrees and 73.74 degrees are suitable.
Yes, since 72+242=252 (sum of squares on smaller two sides equals square on largest side).
The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious. 49, 576, and 625 are the results of squaring the lengths of the side of the. As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.
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Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation , where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have
The number of nickels that Sonji has as per the given equation is 63.
What is the value of N mean?In mathematical operations, “n” is a variable, and it is often found in equations for accounting, physics and arithmetic sequences. A variable is a letter or symbol that stands for a number and is used in mathematical expressions and equations. In an arithmetic sequence, which is a list of numbers that follow a pattern, “n” is a variable representing the number of the term to find.For instance, if students want to find the value of the seventh term, “n” would be 7. In physics, an equation for standing waves uses “n” as an integer symbolizing the harmonic number or number of antinodes. The equation evaluates the length of the string in terms of its wavelength. In accounting, “n” is used in the equation for compound interest. It represents the number of compounding in 1 year.We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.
0.10d + 0.05n = 5.25
0.10(21) + 0.05n = 5.25
2.10 + 0.05n = 5.25
0.05n = 3.15
n = 3.15 / 0.05
n = 315 / 5
n = 63
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What is the numerical coefficient of the term − 6xy?
The numerical coefficient of xy in the given expression 6xy is 6.
In mathematical terms, a coefficient is a numerical value that is multiplied by a variable in an algebraic expression. The coefficient is the number that appears in front of the variable.
For example, in the expression 3x, the coefficient is 3. In the expression 2[tex]y^2[/tex], the coefficient is 2. In the expression -5[tex]z^3[/tex], the coefficient is -5.
In the case of a constant term in an expression, the coefficient is the constant term itself.
For example, in the expression 3x + 4, the coefficient of x is 3 and the coefficient of the constant term 4 is 4.
Here, in the expression 6xy, the numerical coefficient of xy is 6.
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Find the median of data 1/3 3/2 1/6 1/4 2/3
Answer:
median= 1/3
Step-by-step explanation:
Simplify (s^-5)^3. Write your answer using only positive exponents.
The given expression (s⁻⁵)³ is equivalent to (1/s)¹⁵.
What is exponent?Exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression. Mathematically -
[tex]$b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]
where -
[b] = base of the logarithm
[x] = exponent
Given is the expression as follows -
(s⁻⁵)³
We can write the expression as -
(s⁻⁵)³ = (1/s⁵)³ = (1/s¹⁵) = (1/s)¹⁵
Therefore, the given expression (s⁻⁵)³ is equivalent to (1/s)¹⁵.
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When two rotations are performed on a single figure, does the order of the rotations sometimes, always, or never affect the location of the final image? Explain.
When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.
What is the rotation?In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.
Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.
There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).
Here two times rotation means 180 degrees that means no change in the final image.
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