Graph triangle lmn with vertices l(1,6), m(-2,4), and n (3,2) and its
image after the composition.
Rotation: 90 about the origin
Translation: (x,y) (x-3,y+2)
Answers
The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).
What is Translation of graph?
A graph can be horizontally translated by moving the base graph to the left or right in relation to the x-axis. Each point on a graph is moved by k units in order to translate it horizontally.
To graph triangle LMN and its image after the composition of a 90 degree rotation about the origin and a translation of (x, y) (x-3, y+2), we can first plot the vertices of triangle LMN on the coordinate plane.
pair L = (1,6);
pair M = (-2,4);
pair N = (3,2);
Next, we can apply the 90 degree rotation about the origin to the vertices of the triangle. The rotation matrix for a 90 degree rotation about the origin is given by:
[cos(90) -sin(90)][x] [y]
[sin(90) cos(90)][y] = [-x]
Substituting the coordinates of the vertices into the rotation matrix, we get:
[cos(90) -sin(90)][1] [6]
[sin(90) cos(90)][-2] = [4]
[3] [2]
Therefore, the image of triangle LMN after the rotation is triangle L'M'N' with vertices L'(-6,1), M'(4,-2), and N'(-2,3).
Finally, we can apply the translation of (x, y) (x-3, y+2) to the vertices of the rotated triangle to get the final image of triangle LMN. The translation matrix is given by:
[tex][1 \ 0][x] [y][-3 \ 2][y] = [x-3][/tex]
Substituting the coordinates of the rotated vertices into the translation matrix, we get:
[1 0][-6] [1]
[-3 2][4] = [-1]
[-2] [3]
Therefore, The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).
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Related Questions
Suppose a sightseeing tour company charges $7.50 for each hour you rent a motorized scooter, plus a non-refundable fee of $45. Write an equation that represents the total cost, y, of renting the scooter in relation to the number of hours, x.
Answers
An equation that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45
What is meant by an equation?3x - 5 = 16 is an illustration of an equation. By solving for x, we discover that the variable's value is 7, or x = 7. By deleting parenthesis and merging related terms, you can simplify either side of an equation and obtain the solution. Together with the variables for which the equation must be solved, the values of the variables that must satisfy the equality to compose the answer are referred to as the unknowns. Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
Given,
You must pay a non-refundable $45, plus $7.50 per hour, to rent a motorized scooter from a sightseeing tour company.
The equation is y=7.50x+45
Therefore, a formula that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45.
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The Morgan family and the Collins family each used their sprinklers last summer. The Morgan family's sprinkler was used for 35 hours. The Collins family's sprinkler was used for 40 hours. There was a combined total output of 1725 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 45 L per hour?
Answers
Answer:
you have to multiply 45^2
2025
Which one doesn't belong?
1. 5 + 7 = 7 + 5
2. 5 * 7 = 7 * 5
3. 2 = 7 - 5
4. 5 - 7 = 7 - 5
Write a post sharing which equation you think doesn't belong and why.
Answers
Answer:
3 does not belong because its not long enough
y = 1/4x+1 y =1/4x-1
How many solutions does this system
of equations have?
Answers
Answer:
3
Step-by-step explanation:
3 because you have to find x, you have to find x and y and then the overall answer
The given system of equations,
y = 1/4 x + 1
y = 1/4 x - 1
has no solution.
Given a system of equations.
There are two equations in the system.
We have to find the number of solutions for the system if it exists.
Consider the equations,
y = 1/4 x + 1
y = 1/4 x - 1
Since both the equations are in y value, they are equal.
1/4 x + 1 = 1/4 x - 1
1/4 x - 1/4 x = -1 - 1
0 = -2
This is not possible.
This means that the given system has no solution.
Hence the given system of equations has no solution.
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How might you use a perpendicular bisector or an angle bisector in your everyday life?
And why would an orthocenter be the most difficult part of a triangle for someone to identify and use?
Answers
You use a perpendicular bisector or an angle bisector in your everyday life and orthocenter be the most difficult part of a triangle.
Everyday life example :
On a clock, the second hand in the middle of the hour hand and minute hand, is working as the angle bisector.
For a perpendicular bisectors, take two ends of a compass needle, with the long end on the North, the short end is pointing South, and the lines of East and West are on the left and right.
Orthocenter :
The orthocenter is the point of intersection of the three altitudes of a triangle. It is the hardest part of the triangle to find because :
It can lie inside a triangle or outside the triangle as it depends on the type of type of the triangle whether it is acute or obtuse. So, in order to identify it we must first know the type of the triangle.
And secondly, the formula for finding orthocenter is quite complicated so it is the hardest part of the triangle to identify and use.
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seasonality causes comparability problems in ratio analysis. a common solution is to use an average account balance as opposed to an ending account balance. t or f
Answers
The given statement is true.
Seasonal inventory or revenue fluctuations that are not based on sales can artificially inflate or deflate the value of the company's assets.
What is Seasonal inventory ?
Products with a seasonal inventory are those that sell more frequently at particular times of the year. Weather, events, and holidays can affect how much demand there is for these products.
Holiday merchandise was probably your first thought when thinking about seasonal inventory. Labor Day weekend, Halloween, and Christmas are a few examples of holiday inventory. Every one of them sells particular goods that people only purchase around the holidays.
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What is 1+1
A. 2
B. 3
C. -24,000
D. Some ridiculous number
Answers
Answer:
a
Step-by-step explanation:
ik my math
Write the following expression using an exponent. (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Answers
For the given expression the exponent would be [tex](2y-9)^5$[/tex].
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = [tex](2y-9)^5$[/tex]
Hence, for the given expression the exponent would be [tex](2y-9)^5$[/tex].
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For the given expression the exponent would be (2y-9)⁵.
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = (2y-9)⁵
Hence, for the given expression the exponent would be (2y-9)⁵.
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Need some help with this!
Answers
Answer:
4 liters
Step-by-step explanation:
We need to first figure out what the proportional value is.
(Y ×? = X)
10(Y) × 2.5 = 25 (X)
If the capacity of X is equivalent to 10 liters, then we need to use the same proportional value to get the number of liters for Y.
10 ÷ 2.5 = 4
Trough Y can contain 4 liters
An item on sale costs 45% of the original price. The original price was $39.
Use the ALEKS calculator to find the sale price.
$0
X
S
Answers
The sales price of the item is $17.55
How to determine the sales priceFrom the question, we have the following parameters that can be used in our computation:
Sales price = 45% of the original price
The original price = $39
The above parameters mean that
Sales price = 45% * original price
Substitute the known values in the above equation, so, we have the following representation
Sales price = 45% * $39
Evaluate
Sales price = $17.55
Hence, the sales price is $17.55
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How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen? PLSSSS EXPLAIN!!!!
Answers
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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Find the measure of each angle indicated.
Answers
Answer:
answer is 124 degree ....
2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
Answers
The zeros of the polynomial function should be between
(2.5, 1.1) & (3.0 -0.8) and (4.0, -0.3) & (4.5, 0.7)How to know the zeros of the polynomial functionThe zeros of a polynomial function is the point where the polynomial crosses the x axis
At this point, the y axis has a value of zero. This point can be seen on the graph easily as the graph will show the x intercept,
For the table, examining the values of the y coordinate to see where the signs change will help to know where the zero will lie.
The table shows that the y values changed sign at 1.1 to -0.8 and -0.3 to 0.7 and hence the zeros will lie between (2.5, 1.1) & (3.0 -0.8) and (4.0, -0.3) & (4.5, 0.7)
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Hello factor the polynomial completely with steps please
Answers
The factor form of the cubic equation y = x³ + 3 · x² + x + 3 is y = (x² + 1) · (x + 3).
How to factor a cubic equation
In this problem we find a cubic equation, that is, a polynomial of the form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are the real coefficients of the polynomial. Herein we must use algebra properties to find the factor form of the expression:
y = a · Π (x - rₙ) for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficient.m - Grade of the polynomial.First, write the entire equation:
y = x³ + 3 · x² + x + 3
Second, use distributive property of real mumbers:
y = x² · (x + 3) + 1 · (x + 3)
Third, use distributive property of real numbers once again:
y = (x² + 1) · (x + 3)
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A rectangular box has dimensions 40 cm by 35 cm by 30 cm.
calculate the largest number of cubes of length 10 cm that can be placed inside the box.
Answers
The largest number of cubes that can be placed in the rectangular box is 42
How to find the cubes the box can containThe problem is solved by solving for the volume of the rectangular box and dividing by the given size of cube
The formula for the volume of rectangular box is given by
= length * width * height
= 40 * 35 * 30
= 42000 cm³
A cube of length 10 cm has a volume of 1000
= 10 * 10 * 10 = 1000
the largest number of cubes of length 10 cm that can be placed inside the box.
= 42000 / 1000
= 42
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In 1995, the standard bus fare in a city was $0.25. In 2022, the standard bus fare was $3.25. Find the percent
increase. (Round to the nearest tenth of a percent.)
Answers
Answer: 1200 percent increase
Step-by-step explanation:
Increase = New Number - Original Number
divide the increase by the original number and times 100
3.25-0.25=3
3/0.25=12*100
1200 percent
find the range for 46 22 46 49 45 39 40 42 41 39 40 36
Answers
Answer: 27
Step-by-step explanation: 46 22 46 49 45 39 40 42 41 39 40 36
The range is calculated by subtracting the lowest value from the highest value.
So the lowest number is 22 and the highest is 49.
Then we subtract 22 from 49 to find the range.
not allowed
a) Find the mode shown below.
15, 8, 21, 2, 12, 22, 19, 8, 19, 8
Answers
Answer:8
Step-by-step explanation: Mode is the value or values in the data set that occurs most frequently.
Anna is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y=3+2. 3xy=3+2. 3x, where yy represents the total cost in dollars and cents, and xx represents the number of miles she travels. What could the number 3 represent in the equation?.
Answers
Answer:
The number 3 represents the fixed cost in the equation which is the flat charge.
help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answers
Answer:
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
Answers
The t-test is appropriate because it can handle small sample sizes and is robust to violations of normality assumptions.
What are Statistical Tests?Mathematical statistical tests are techniques for data analysis and drawing conclusions about a population from a sample. These tests employ mathematical formulae and probability theory to assess if a participant's result is statistically significant, implying that it is unlikely to have happened by chance. Comparing two or more groups, figuring out how variables relate to one another, and assessing the accuracy and validity of data may all be done using statistical tests. They are frequently used to derive inferences from experimental or observational data in disciplines including psychology, economics, and sociology.The outcomes of these tests are used to determine whether to accept or reject a hypothesis and can offer important insights into the underlying patterns and relationships in data.
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help asappppp i dont understand graphs
Answers
The function that is represented by the graph is defined as follows:
A. f(x) = (x - 1)(x + 2)(x + 4).
How to obtain the function represented by the graph?The function represented by the graph is obtained using the Factor Theorem, as we can identify the roots of the function from the graph.
The Factor Theorem states that the function can be declared according to it's linear factors, as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which:
a is the leading coefficient of the polynomial.[tex]x_1, x_2, \cdots, x_n[/tex] are the roots of the polynomial.From the graph given in this problem, the roots of the polynomial are listed as follows:
-4, -2 and 1.
Hence the function can be defined as follows:
f(x) = (x - 1)(x + 2)(x + 4).
Considering a leading coefficient of 1, option A is correct.
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Evan saved $30 on a new TV. If the percent of discount was 20%, how much money did the
TV originally cost?
Answers
Answer:
$150
Step-by-step explanation:
we can make a ratio
20/100=30/x
cross multiple
20x=30(100)
20x=3,000
/20 /20
x=150 hopes this helps
After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?
After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?
y = 2x
y = –x
x = 2
y = 2
Answers
Line of reflection for the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) will be x = 2..
What is mean by Reflection?
Reflection is the process of taking the time to think deeply about the experiences, events, and choices that shape our lives. Reflection allows us to consider how our views and opinions have changed over time, and to take stock of our successes and failures. Reflection can also help us understand our personal values and beliefs and how we can use them to make more informed decisions in the future. Reflection involves looking inward and assessing our thoughts and feelings, as well as looking outward and considering our interactions with the world around us. Taking time for reflection can help us gain insight into our behaviors and motivations, as well as identify areas of our lives that need improvement. It can also help us stay mindful of our goals and stay on the path to achieving them. Reflection is an important part of personal growth and development, and can be a valuable tool for gaining self-awareness and increasing our emotional intelligence.
Given that;
After a reflection of the figure,
The image vertices are A'(5, 1), B'(3, –1), and C'(7, –1).
And, In the figure;
The vertices are A(-1, 1), B'(1, –1), and C'(-3, –1).
Now, When we take the reflection about the line x = 2.
Then, we get the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) of the vertices A(-1, 1), B'(1, –1), and C'(-3, –1).
Therefore, Line of reflection for the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) will be x = 2.
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Choose the system of inequalities that best matches the graph below.
y
5
4
3
KE
-6-5-4-3-2-1 01 23 4 5 6
-1
IN
03
3
S
X
Answers
The inequalities that represent the line in the graph will be y < x - 3 and y = -(2/3)x. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the blue line has a slope of 1 and the y-intercept is at (0, -3), then the inequality is calculated as,
y < x - 3
The red line is passing through the origin and (3, -2), then the equation is given as,
y - 0 = [(-2 - 0) / (3 - 0)](x - 0)
y = -(2/3)x
The disparities that address the line in the chart will be y < x - 3 and y = - (2/3)x. Then the right choice is B.
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Mr. Reynolds is a car salesman. He makes a salary of $55,000 a year. He
also earns a commission of of his total sales for the year. This year, Mr.
Reynolds has a sales total of $295,200. Write and evaluate a function to find
Mr. Reynolds's total earnings for the year.
Answers
Answer:you speak French pls
Step-by-step explanation:
:::
What is the image point of (0,1) after translation right 5 and up 5 units?
Answers
Answer: (5,6)
Step-by-step explanation: 5 units right is adding 5 to your X. 5 units up is adding 5 to your Y.
For left and down, you'd subtract 5. For instance, "What is the image point of (8,9) after a translation of 5 units left, and 5 units down. The answer would be (3,4)
a rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. what is the length, in units, of the longer diagonal?
Answers
The length of the longer diagonal of the given rhombus with side length 51units and shorter diagonal 48 units is equal to 90units.
As given in the question,
Side length of the given rhombus 's' = 51 units
Length of the shorter diagonal of given rhombus 'a' = 48 units
Let us consider length of the longer diagonal of the given rhombus be 'b'
As per the property of the rhombus:
Diagonals of the rhombus bisects each other at right angle
Triangle formed by side length bisecting diagonals is right angled triangle.
Using Pythagoras theorem we have,
(Side length)² = (a/2)² + (b/2)²
Substitute the values
⇒ (51)² = (48/2)² + (b/2)²
⇒2601 = 576 + (b/2)²
⇒(b/2)² = 2601 -576
⇒(b/2)² = 2025
⇒b/2 = √2025
⇒ b/2 =45
⇒ b = 90units
Therefore, the length of the longer diagonal of the given rhombus is equal to 90units.
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13) An airline know from experience that the ditribution of the number of uitcae that
get lot each week on a certain route i approximately normal with μ = 15. 5 and σ = 3. 6. In one year, how many week would you expect the airline to loe between 10 and 20
uitcae?
Answers
The probability of losing 10 to 20 suitcase between a week is 0.8313 by the airline company.
Given what we know,
μ = 15. 5 and σ = 3. 6
Additionally, the weekly distribution of missing baggage along a particular route is roughly average.
z =( x - μ ) / σ
Therefore,
z(20) = (20-15.5)/3.6
= 1.25
P(x < 20)
= P(z < 1.25)
= 0.8944
Therefore, the probability that during a given week the airline will lose between 10 and 20 suitcases = 0.8313
The ratio of good outcomes to all possible outcomes of an event is known as the probability.
The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results
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Solve each system by elimination: 2x+y=5 3x-2y=4
Answers
Answer: 2x+y +5 we know that because if u get 2x+y we do 2xxy and get 2xy
Step-by-step explanation: