Answers
The formulas for the rigid transformations of the figures are listed below:
Case 1: (x, y) → (x - 10, y + 9)
Case 2: (x, y) → (- y, x)
Case 3: (x, y) → (- x, y)
Case 4: (x, y) → (- y, x)
Case 5: (x, y) → (x, - y)
Case 6: (x, y) → (x, y + 10)
How to determine the transformation rule for each case
In this question we find six cases of rigid transformations applied on figures. The most common rigid transformations are listed below:
Translation: (x, y) → (x + a, y + b), where a, b are real numbers.Reflection about x-axis: (x, y) → (x, - y)Reflection about y-axis: (x, y) → (- x, y) Rotation: (x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ), where θ is the angle of rotation.Then, by direct inspection, we derive the following rigid transformations:
Case 1 (Translation)
(x, y) → (x - 10, y + 9)
Case 2 (Rotation)
(x, y) → (x · cos (- 270°) - y · sin (- 270°), x · sin (- 270°) + y · cos (- 270°))
(x, y) → (- y, x)
Case 3 (Reflection about y-axis)
(x, y) → (- x, y)
Case 4 (Rotation)
(x, y) → (x · cos 90° - y · sin 90°, x · sin 90° + y · cos 90°)
(x, y) → (- y, x)
Case 5 (Reflection about x-axis)
(x, y) → (x, - y)
Case 6 (Translation)
(x, y) → (x, y + 10)
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Related Questions
can someone please help me i dont understand this question......A first-time homebuyer is financing a house for $128,900. The buyer has to pay $300 plus 1.05% for a brokerage fee. How much are the mortgage brokerage fees? $1,653.45 $1,353.45 $1,356.60 $1,365.45
Answers
The required mortgage brokerage fee is $1,654.45, which is closest to option A: $1,653.45.
What is the percentage?The percentage is the ratio of the composition of the subject to the overall composition of the subject multiplied by 100.
Here,
To calculate the mortgage brokerage fees, you need to add the fixed fee of $300 to 1.05% of the house price. Here's how to calculate it:
Calculate 1.05% of $128,900:
0.0105 x $128,900 = $1,354.45
Add the fixed fee of $300 to the result:
$1,354.45 + $300 = $1,654.45
Therefore, the answer is $1,654.45, which is closest to option A: $1,653.45.
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Graph the system, and find the solution: y = 2x - 1 and y = -1/3x +3, HELP PLEASE, I HAVE A TEST ON THIS TOMORROW ILL GIVE YOU BRAINLIEST
Answers
The solution to the system of equations y = 2x - 1 and y = -1/3x + 3 is given as follows:
(1.714, 2.429).
How to obtain the solution to the system of equations?The system of equations for this problem is defined as follows:
y = 2x - 1 y = -1/3x + 3.We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
(1.714, 2.429).
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7(3+5)___+___
and Its not 7+8 I need help
Answers
Answer:
21+35
Step-by-step explanation:
7(3+5)=7x3+7x5=21+35
brainliest, 100 points, and multiple choice!!!!!!!
Answers
Answer:
The answer is D
Step-by-step explanation:
Answer:
The answer to the following is infinitely many.
Step-by-step explanation:
You could solve this in many ways, for instance, by simplifying it and solving it. Adding a number in the place of x, etc.
I hope this helps!
100 points, brainliest, and multiple choice!!!!!!
Answers
Answer:
(2,1)
Step-by-step explanation:
To find the solution for the system on a graph, look where the two lines intersect, that coordinate is your answer.
What are the 5 rules of scientific notation?
Answers
5 rules of scientific notation which helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent.
The exponent is either positive or negative depending on how big or little the number is. Learn about power and exponents to have a deeper understanding. The five golden rules of the scientific notation:
Base should be always 10The exponent must be a non-zero integer, that means it can be either positive or negativeThe absolute value of the coefficient is greater than or equal to 1 but it should be less than 10 Coefficients can be positive or negative numbers including whole and decimal numbersThe mantissa carries the rest of the significant digits of the number of the exponent.Hence there are the rules of the the scientific notation.
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Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the value of the test statistic?
Answers
Based upon this information, the value of the test statistic is 0.23.
The term "test statistic" refers to a quantity obtained from the sample and used in statistical hypothesis testing.
The sample proportion, or ratio of the sample size to the number of "yes" responses (23), would be the test statistic in this situation (100). The sample proportion is computed in the following manner:
The test statistic is p = 23/100, or 0.23.
So, 0.23 is the test statistic. The percentage of dog owners that routinely feed their dogs Woof Chow dog food is represented by this sample estimate.
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PLS SOME1 HELP ITS DUE IN 20 MIN!!!!!!!!!!!!!!!!!!!!!!!
A quilter created the following shape to use in a block for a new quilt. A six-sided figure with a large base of 10 and three-fifths inches. The side to the right of the base is 6 inches. The small side parallel to the base is 4 and one-fifth inches. There are two sides that form a point at a right angle. The smaller is 4 inches, and the larger is 5 inches. What is the area of the shape for the quilt block?.
Answers
The area of the shape for the quilt block is eighty three three - fifth (83 3/5) inches square.
How to calculate the areaIt should be noted that to find the area of this six-sided figure, we can break it down into two right triangles and a rectangle.
First, let's find the area of the right triangle with the 4-inch side. This triangle has a base of 4 inches and a height of 5 inches, so the area is (1/2) * 4 * 5 = 10 square inches.
Next, let's find the area of the right triangle with the 5-inch side. This triangle has a base of 5 inches and a height of 4 inches, so the area is (1/2) * 5 * 4 = 10 square inches.
Finally, let's find the area of the rectangle. This rectangle has a base of 10 and three-fifths inches and a height of 6 inches, so the area is (10 + 3/5) * 6 = 63 3/5 square inches.
The total area of the six-sided figure is:
= 10 + 10 + 63 3/5
= 83 3/5 square inches.
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Ryan calculated the missing measure in the diagram shown. What was his mistake?
2.6
4.8
=
h
14.4
14.4 ×
2.6
4.8
=
h
14.4
× 14.4
37.44
4.8
= h
7.8 = h
Ryan should have
(select)
14.4 and 4.8 to get a denominator of
on the right side of the first line. Doing so gives the correct value, h =
cm.
Answers
Answer:
Ryan's mistake was in multiplying the numerator and denominator of the fraction 2.6/4.8 by 14.4. This resulted in a value of 37.44 in the numerator, which is incorrect.
To correctly calculate the missing measure, Ryan should have multiplied the numerator and denominator of 2.6/4.8 by 14.4/4.8, which would simplify to 3. This gives:
2.6/4.8 = h/14.4
Multiplying both sides by 14.4:
h = 14.4 × 2.6/4.8
h = 7.8 cm
So, Ryan should have selected "3" as the denominator for the fraction 2.6/4.8.
Step-by-step explanation:
I really would appreciate if you guys help me
Answers
Answer:
He attended school for 9 hours everyday
Step-by-step explanation:
612/68=9
This is because he did 9 hours everyday for 68 days until he go 612 hours of barber school, which means that 612 hours/68 days=hours attended per day
A store is going out of business. Everything is marked down by 40%. How much do you pay now for an item that used to cost $50?
Answers
Answer:
= $20.
Step-by-step explanation:
items pay now = x
40 : 100 = x : 50
40/100 = x/50
40× 5o = 100x
2000 = 100x
2000/100 = 100x/100
$20= x
therefore you pay $20 item that used to cost $50.
A bird drops a stick from a height of 52 ft. The function h=-16t^2+52 gives the sticks approximate height h above the ground, in feet, after the seconds. Graph the function. About what time does the stick hit the ground?use inequalities to describe a reasonable domain and range for the function.
Answers
Answer:
Step-by-step explanation:
To graph the function h = -16t^2 + 52, we can create a table of values and plot the points:
t h
0 52
0.5 42
1 36
1.5 34
2 36
2.5 42
3 52
Then we can plot these points on a coordinate system to get the graph of the function:
Graph of h = -16t^2 + 52
To find the time at which the stick hits the ground, we need to set h = 0 and solve for t:
0 = -16t^2 + 52
16t^2 = 52
t^2 = 3.25
t = ±√3.25
Since time cannot be negative in this context, we take the positive value:
t ≈ 1.8 seconds
Therefore, the stick hits the ground after approximately 1.8 seconds.
To describe a reasonable domain and range for the function, we need to consider the context of the problem. Since the height of the stick is measured in feet, we can assume that t represents time in seconds. In this case, a reasonable domain for the function would be t ≥ 0, since time cannot be negative. For the range, we can see from the graph that the maximum height of the stick is 52 feet, and the minimum height is 0 feet (when the stick hits the ground). Therefore, a reasonable range for the function would be 0 ≤ h ≤ 52.
If a fair six-sided number cube was rolled
510 times, how many times would
you predict that a 4 or 5 would be rolled?
Answers
We would anticipate that a fair six-sided number cube would roll a 4 or 5 roughly 170 times out of 510 rolls.
How is probability determined?The likelihood of rolling a 4 or a 5 on any given roll, supposing the six-sided number cube is fair, is 2/6 or 1/3. This indicates that we should anticipate seeing a 4 or a 5 roughly one-third of the time out of 510 rolls.
We may determine this by dividing the total rolls by the likelihood of rolling a 4 or a 5, as follows:
510 * 1/3 = 170
It's crucial to keep in mind that this is merely a prediction based on probability and that the actual outcomes could change as a consequence of chance or other circumstances.
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What is 2008 AP Multiple Choice AB answers and solutions?
Answers
The 2008 AP Multiple Choice AB answers and solutions can be found on the College Board website or through other online resources.
However, it is important to remember that simply looking up the answers will not help you in the long run. It is important to understand the concepts and methods behind each question in order to be successful on the AP exam.
Here are the answers to the 2008 AP Multiple Choice AB exam:
1. B
2. D
3. C
4. B
5. A
6. D
7. D
8. C
9. B
10. D
11. C
12. B
13. D
14. A
15. D
16. B
17. C
18. D
19. A
20. D
21. B
22. C
23. D
24. B
25. C
26. D
27. A
28. B
It is important to remember that simply knowing the answers will not guarantee success on the AP exam. It is important to understand the concepts and methods behind each question in order to be successful. If you are having difficulty with a particular question or concept, it is recommended that you seek out additional resources or assistance from a teacher or tutor.
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If the length of diagonal of square is √2 then what is the length of
each side ?
Answers
Answer:
1
Step-by-step explanation:
The diagonal is √2 times the length of any side. So √2/√2 is 1.
The angles that share the same sine value as sin(45°) have terminal sides in quadrant .
Answers
The angles that share the same sine value as sin(45°) have terminal sides in second quadrant .
The sine function relates the ratio of the length of the side opposite an acute angle to the length of the hypotenuse of a right triangle. The sine of an angle is always between -1 and 1.
The sine of 45 degrees is √2/2, which is a positive value. Since the sine of an angle is positive in the first and second quadrants, the angles that share the same sine value as sin(45°) must have their terminal sides in the first or second quadrant.
To find the angles that have the same sine value as 45 degrees, we can use the inverse sine function, also known as the arcsine function. The arcsine of √2/2 is 45 degrees or π/4 radians, which is an angle in the first quadrant.
However, since the sine function is periodic, there are infinitely many angles with the same sine value as 45 degrees, and they are all separated by integer multiples of 360 degrees or 2π radians.
Therefore, the angles that share the same sine value as sin(45°) have terminal sides in second quadrant, and can be represented by the formula:
θ = n(360°) ± 45°
or
θ = n(2π) ± π/4
where n is an integer.
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Answer: ( ll ) edgen
Step-by-step explanation:
how do you find the population mean for a set of data?
Answers
Answer:The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.
please help me on this
Answers
Answer:
I got 5/16 as my answer
Step-by-step explanation:
I used a calculator to solve the equation :/
We make 72 cookies and 18 cookies are eaten. What fraction represents the portion of the whole batch that remains?
Answers
Answer:
1/4
Step-by-step explanation:
Create a chart 18 over 72 and x over 100
Now we multiply 18 by 100 to get 1800
We take that 1800 and divide it by 72 to get 25/100
We can simplify this to 1/4
In the parallelogram below, y= ? Degrees
Answers
The value of angle y is 33 degrees
How to determine the value of the angleIt is important to note the properties of a parallelogram;
The opposite sides are equal and are parallelThe opposite angles are congruent The consecutive or adjacent angles are supplementary to each otherIf any one of the angles is a right angle, then all the other angles are right angleThe two diagonals bisect each other at 90 degreesAlso, it is important to note that adjacent angles are equal in magnitude
From the diagram, we can see that the angles 33 degrees and y are alternating angles.
Then, the value is 33 degrees
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sketch a graph for days 0-9
Answers
The sketch for the graph is added as an attachment
The sketch for the graphFrom the question, we have the following parameters that can be used in our computation:
The table of values
Next, we plot the points on the graph using the following scale on the y-axis
1 unit = 1000000000 people
See attachment for the graph
From the graph, we can see that
The curve never intersects with the y-axis
This means that
y ≠ 0
The interpretation of this is that the scientists were not able to completely turn all the zombies to human
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Determine the approximate circumference of a circle that has an area of 200. 96 cm 2.
Answers
If an area of the circle is 200.96 cm^2 , then the circumference of the same circle is approximately around 28.28 cm^2.
The formula for the area of a circle is given by:
A = πr^2,
where A is the area and r is the radius of the circle.
To find the circumference of a circle, we can use the formula:
C = 2πr,
where C is the circumference and r is the radius.
To solve for the circumference, we first need to find the radius of the circle. We can use the formula for the area to find the radius:
A = πr^2
200 = πr^2
r^2 = 200 / π
r = √(200 / π)
Next, we can substitute the value of r into the formula for the circumference to find the circumference:
C = 2πr
C = 2π * √200 / π)
C = 2 * √(200)
Approximating √(200) to 14.14, we get:
C ≈ 2 * 14.14 = 28.28
So the approximate circumference of a circle with an area of 200 square cm is 28.28 square cm.
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b) Lizzie has gross monthly pay of £1,480. She has to pay income tax of £112.67 and NICs of £96.48. How much is her net pay?
Answers
Her net pay is 1270.85 pounds
What is Net Pay?
Net Pay is the take-home pay an employee receives after you withhold deductions. You can find net pay by subtracting deductions from gross pay.
where,
Gross monthly pay = 1,480 pounds
Income tax = 112.67 pounds
NICs = 96.48 pounds
Net pay = Gross pay - Deductions
Net pay = 1,480 - (112.67 +96.48)
Net pay = 1480 - 209.15
Net pay = 1270.85 pounds
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What is the value of a 2 + 3 b + c − 2 d , w h e n a = 3 , b = 8 , c = 2 , a n d d = 5 ?
Answers
Answer:
Step-by-step explanation:
3*2+3*8+2-2*5=6+24-10+2=22
what is difference between parameter and statistic
Answers
Answer:
One and the same
Step-by-step explanation:
what is 3 5 as a decimal
Answers
To convert 3/5 to a decimal, we divide the numerator by the denominator and we get 0.6. 3/5 as a decimal is 0.6.
To convert 3/5 to a decimal, we divide the numerator (3) by the denominator (5):
3 ÷ 5 = 0.6
Therefore, 3/5 as a decimal is 0.6.
Converting a fraction to a decimal involves dividing the numerator by the denominator. To convert 3/5 to a decimal, we can use long division or a calculator to perform the division. In this case, 3 divided by 5 equals 0.6. Alternatively, we can also recognize that the fraction 3/5 can be written as a decimal by dividing the numerator by the denominator. Since 3 is the same as 3.0, we can add a decimal point after 3 and divide by 5 to get 0.6. The decimal form of a fraction can be useful for making comparisons or performing calculations with other decimal numbers.
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Complete Question
what is 3/5 as a decimal?
Which of the following systems of equations has the solution (–1, 5)?
A.
y = 3x + 8
y = –x + 4
B.
y = 3x + 8
y = –x – 4
C.
y = 3x – 8
y = –x + 4
D.
y = 3x – 8
y = –x – 4
Answers
The correct option for the systems of equations that has the solution (–1, 5) is - A. y = 3x + 8 and y = –x + 4.
Explain about the term systems of equations?According to the discussion above, a system of equations is a collection of equations that aim to find a similar solution for all of the variables.
When there are multiple unknowns and there is sufficient data to arranged equations in those unknowns, systems of equations are utilised to solve applications. Generally speaking, when we have n uncertainties, we require n equations set up in those unknowns.For the given solution of (–1, 5).
It must satisfy the given systems of equations.
Put x = - 5 and if y = 5 comes, it satisfies the equation.
Thus,
Option A:
y = 3x + 8
Put x = -1
y = 3(-1) + 8 = 5
y = –x + 4
Put x = -1
y = -(-1) + 4
y = 5
Thus, option A satisfies the given systems of equations.
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Answer: A: y = 3x + 8
y = –x + 4
Step-by-step explanation:
10. You have $35 in your bank account and deposit $10 each week. At the same time, your cousin has
$1855 in his account, but is withdrawing $25 each week. How many weeks will it take for both account
balances to be the same?
Answers
Answer:
52 weeks
Step-by-step explanation:
Cousins bank account
52 x 25 = 1300
1855 - 1300 = 555
My bank account
52 x 10 = 520
520 + 35 = 555
Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base
diameter and height are always the same. How fast is the height of the pile increasing when the pile is 14 feet high? Recall that the volume of a
right circular cone with height h and radius of the base r is given by V=pi/3 r²h.
Your answer: ______
feet per minute.
Answers
Answer:
The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.
Please help! 100 points!
Translation – (x+3,y-3)
Dilation – Reduce the figure by ½
Reflection- Reflect over the line y = x
Rotation – Rotation of 180 degrees around the origin.
Answers
1. Translation – (x+3, y-3) :
To move the figure 3 units to the right in the x-direction and 3 units down in the y-direction.
2. Dilation – Reduce the figure by ½ is:
When reducing a figure by ½, every dimension of the figure is divided by 2.
3. Reflection- Reflect over the line y = x
Reflecting over the line y = x means that every point in the figure is reflected over the line that goes diagonally from the lower left to the upper right.
4. Rotation – Rotation of 180 degrees around the origin.
When rotating a figure 180 degrees around the origin, every point in the figure is moved to a new location that is 180 degrees around the origin from its original location.
Transforming FiguresTranslation – (x+3,y-3)Translated to plain English, this means to move the figure 3 units to the right in the x-direction and 3 units down in the y-direction. When we apply the translation (x+3,y-3) to a figure, it means that we move the entire figure 3 units to the right in the x-direction, and 3 units down in the y-direction. So, the translation (x+3,y-3) simply shifts the figure to a new location that is 3 units to the right and 3 units down from its original location.
Dilation – Reduce the figure by ½Dilation is a transformation that changes the size of a figure. When reducing a figure by ½, every dimension of the figure is divided by 2. In other words, every point in the figure is moved to a point that is half the distance from the center of dilation.
Reflection – Reflect over the line y = xReflecting a figure over a line means to create a mirror image of the figure on the other side of the line. Reflecting over the line y = x means that every point in the figure is reflected over the line that goes diagonally from the lower left to the upper right.
Rotation – Rotation of 180 degrees around the originRotating a figure means to turn it around a fixed point. When rotating a figure 180 degrees around the origin, every point in the figure is moved to a new location that is 180 degrees around the origin from its original location. This means that every point is flipped over to the opposite side of the origin.
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