find the matrix a in the linear transformation y = ax whjere x = [x1 x2]
Answers
The matrix a for the linear transformation y = ax where x = [x1 x2] is given by:\(\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}\)
To find the matrix a in the linear transformation y = ax where x = [x1 x2], we need to use the formula for a linear transformation matrix which is given by:\(\begin{pmatrix}y_1\\y_2\\\vdots\\y_n\end{pmatrix}\) = \(\begin{pmatrix}a_{11}&a_{12}&\cdots&a_{1n}\\a_{21}&a_{22}&\cdots&a_{2n}\\\vdots&\vdots&\ddots&\vdots\\a_{m1}&a_{m2}&\cdots&a_{mn}\end{pmatrix}\) \(\begin{pmatrix}x_1\\x_2\\\vdots\\x_n\end{pmatrix}\)
Where a11, a12, a21, a22 are the coefficients of the linear transformation matrix a. So, using this formula, we can write:y = ax\(\implies\) \(\begin{pmatrix}y_1\\y_2\end{pmatrix}\) = \(\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}\) \(\begin{pmatrix}x_1\\x_2\end{pmatrix}\)
Comparing this with the general formula for a linear transformation matrix, we can see that:\(m=n=2\)\(a_{11},a_{12},a_{21},a_{22}\) are the coefficients of the matrix a.
Therefore, the matrix a for the linear transformation y = ax where x = [x1 x2] is given by:\(\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}\)
To know more about matrix visit:
https://brainly.com/question/27929071
#SPJ11
Related Questions
Please answer correctly !!!!!!!!!!! Will mark BRIANLIEST !!!!!!!!!!!
Answers
Answer:
smaller x = -5
larger x = 5
Step-by-step explanation:
-x^2 - 8 = -33
Add 8 to each side
-x^2 - 8+8 = -33+8
-x^2 = -25
divide each side by -1
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
x = -5, x = 5
Answer:
\(lesser \: \: \: x =( - 5 )\\ greater \: \: \: x =( 5)\)
Step-by-step explanation:
\( - {x}^{2} - 8 = - 33 \\ - {x}^{2} = - 33 + 8 \\ - {x}^{2} = - 25 \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = + 5 \\ x = - 5\)
hope this helps
brainliest appreciated
good luck! have a nice day!
help help help help help
Answers
Answer: (1) A (2) C (3) B (4) D (5) E
Step-by-step explanation:
Use the following conversions:
1 rev = 2π
1 hr = 60 min
1 min = 60 sec
1 mi = 5280 ft
\(1)\qquad \dfrac{40\ rev}{min}\times \dfrac{2\pi}{1\ rev}\times \dfrac{1\ min}{60\ sec}=\large\boxed{\dfrac{4\pi}{3}}\longrightarrow A\)
\(2)\qquad \dfrac{80\ rev}{hr}\times \dfrac{1\ hr}{60\ min}=\large\boxed{\dfrac{4}{3}}\longrightarrow C\)
\(3)\qquad \dfrac{55\ mi}{hr}\times \dfrac{5280\ ft}{1\ mi}\times \dfrac{1\ hr}{60\ min}\times \dfrac{1\ min}{60\ sec}=\large\boxed{\dfrac{242}{3}}\longrightarrow B\)
\(4)\qquad \dfrac{8\ rad}{min}\times \dfrac{1\ rev}{2\pi}=\large\boxed{\dfrac{4}{\pi}}\longrightarrow D\)
\(5)\qquad \dfrac{240\ rev}{hr}\times \dfrac{2\pi}{1\ rev}\times \dfrac{1\ hr}{60\ min}=\large\boxed{8\pi}\longrightarrow E\)
Eight independent measurements were made along a line and the standard deviation was found to be ±0.42. Determine the error at 99.7% probability. State you answer to two decimal places
Answers
The error at 99.7% probability is ±0.88.
To determine the error at 99.7% probability, we use the concept of confidence intervals. In a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the standard deviation of the measurements is ±0.42, we can multiply it by three to obtain the error at 99.7% probability.
3 * 0.42 = 1.26
However, since the error is given as ±0.42, we divide the calculated value by two to get the error on one side:
1.26 / 2 = 0.63
Therefore, the error at 99.7% probability is ±0.63. Rounding it to two decimal places, we have ±0.63 ≈ ±0.88.
Hence, the error at 99.7% probability is approximately ±0.88.
to learn more about probability click here:
brainly.com/question/29221515
#SPJ11
help!
C + -328 = 477
Answers
the answer is
c = -119
A bag contains 20 coloured marbles. Copy and
complete the table below to show the probability of
picking each colour at random and the number of
each colour marble in the bag. What is the
probability, as a percentage (%), of picking a purple
marble at random? How many purple marbles are in
the bag?
Colour
Yellow
Blue
Green
Purple
Probability
10%
15%
Number of marbles
6
Answers
Blue Probability = 30 %
Green No. of balls = 3
Purple Probability = 45 %
Purple No. of balls = 9
What is the shape of the cross section of a sphere?
Rectangle
triangle
ellipse
circle
Answers
Answer:
the correct answer is circles
Step-by-step explanation:.
how do i solve this?
Answers
Answer: the first box put 2
The second box put 3
Step-by-step explanation:
i will explain in the comments below
Kevin needs of a yard of fabric to make a pillow. He has 35 yards of fabric.
Answers
Answer:
Kevin can make 35 pillows.
Step-by-step explanation:
I assume that your question would be, "How many pillows can Kevin make?" If this is not the answer that you were looking for, you need to input your question.
The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell x muffins at $0.35 apiece and y bags of carrot sticks at $0.15 apiece, the total number of dollars raised will be T = 0.35x + 0.15y. How many dollars will they raise if they sell 210 muffins and 120 bags of carrot sticks?
Answers
Answer:
$91.5
Step-by-step explanation:
muffins: 210 carrot sticks:120
T= 0.35x + 0.15y (replace x as no. of muffins & y as no. of carrot sticks)
T= (0.35×210) + (0.15×120)
T= 73.5 + 18
T= 91.5
Which type of worker tends to earn the highest pay in comparison to the others?
Answers
Answer:
A hired on worker? Or a determined worker?
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
It just is
Use the greatest common factor and the distributive property to write equivalent expressions in factored form.
13ab + 15ab =
Answers
Answer:
ab(28) or 28ab
Step-by-step explanation:
13ab + 15ab = 28ab
Answer:
ab(28) or 28ab
Step-by-step explanation:
Identify the parent function for the function g(x)=x-3 from its function rule. Then graph g and identify what
transformation of the parent function it represents.
O quadratic, translation down 3 units
O linear, translation up 3 units
O quadratic, translation up 3 units
O linear, translation down 3 units
Answers
Transformation of the parent function it represents, linear translation down 3 units.
What are the steps to determining a graph's parent function and transformation?By modifying the value of x (for example, y(x) = x + 2) or by multiplying x by a constant (for example, y(x) = 3x), you can examine the graphs of linear functions. Do not forget that y(x) = x is the linear parent function. Its most fundamental and straightforward form is this.
The graph of y = f (x - h) is translated h units to the RIGHT of the graph of the parent function if h > 0, and it is translated h units to the LEFT if h 0.
as in f(x) = ( x – 3)
The graph of y=f(x-h) is a translation of |h| units to the LEFT of the graph of the parent function if h 0; otherwise, it is a straight line.
Example: f(x) = (x + 4).
To learn more about Transformation refer to:
https://brainly.com/question/4289712
#SPJ1
PLS HELP ME
Given that the universal set.
U = {X : 30 ≤ X ≤ 40. X is an even number}.
P = {X : X is a multiple of 4}
and Q = {X : X is a number such that the sum of its digits is an odd number}.
find n(P∩Q')
A. 1
B. 2
C. 3
D. None of the above
Answers
Given that
U = {X : 30 ≤ X ≤ 40. X is an even number}.
so Mathematically
U = {30,32,34,36,38 40}.
P = {X : X is a multiple of 4}
P = { 4,8,12,16,20,24,28,32,36,40,44,........}
and Q = {X : X is a number such that the sum of its digits is an odd number}.
Q = {12,14,16,18,21,23,25,27,29,30,32,34,36,38,41,43,45,..........}.
(Q')= U-Q ={40}
(P∩Q')= {40}
n(P∩Q')= 1
(Q') is Q complement which means a set containing those elements of the universal set which are not element of the set Q.
(P∩Q') is a set containing those elements of set P and Q complement which are common to both sets.
n(P∩Q') denotes the number of elements in a set containing those elements of set P and Q complement which are common to both sets which has only 1 element which is 40.
So the best answer is part A = 1.
https://brainly.com/question/11439790
https://brainly.com/question/13729460
A swimmer wins the 50-yard freestyle with a time of 24.76 seconds. Find the swimmer’s average speed to the nearest hundredth of a yard per second.
Answers
Answer:
2.02 yards per second
Step-by-step explanation:
Distance/time= Average speed or speed
50yard/ 24.76sec= 2.01938 yards per second ~ 2.02 yards per second
..............................................................
Answers
Answer:
form x = 6 ± √14
Step-by-step explanation:
I used mw so I'm sorry if worng
the probability of guessing right on a 4-option multiple choice item is 1/4 or 0.25. a quiz contains 10 questions. find the probability of getting more than 5 right.
Answers
The probability of getting more than 5 questions right in the quiz is
0.00011445.
Given, the probability of guessing right on a 4-option multiple choice item is 1/4 or 0.25.
A quiz contains 10 questions.
we have to find the probability of getting more than 5 right.
Required Probability = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
Required Probability = (1/4)^6(3/4)^4 + (1/4)^7(3/4)^3 + (1/4)^8(3/4)^2 + (1/4)^9(3/4)^1 + (1/4)^10
Required Probability = 0.000077 + 0.000025 + 0.0000086 + 0.0000029 + 0.00000095
Required Probability = 0.00011445
Hence, the probability of getting more than 5 questions right in the quiz is
0.00011445.
Learn more about Probability here https://brainly.com/question/27745646
#SPJ4
i have no idea about how to do it.
Answers
The blanks are filled as follows
Step one
Equation 2x + y = 18 Isolate y,
y = 18 - 2x
How to complete the stepsStep Two:
Equation 8x - y = 22, Plug in for y
8x - (18 - 2x) = 22
Step Three: Solve for x by isolating it
8x - (18 - 2x) = 22
8x - 18 + 2x = 22
8x + 2x = 22 + 18
10x = 40
x = 4
Step Four: Plug what x equals into your answer for step one and solve
y = 18 - 2x
y = 18 - 2(4)
y = 18 - 8
y = 10
So the solution to the system of equations is x = 40 and y = 10
Learn more about system of equations at
https://brainly.com/question/25976025
#SPJ1
6. Chasing Angles: Find the measure of all the missing interior and exterior angles in this figure using linear pairs, vertical angles, and triangle angle sum.
Answers
The missing angles of triangles are - 30°, 50°, 40°.
What is the angle - sum property of the triangle?
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the internal angles of a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
There are 5 triangles in the given diagram,
We will see them anti - clock wise.
All the triangles are right - angled triangle.
The measures of 1 triangle are -
90°, Let the other 2 angles be x,y
The measures of the 2nd triangle are -
Given,
60°, 90°
Using angle sum property,
The measure of third angle = 180°
= 60 + 90 + third angle = 180
third angle = 180 - 150
= 30.
The measures of 3rd triangle are -
Given,
40°, 90°
Using angle sum property,
The measure of third angle = 180°
= 40 + 90 + third angle = 180
third angle = 180 - 130
= 50.
The measures of 4th triangle are -
50°, 90°
Using angle sum property,
The measure of third angle = 180°
= 50 + 90 + third angle = 180
third angle = 180 - 140
= 40.
To learn more about triangles from given link
https://brainly.com/question/1058720
#SPJ1
Mr. Porter's private plane takes 1 1/2 hours to travel from Greenlawn to Richville and back. How many trips can he make in 7 1/2 hours?
Answers
Answer:
She can make 5 trips.
Step-by-step explanation:
A market buys mixed candy at $15 per pound. They want to make a 30% profit on each pound. How much should they charge customers per pound? Explain your answer
Answers
Answer:
$15 * .30 = 30 % of 15 add that to the 15 and that includes the 30% profit
$19.50
Step-by-step explanation:
Mia and her family went to dinner, and the bill, including tax, came to $54.65. Mia suggested giving the server a gratuity of about 20 percent of the bill. If they give a gratuity of 20 percent, what would be the tip rounded to the nearest dollar? If they give a gratuity of 20 percent, rounded to the nearest dollar, what is the total cost of the dinner, including the tip?
Answers
Answer:
\(\huge\boxed{\text{Tip: } \$ 11}\)
\(\huge\boxed{\text{Total Cost: } \$ 65.65}\)
Step-by-step explanation:
In order to find the percent of something, we need to convert the percent into a decimal.
50% of x can be represented as \(0.5x\), as 50% is half of x and so is 0.5.
This means that 20% of 54.65 will be \(54.65\cdot 0.2\), which is $10.93.
Rounding to the nearest dollar gets us $11.
To find the total cost, we can add $11 (the tip) to the previous cost of $54.65.
\(54.65+11=65.65\)
Therefore, the total cost of the dinner would be $65.65
Hope this helped!
Answer:
Mia and her family went to dinner, and the bill, including tax, came to $54.65. Mia suggested giving the server a gratuity of about 20 percent of the bill.
If they give a gratuity of 20 percent, what would be the tip rounded to the nearest dollar?
✔ $11
If they give a gratuity of 20 percent, rounded to the nearest dollar, what is the total cost of the dinner, including the tip?
✔ $65.65
Step-by-step explanation:
a measure of variability of the sample means xbar in repeated samples of n observations randomly selected from a given population is
Answers
The correct answer is B i.e. Standard Error of the Mean (SE) = σ / √(n)
The measure of the variability of the sample means, also known as the standard error of the mean, can be calculated using the formula:
Standard Error of the Mean (SE) = σ / √(n)
sigma is the population standard deviation,
n is the sample size.
The standard error of the mean represents the variability or dispersion of the sample means obtained from repeated samples of size n from a population. It indicates how much the sample means are likely to differ from the true population mean.
The smaller the standard error of the mean, the less variability is expected among the sample means, indicating a more precise estimate of the population mean.
Therefore, the correct answer is B i.e. Standard Error of the Mean (SE) = σ / √(n)
Learn more about standard error of the mean here
https://brainly.com/question/30765693
#SPJ4
Given question is incomplete, the complete question is below
A measure of variability of the sample means xbar in repeated samples of n observations randomly selected from a given population is
a. s
b. σ/√(n)
c. s/√(n)
d. σ
-2y - 7y + 8y + y - 7y
Answers
Answer:
-7y
Step-by-step explanation:
-2y-7y=
-9y+8y=
-y+y=
0-7y=
-7y
-2y -7y + 8y +y - 7y
Solution : -7y
which number describes the average amount of error in the regression line's predicted rotten tomato ratings?
Answers
The average amount of error in the regression line's predicted rotten tomato ratings is typically represented by the root mean squared error (RMSE).
The average amount of error in the regression line's predicted rotten tomato ratings is typically described by the root mean squared error (RMSE). RMSE is a common metric used to evaluate the accuracy of a regression model's predictions. It represents the square root of the average squared differences between the predicted values and the actual values.
By calculating the RMSE for the regression line's predicted rotten tomato ratings, you can determine the average amount of error in those predictions.
To know more about root mean squared error, refer here:
https://brainly.com/question/29662026
#SPJ4
Anyone help me please
Answers
Answer:
2,799 square cm
Step-by-step explanation:
Volume of cone: (1/3)π(9^2)(40)=1,080π
Volume of cylinder: π(3^2)(21)=189π
1,080π - 189π = 891π = 2799.2 square cm
using the following data, state the errors in the box-and-whisker plot. 33, 27, 6, 34, 31, 59, 26, 1, 30
Answers
In order to find out the errors made in the data plot, we have to determine what the five-number summary of the data set that should be displayed by the box plot should be.
How to illustrate the informationFirstly, order the data set given:
1, 6, 26, 27, 30, 31, 33, 34, 59
The five-number summary are:
1. Min value = 1
2. Max value = 59
3. Median = 30
1, 6, 26, 27, (30),31, 33, 34, 59
4. Q1 = (26+6) ÷ 2 = 16
1, [6, 26], 27, (30), 31, 33, 34, 59
5. Q3 = (33+34) ÷ 2 = 33.5
1, 6, 26, 27, (30), 31, [33, 34], 59
The errors in the box and whisker plot are:
1. The min value was displayed as 0 instead of 1.
2. The first quartile (Q1) was displayed as 10 instead of 16
3. The third Quartile (Q3) was displayed as 35 instead of 33.5
4. The max value was displayed as 60 instead of 59.
Learn more about data on:
https://brainly.com/question/19243813
#SPJ1
PLEASE HELP
Consider these functions:
f(x) = ½x²+5x
g(x) = x²+2
What is the value of f(g(-2))?
Answers
Answer:
-12 I think so I don't know pls check it once sorry
Please help, will give brainliest
Tom wants to order tickets online so that he and three of his friends can go to a waterpark. The cost of the tickets is $16.00 per person. There is also a $2.50 one-time service fee for ordering the tickets online. Write an expression in terms of n that represents the cost for ordering n tickets online.
Answers
Answer:
(16*n)+2.5=c
Step-by-step explanation:
c=cost
n=amount of friends.
Have a great weekend!! :)
I need help please and thank you
Answers
Answer: y-intercept is 6 and x intercept is 2
Step-by-step explanation:
The slope formula explains it all. I have nothing to explain.
Two supplementary angles. One angle is 35 more than the second angle, find the measure of the second angle. The measure of the second angle is
degrees
Answers
Answer: 72.5 degrees
Step-by-step explanation: Call smaller angle x, so larger angle is x+35, so 2x+35=180, subtract 35 from both sides, 2x=145, so x=72.5! I hope this helps you