What is an angle?
It is the opening that forms the intersection of two lines.
The sum of two angles:
Two angles are complementary if their sum equals 90°.Two angles are supplementary if their sum equals 180°.
What is a rectangle?
A rectangle is a polygon with four sides, with the characteristic that its opposite sides are equal.
What is the measure of the angle formed by the diagonals of the rectangle ABCD?
The area of a rectangle can be determined by knowing its diagonals and the angle they form between them.
A = D² Sen(γ)/2
Being;
D: diagonalγ: angle
Being;
A = (7)(6)
A = 42cm²
Apply the Pythagorean theorem to determine D.
D² = AB² + AD²
replace;
D² = (7)² + (6)²
D² = 49 + 36
D² = 82
Substitute in A;
42=82 Sen(γ)/2
Solve for γ;
84=82 Sen(γ)
γ = Sen⁻¹(84/82)
γ =
Problems 15 & 16. Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement.
Part A : From Angle Angle similarity, ΔMBR and ΔZLP are similar.
Part B.: As the ratios of sides are not equal, triangles are not similar.
Explain about the similar triangles:Congruent triangles and similar triangles are two different but closely related concepts. Similar triangles are any two or more triangles having the identical proportions of their corresponding sides, an equal pair of corresponding angles, and their similar shape.
Part A:
using the equal sides property of triangle:
In ΔRBM,
side BM = side RM
So,
angle B = angle R (eq 1)
In triangle ZLP and PL = LZ
So, angle P = angle Z (eq 2)
And angle B = angle P
∠B = ∠R = ∠P = ∠Z
By Angle Angle similarity, triangle RBM and triangle ZLP are similar.
Part 16.:
In right angle triangle: KLN.
(KL)² = LN² + KN²
(KL)² = 8² + 15²
(KL)² = 64 + 225
(KL)² = 289
(KL) = 17
taking the ratios of sides:
27/8 = 30.6/17
3.375 ≠ 1.8
As the ratios of sides are not equal, triangles are not similar.
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need help there's the image
This means that the only restricted value of [tex]x[/tex] is [tex]x=6[/tex], since using this value in the original equation would lead to both denominators being equal to [tex]0[/tex].
What is equation?In mathematics, an equation is a claim that two expressions are equivalent. Two sides that are separated by the algebraic symbol (=) make up an equation.
For instance, the claim "[tex]2x+3=9[/tex]" contends that the number "[tex]9[/tex]" is equal to the statement Finding the value or values of the variable(s) necessary for the equation to be true is the goal of equation solving.
Equations can include one or more parts and be straightforward or complex, regular or nonlinear. The formula "[tex]x^{2} +2x-3=0[/tex]" raises the variable x to the second power.
In many different branches of mathematics, including algebra, calculus, and geometry, lines are used.
[tex]4+2/(x-6)= 6/(x-6)\\4(x-6) +2 =6\\4x -22 = 0\\4x = 22\\x = 11/2\\[/tex]
Therefore the only restricted value of [tex]x[/tex] is [tex]x=6[/tex], since using this value in the original equation would lead to both denominators being equal to [tex]0[/tex].
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There are 8,246 registered to vote in the town of mayfield. About how many people voted in the election? Explain(there are 74 voters)
We can estimate that about 74 people voted in the election, which is the same as the actual number of voters.
What are the voters?
To estimate the number of people who voted in the election, we can use the proportion of registered voters who actually voted.
If we know that there are 8,246 registered voters in the town of Mayfield and 74 voters cast their vote, we can calculate the proportion of registered voters who voted as follows:
Proportion of voters = Number of voters / Number of registered voters
Proportion of voters = 74 / 8,246
Proportion of voters = 0.00897
We can then use this proportion to estimate the number of people who voted by multiplying it by the total number of registered voters:
Estimated number of voters = Proportion of voters x Number of registered voters
Estimated number of voters = 0.00897 x 8,246
Estimated number of voters = 73.9 (rounded to the nearest whole number)
Therefore, we can estimate that about 74 people voted in the election, which is the same as the actual number of voters.
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Complete question is: There are 8,246 registered to vote in the town of mayfield, about 74 people voted in the election, which is the same as the actual number of voters.
Divide 2x^4-9x^3 5x^2 3x-8 by x^2-4x 1 and verify the division algorithms
Answer:
give up on math this just too hard
Step-by-step explanation:
no
PLS HELP ASAP THANKS
Answer:
(x-4) (x+4)
Step-by-step explanation:
(a-b)(a+b) results a^2 - b^2
So, x is our "a" and 4 is our "b"
find the value of x.
A silver statue has a volume of
38 cm³ and a mass of 359.1 g.
Work out the density of the statue.
Give your answer to 2 d.p.
In the given situation with the help of the given mass and volume, the density is 9.45 g/cm³ respectively.
What do we mean by density?Mass per unit volume is the definition of a material's density.
In essence, density is a measurement of how closely stuff is packed.
It is a particular physical characteristic of a specific thing.
The Greek scientist Archimedes made the discovery of the density principle.
We can travel through low-density materials like air, which has a density significantly lower than that of human tissue.
Granite is a different material altogether.
Never attempt to traverse stone.
So, we have:
Volume: 38 cm
Mass: 359.1 g
Now, the density:
D = m/v
Insert values as follows:
D = m/v
D = 359.1/38
D = 9.45 g/cm³
Therefore, in the given situation with the help of the given mass and volume, the density is 9.45 g/cm³ respectively.
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according to the 2020 report to congress on the prevention and reduction of underage drinking, what percentage of individuals in the us , between the ages of 12 and 20, reported consuming alcohol in the past month when being surveyed?
According to the 2020 report to Congress on the prevention and reduction of underage drinking, approximately 16.8% of individuals in the United States, between the ages of 12 and 20, reported consuming alcohol in the past month when being surveyed.
The report is based on data from the 2019 National Survey on Drug Use and Health (NSDUH), which is an annual survey conducted by the Substance Abuse and Mental Health Services Administration (SAMHSA). There are approximately 16.8% of individuals in the United States consume alcohol in the past month when being surveyed, between the ages of 12 and 20.
It is important to note that consuming alcohol before the age of 21 is illegal in the United States, and underage drinking can lead to a variety of negative consequences, including impaired driving, risky sexual behavior, and increased risk of alcohol use disorder later in life.
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Max build a skateboard ramp that is 16 inches high. The angle formed by the ramp in the ground is 21. What is the length of the Ramp?
Answer:
19.124
Step-by-step explanation:
sin 21=16/x
do the reciprocal and u will find
x/16=1/sin 21
multiply both sides by 16
x=1/sin21×16
the answer will be 19.124
Please some one help and including answer this is due today hurry please.
To find the minimum value of a quadratic function most efficiently, we would like to see the quadratic function in its vertex form.
How to solveThe vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) is the vertex of the parabola, and "a" determines the direction and the "stretch" of the parabola.
If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.
The minimum value of the function occurs at the vertex if the parabola opens upwards (a > 0), and the maximum value occurs at the vertex if the parabola opens downwards (a < 0).
In this case, since we're looking for the minimum value, we would want a quadratic function where a > 0. Once we have the vertex form, we can easily identify the vertex (h, k), and the minimum value of the function will be k.
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Write the quadratic function in vertex form that has a
vertex of (2, 1) and goes through the point (4, 5)
Answer:
Sure, I can help you with that! First, we know that the vertex form of a quadratic function is: f(x) = a(x - h)^2 + k where (h, k) is the vertex of the parabola. So we can plug in the values we have: f(x) = a(x - 2)^2 + 1 Now we just need to find the value of "a". To do that, we can use the fact that the function goes through the point (4, 5). So we can plug in those values: 5 = a(4 - 2)^2 + 1 Simplifying, we get: 5 = 4a + 1 4a = 4 a = 1 So now we know that the quadratic function is: f(x) = (
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Burger Quick is able to estimate their wait time more consistently because it has a smaller IQR (Interquartile Range).
What is an IQR?
The IQR represents the range of the middle 50% of the data, and is a measure of the spread of the data. A smaller IQR indicates that the data is less spread out and more consistent. Therefore, since Burger Quick has a smaller IQR than Super Fast Food, it is able to estimate their wait time more consistently.
It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. The quartiles are values that split the data into four equal parts: Q1 represents the 25th percentile, Q2 (also known as the median) represents the 50th percentile, and Q3 represents the 75th percentile. The IQR therefore represents the range of the middle 50% of the data.
The IQR is a useful measure of variability because it is less sensitive to outliers than the range or standard deviation, which can be skewed by extreme values in the data. The IQR is often used in box plots to show the spread of the data and identify potential outliers.
What is Burger Quick?
Burger Quick is likely a hypothetical or fictional drive-thru restaurant used in a statistical analysis or problem. It was mentioned in a question about box plots and wait times at drive-thru restaurants, and may not actually exist as a real establishment.
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i need help with this badly im really confused
evaluate the question when m=8 m^2 + 9
Here is your answer hope this helps:
m=8
8x8=64
64+9= 73
Which expression is equivalent to 4(15 - 7)?
The expression equivalent to 4(15 - 7) is 32.
What is an expression?
An expression is a combination of values, variables, operators, and function calls that are evaluated to produce a result. An expression can be as simple as a single value or as complex as a multi-level nested set of calculations.
We can simplify the expression 4(15 - 7) by performing the operation inside the parentheses first (since parentheses take precedence over multiplication). We get:
15 - 7 = 8
Substituting this value back into the expression, we get:
4(8)
Multiplying 4 by 8, we get:
32
Therefore, the expression equivalent to 4(15 - 7) is 32.
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Complete question is: The expression equivalent to 4(15 - 7) is 32.
focus groups of 10 people are randomly selected to discuss products of the famous company. it is determined that the mean number (per group) who recognize the famous brand name is 4.80000019, and the standard deviation is 0.73. would it be unusual to randomly select 10 people and find that greater than 8 recognize the famous brand name? group of answer choices
Yes 10 people would be unusual as it falls outside of 2 standard deviation of mean.
Here, the mean number of the famous brand name is 4.80000019, and the standard deviation is 0.73
so, μ = 4.80000019 and σ = 0.73
the number of people = 10
⇒ n = 10
Consider μ ± 2σ
= 4.80000019 ± 2(0.73)
= 4.80000019 ± 1.46
= [4.80000019 - 1.46, 4.80000019 + 1.46]
= [3.34000019, 6.26000019]
As we know 6.26000019 < 8
This means that, it falls outside of 2 standard deviation of mean.
Therefore, it would be unusual to randomly select 10 people and find that greater than 8 recognize the famous brand name.
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You paid $16 in sales tax on a new phone. The phone costs $320. What is the percent of sales tax?
If you paid $16 in sales tax on a new phone. The phone costs $320. the percent of sales tax is 5%.
How to find the sales tax percentage?To find the percent of sales tax, we need to divide the amount of sales tax by the cost of the phone, and then multiply by 100 to convert to a percentage:
Percent of sales tax = (Sales tax / Cost of phone) x 100%
Percent of sales tax = (16 / 320) x 100%
Simplifying the expression inside the parentheses:
Percent of sales tax = 0.05 x 100%
Multiplying:
Percent of sales tax = 5%
Therefore, the percent of sales tax is 5%.
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PLEASE HELP ASAP MARKING BRAINLEIST
Struggling with this question as well. I suck at maths!
Answer:
Yes, the triangle with side lengths 6, 8, and 10 is a right triangle.
Explaination:
We can use the Pythagorean theorem to check if a triangle is a right triangle or not. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse). In other words:
a^2 + b^2 = c^2
where a and b are the lengths of the two shorter sides, and c is the length of the longest side (the hypotenuse).
In this case, the two shorter sides are 6 and 8, and the longest side (the hypotenuse) is 10. So we can plug these values into the equation above:
6^2 + 8^2 = 10^2
Simplifying:
36 + 64 = 100
100 = 100
Since the equation is true, this means that the triangle satisfies the Pythagorean theorem, and therefore it is a right triangle.
In the figure M and N are mid point at QP and PR prove that: respectively (1) MN = 1/2 QR →>> (ii) MN // QR M Q P N R
By the property of the mid point theorem of triangle:
(1) MN = 1/2 QR and (ii) MN || QR
Explain about the mid point theorem:A point that divides a line segment into two equal halves is the midway of the segment. The line segment's midpoint is located precisely in the middle.
According to the midpoint theorem, a segment is half the length of a triangle's third side if it is created by joining the midpoints of two of its sides.According to the midpoint theorem, a segment must be parallel toward the third side if it is created by joining the midpoints of two triangle's sides. Furthermore, it mentions that the length of that section is equal to that of the third side.(1) MN = 1/2 QR
By the property of the mid point theorem of triangle:
MN = 1/2 QR , As M and Na are the mid points sides QP and PR of triangle .
(ii) MN || QR
And thus, both the lines MN and QR will be parallel.
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complete question:
In the figure M and N are mid point at QP and PR prove that: respectively
(1) MN = 1/2 QR
(ii) MN || QR
The figure is attached.
i need help im confused
The parallelogram therefore has a 3/4 square inch area.
What is a parallelogram?A parallelogram is a geometric figure with four equal sides that are parallel to one another. It has equal opposed angles and two sets of parallel sides.
The base length and height of a parallelogram must be multiplied to determine its area. In this instance, the parallelogram's shorter side is specified as 1 inch and its longer side as 4 inches. It states that the height is 3/4 inch.
Hence, the parallelogram's area is:
Area = base x height
= 1 inch x 3/4 inch
= 3/4 square inches
3/4 square inches is equal to 1 inch by 3/4 inch by the base and height.
The parallelogram therefore has a 3/4 square inch area.
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Mrs. Harper is teaching a 5th grade class. She is
standing 6 meters in front of Annie. Javier is
sitting to Annie's right. If Javier and Mrs. Harper
are 8 meters apart, how far apart are Annie and
Javier? If necessary, round to the nearest tenth.
This is a Pythagorean theorem word problem
Answer:
Annie and Javier are 10 meters apart.
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Let's call the distance between Annie and Javier "x". Then, we have two right triangles:
The first right triangle is formed by Mrs. Harper, Annie, and the distance between Mrs. Harper and Annie. We know that Mrs. Harper is 6 meters in front of Annie, so the hypotenuse of this triangle is 6 meters.
The second right triangle is formed by Mrs. Harper, Javier, and the distance between Mrs. Harper and Javier. We know that Mrs. Harper and Javier are 8 meters apart, so the hypotenuse of this triangle is 8 meters.
Since Mrs. Harper is the common point of both triangles, we can combine them to form a larger right triangle with sides of 6 meters, 8 meters, and x meters:
Using the Pythagorean theorem, we have:
6^2 + 8^2 = x^2
Simplifying:
36 + 64 = x^2
100 = x^2
Taking the square root of both sides:
x = 10
Therefore, Annie and Javier are 10 meters apart.
29 out of 50 people interviewed said they liked orange juice with their breakfast what percent of those interviewed said they like orange juice for breakfast
The percent of those interviewed said they like orange juice for breakfast is 58%.
What is a percentage?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent.
The percent of those interviewed said they like orange juice for breakfast will be:
= Orange juice taker / Total respondent
= 29/50
= 0.58
= 58%
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G is the incenter of ABC
GD:
BG:
FC:
BF:
For the given triangle when G is the incenter of ABC the value of DG = 12, FC = 35, BG = 13.41, BF = 6.
What is incenter?The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It may be thought of as the intersection of the triangle's internal angle bisectors. Due to the junction point of the central axis being the centre of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides.
The centre of a triangle's inscribed circle, which is the biggest circle that can fit within the triangle, is known as the incenter.
Given that, G is the incenter of the triangle.
Thus, EG = GF = DG.
Now, the value of DG is determined using the Pythagoras Theorem:
(37)² = DG² + (35)²
1369 = DG² + 1225
DG = 12
Now, FC = 35.
For, BG we have:
BG² = 6² + 12²
BG² = 36 + 144
BG = 13.41
BF = 6
Hence, for the given triangle when G is the incenter of ABC the value of DG = 12, FC = 35, BG = 13.41, BF = 6.
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Which statement about f(x) = -x squared + 8x-7 is true?
Option D : The statement that is true about the quadratic function f(x)=-x²+8x-7, which states that the zeros are 1 and 7, because f(x) = -(x - 1)(x - 7).
To find the zeros of the quadratic function f(x) = [tex]-x^2 + 8x - 7[/tex], we need to set f(x) equal to zero and solve for x:
[tex]-x^2 + 8x - 7 = 0[/tex]
We can solve this quadratic equation using the quadratic formula or by factoring. Let's use factoring.
We can rewrite the quadratic expression as:
[tex]-(x^2 - 8x + 7)[/tex]
To factor the expression, we need to find two numbers whose product is 7 and whose sum is -8. These numbers are -1 and -7. Therefore, we can rewrite the expression as:
-(x - 1)(x - 7)
So the zeros of the function are x = 1 and x = 7.
Therefore, the statement that is true is option D: The zeros are 1 and 7, because f(x) = -(x - 1)(x - 7).
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Which statement about f(x)=-x²+8x-7 is true?
A. The zeros are 1 and -7, because f(x)=-(x-1)(x+7)
B. The zeros are -1 and -7, because f(x)=-(x+1)(x+7)
C. The zeros are -1 and 7, because f(x)=-(x+1)(x-7)
D. The zeros are 1 and 7, because f(x)=-(x-1)(x-7)
PLS ANSWER! THIS WAS DUE SO ON MARCH 27TH AND THIS IS ONE OF THEM!
Answer:
444 in
Hope this helps!
Step-by-step explanation:
Area of a triangle is [tex]\frac{1}{2}[/tex] × B × H
Already given, the base is 12 and the height is 12.5, [tex]\frac{1}{2}[/tex] and 12 can simplify to get 6 so 6 × 12.5 is 75. One triangle has the area of 75, the 4 triangles have a total area of 300.
The base is a square, so the formula for that is L × W, which would be 12 × 12 = 144. Add that to 300 and the surface area of the pyramid is 444.
a triangular prism has a volume of 27.36 cubic units.the prism is 2.88units tall. what is the area of the triangular base
The area of the triangular base of the prism is 9.5 unit².
What is an area?
To find the area of the triangular base, we need to use the formula for the volume of a triangular prism:
V = (1/2)×b×h×H
Where b is the length of the base of the triangle, h is the height of the triangle, and H is the height of the prism.
We know that the volume of the prism is 27.36 unit³ and the height of the prism is 2.88 units. So we can plug these values into the formula:
27.36 = 1/2×b×h×2.88
Simplifying this equation, we get:
b×h = 19
We don't know the values of b and h separately, but we can use the fact that the area of a triangle is equal to (1/2)×b×h. So we can rewrite the equation as:
2 × (Area of triangular base) = 19
Dividing both sides by 2, we get:
Area of triangular base = 9.5 units²
Therefore, the area of the triangular base of the prism is 9.5 unit².
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Write (9m)⁴ without exponents.
we can multiply 6561m⁴ by 1 to get the final answer of 6561m⁴.
How to solve the problem?
In mathematics, an exponent refers to a numerical representation of repeated multiplication. An exponent is usually written as a small number that appears to the right and above a larger number, called the base. The exponent indicates how many times the base should be multiplied by itself. For example, in the expression 3², the base is 3, and the exponent is 2. This means that 3 should be multiplied by itself 2 times, resulting in 3 multiplied by 3, which equals 9.
Exponents are a shorthand way of representing repeated multiplication and can be used to simplify complicated expressions. They are widely used in algebra, calculus, and other branches of mathematics. Exponents can be positive, negative, or zero, and they can be fractions or irrational numbers. The rules of exponents, such as the product rule and power rule, allow for easy manipulation of expressions involving exponents.
To write (9m)⁴ without exponents, we need to perform the multiplication four times.
First, we can multiply 9m by 9m to get 81m².
Next, we can multiply 81m² by 9m to get 729m³.
Then, we can multiply 729m³ by 9m to get 6561m⁴.
Finally, we can multiply 6561m⁴ by 1 to get the final answer of 6561m⁴.
In summary, (9m)⁴ can be written as 6561m⁴ by performing multiplication four times using the distributive property of multiplication. It is important to note that exponents are a shorthand way of writing repeated multiplication, but the same result can always be obtained by performing the multiplication explicitly. This process may become more cumbersome for larger exponents, which is why exponents are a useful notation for expressing repeated multiplication in a more concise way.
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. what is the value of the 30th percentile for the data set? 7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 6
The required value of the 30th percentile of the given data set 7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 6 is equal to 5.
To find the value of the 30th percentile,
We need to sort the data set in ascending order first,
1, 2, 3, 3, 4, 5, 6, 7, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20
The 30th percentile is the value below which 30% of the data falls.
To find this value, we can use the formula,
P = (n / 100) × x
where P is the desired percentile (30th percentile in this case),
n is the total number of data points,
And x is the rank of the value corresponding to the desired percentile.
Here,
The total number of data points n = 20
x = (30 / 100) × 20
= 6.
This means that the value corresponding to the 30th percentile is the 6th value in the sorted data set, which is 5.
Therefore, the value of the 30th percentile for the given data set is 5.
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Choose the mapping statement that represents each rotation.
a. 90 degree clockwise rotation about the origin (x, y) → (y , -x). b. 180 degree clockwise rotation about the origin (x, y) → (-x, - y). c. 270 degree clockwise rotation about the origin (x, y) → (-y, x).
What is transformation?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
The mapping statement for each rotation in the is given as:
a. 90 degree clockwise rotation about the origin (x, y) → (y , -x)
b. 180 degree clockwise rotation about the origin (x, y) → (-x, - y)
c. 270 degree clockwise rotation about the origin (x, y) → (-y, x).
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