Answers
The value of matrix A is [tex]A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right][/tex]
How to determine the matrix A?The given parameters are:
[tex]\lambda_1 = 4[/tex] at [tex]v_1 = \left[\begin{array}{c}1&1\end{array}\right][/tex]
[tex]\lambda_2 = 8[/tex] at [tex]v_2 = \left[\begin{array}{c}1&2\end{array}\right][/tex]
The matrix A is calculated using:
A = S ∧ S⁻¹
Where:
[tex]S = \left[\begin{array}{cc}v_1&v_2\end{array}\right][/tex]
[tex]\lambda = \left[\begin{array}{cc}\lambda_1&0\\0&\lambda_2\end{array}\right][/tex]
[tex]\lambda =\left[\begin{array}{cc}4&0\\0&8\end{array}\right][/tex]
Next, we have:
[tex]S = \left[\begin{array}{cc}v_1&v_2\end{array}\right][/tex]
This gives
[tex]S =\left[\begin{array}{cc}1&1\\1&2\end{array}\right][/tex]
Calculate the determinant of S
|S| = 1 * 2 - 1 * 1
|S| = 1
So, the inverse of S is:
[tex]S^{-1} = \frac{1}{1} * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\\[/tex]
Evaluate
[tex]S^{-1} = \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\\[/tex]
Recall that:
A = S ∧ S⁻¹
So, we have:
[tex]A =\left[\begin{array}{cc}1&1\\1&2\end{array}\right] * \left[\begin{array}{cc}4&0\\0&8\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right][/tex]
Multiply the first two matrices
[tex]A =\left[\begin{array}{cc}1 * 4 + 1 * 0&1 * 0 + 1 * 8\\1 * 4 + 2 * 0&1 * 0 + 2 * 8\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right][/tex]
Evaluate
[tex]A =\left[\begin{array}{cc}4&8\\4&16\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right][/tex]
Evaluate the product
[tex]A =\left[\begin{array}{cc}4*2+8*-1&4 * -1 + 8 * 1\\4 * 2 + 16 * -1&4 * -1 + 16 * 1\end{array}\right][/tex]
Evaluate
[tex]A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right][/tex]
Hence, the value of matrix A is [tex]A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right][/tex]
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Related Questions
What are the values for the coefficients and constant term of 2 + 3x² - 5x?
a=
B=
C=
Answers
Answer:
a=3
b=-5
c=2
Step-by-step explanation:
Because first arrange them in decreasing order by their variables powers like this 3x²-5x+2 after that take the the coefficients
Sequences
47, 40, 33,
,19,
,5
400, 299,
,97,-4,
Answers
Answer:
1- Ans; 47 , 40 , 33 , 26 , 19 , 12 , 5
2- Ans; 400 , 299 , 198 , 97 , - 4 , - 105
Step-by-step explanation:
[tex]47 - 40 = 7 \\ 40 - 33 = 7 \\ 5 + 7 = 12 \\ 12 + 7 = 19 \\ 19 + 7 = 26 \\ 26 + 7 = 33[/tex]
[tex]400 - 299 = 101 \\ 299 - 101 = 198 \\ 198 - 101 = 97 \\ 97 - 101 = - 4 \\ - 4 - 101 = - 105[/tex]
Use the drop-down menus to identify the method used to collect data for each scenario.
While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.
Noah researched statistics online about the percentage of babies born with brown eyes.
Lara knew that she had a 25% chance of winning a contest, so she flipped two coins repeatedly to determine how many times two heads occurred.
Answers
The method used to collect data for each scenario is observational study , secondary data , simulation .
What is Data Collection ?The accumulation of data to perform research , experiment or any other study is called data collection
It is done by different methods.
While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there. :
Because all feasible channels and techniques were investigated in order to get accurate data, this study is known as an observational study.
Noah conducted research to learn the data pertaining to the proportion of newborns having brown eyes. Since he didn't perform this directly, it is referred to as secondary data.
Lara repeatedly flipped two coins to see how many times two heads appeared because she knew she had a 25% chance of winning a contest. This is an example of simulation because she wanted to see if she would come up with the same outcome.
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Answer:
A. observational study
B. published data
C. study
Step-by-step explanation:
Did the question in edge 2022
which is the best approximation for the solution of the system of equations y=-2/5x+ 1 , y=3x-2
Answers
Answer:
https://tex.z-dn.net/?f=y%20%3D%20-%5Cdfrac%2025%20x%20%2B1~~~......(i)%5C%5C%5C%5C%5C%5Cy%20%3D%203x-2~~~......(ii)%5C%5C%5C%5C%5C%5C%5Ctext%7BSubstitute%7D~%20y%20%3D%203x%20-2~%20%5Ctext%7Bin%20equation%20(i)%3A%7D%5C%5C%5C%5C%5C%5C3x%20-2%20%3D%20-%5Cdfrac%2025%20x%20%2B1%5C%5C%5C%5C%5Cimplies%203x%20%2B%20%5Cdfrac%7B2x%7D%7B5%7D%20%3D%201%20%2B2%5C%5C%5C%5C%5Cimplies%20%5Cdfrac%7B17x%7D%7B5%7D%20%3D%203%5C%5C%5C%5C%5Cimplies%2017x%20%3D%2015%5C%5C%5C%5C%5Cimplies%20x%20%3D%20%5Cdfrac%7B15%7D%7B17%7D%5C%5C%5C%5C%5C%5C%5Ctext%7BSubstitute%7D~%20x%20%3D%20%5Cdfrac%7B15%7D%7B17%7D~%20%5Ctext%7Bin%20equation%20(ii)%3A%7D%5C%5C%5C%5C%5C%5Cy%20%3D%203%5Ccdot%20%5Cdfrac%7B15%7D%7B17%7D%20-2%20%3D%20%5Cdfrac%7B45%7D%7B17%7D%20-%202%20%3D%5Cdfrac%7B11%7D%7B17%7D%5C%5C%5C%5C%5C%5C%5Ctext%7BHence%2C%7D~~%20(x%2Cy)%3D%20%5Cleft(%5Cdfrac%7B15%7D%7B17%7D%2C%20%5Cdfrac%7B11%7D%7B17%7D%20%5Cright)
Step-by-step explanation: go here
18) Solve for x. (-2x-6° X )
Answers
Answer:
-8x
Step-by-step explanation:
Subtract 6°x from -2x.
Answer: -8
Step-by-step explanation:
Hey Sydney made three times as much as Cassie made. If the difference in their pay was $74 how much money did each make
Answers
Answer: Sydney made $111, Cassie made $37
Step-by-step explanation:
If Cassie's money is x, then Sydney is 3x. 3x - x = $74, so x = $37.
NO LINKS!!!! Find the equation of the circle below
Answers
Centre(-3,2)
diameter=6 units [0-(-6)=6units ]
radius=6/2=3
Equation of circle
[tex]\\ \rm\Rrightarrow (x-h)^2+(y-k)^2=r^2[/tex]
For centre(h,k) and radius rSo our equation
[tex]\\ \rm\Rrightarrow (x+3)^2+(y-2)^2=3^2[/tex]
[tex]\\ \rm\Rrightarrow (x+3)^2+(y-2)^2=9[/tex]
Answer:
[tex](x+3)^2+(y-2)^2=9[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusFrom inspection of the diagram, the center of the circle appears to be at point (-3, 2), although this is not very clear. Therefore, a = -3 and b = 2.
Substitute these values into the general form of the equation of a circle:
[tex]\implies (x-(-3))^2+(y-2)^2=r^2[/tex]
[tex]\implies (x+3)^2+(y-2)^2=r^2[/tex]
Again, from inspection of the diagram, the maximum vertical point of the circle appears to be at y = 5. Therefore, to calculate the radius, subtract the y-value of the center point from the y-value of the maximum vertical point:
⇒ radius (r) = 5 - 2 = 3
Substitute the found value of r into the equation:
[tex]\implies (x+3)^2+(y-2)^2=3^2[/tex]
Therefore, the final equation of the given circle is:
[tex]\implies (x+3)^2+(y-2)^2=9[/tex]
Find the centre of the circle
x^2 + y^2 + 4x - 6y = 12
Answers
Answer:
centre = (- 2, 3 )
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² + 4x - 6y = 12 ( collect x/ y terms )
x² + 4x + y² - 6y = 12
using the method of completing the square
add ( half the coefficient of the x/ y terms)² to both sides
x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = 12 + 4 + 9
(x + 2)² + (y - 3)² = 25 ← in standard form
with centre (- 2, 3 ) and r = [tex]\sqrt{25}[/tex] = 5
Please help me with the question
Answers
Answer:
marke brainleast I don't know please helpe
Area of composite figures worksheet. How do you solve it. Step-By-Step
Answers
Answer:
The area of the combined figure is 49.8 cm
Step-by-step explanation:
We first see that there is a semicircle, which represents half of a full circle. We must find the area of such an entire circle, so we have to divide its entire area by two since only half of such an area is represented:
The area of a circle is given by:
Ac = π * r²In this case, the radius is given by half the base of the rectangle.
R = 5/2 = 2.5 cmSo much so that the radius of that radius is 2.5cm, we now consider the pi to be a constant measure of 3.14
Ac = 3.14 * (2.5)²Ac = 3.14 * 6.25 cmAc = 19.625 cmRemember that we are only representing half of the circle, therefore, we must divide the area by two:
Ac/2 = 19.625 / 2 = 9.8 ( aproximate )Now we proceed to find the area of the rectangle, whose height is 8 cm, and base equal to 5 cm.
Since the area of a rectangle is given by multiplying the base times the height, we have:
Ar = B * H Ar = 5 cm * 8 cmAr = 40 cmIn this case the figure is complete, there is no need to divide.
To find the full area, we must add the area of the half circle more the area of the newly found rectangle:
Overall area = 9.8 cm + 40 cm = 49.8 cmBy so:
The area of the combined figure is 49.8 cma school logo is in the form of the letter c which is surrounded by a circle. suppose the circle is centred at (0,0) and suppose the point (-2,4) lies on the circle.
write an equation of the circle.
Answers
Solve the the equation tan(x+pi/3) = sqrt 3/3 over the interval [0, 2].
Answers
Rewrite the right side as √3/3 = 1/√3, and recall that tan(x) = 1/√3 when x = π/6. Then since tan is π-periodic, taking the inverse tan of both sides gives
[tex]\tan\left(x + \dfrac\pi3\right) = \dfrac1{\sqrt3} \implies \tan^{-1}\left(\tan\left(x + \dfrac\pi3\right)\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) + n\pi[/tex]
[tex]\implies x + \dfrac\pi3 = \dfrac\pi6 + n\pi[/tex]
where n is any integer. Solving for x, we get
[tex]x = -\dfrac\pi6 + n\pi[/tex]
and the solutions in the interval [0, 2π] are x = 5π/6 and x = 11π/6 (for n = 1 and n = 2).
only answer if you know! no spams :)
Answers
Answer:
0%: Impossible
25%: Unlikely
50%: Equally likely
75%: Likely
100%: Certain
Answer:
See below ~
Step-by-step explanation:
The correct percentages matched with their likelihoods are :
⇒ 0% → c. Impossible
⇒ 25% → b. Unlikely
⇒ 50% → a. Equally likely
⇒ 75% → e. Likely
⇒ 100% → d. Certain
PLSS HELPPP!! Given vector u equals 15 times open angled bracket cos 45 degrees comma sin 45 degrees close angle bracket comma what are the magnitude and direction of −5u?
75; 225°
75; 135°
−75; −135°
−75; 45°
Answers
Answer:
-75;45
Step-by-step explanation:
To start, it cant be a or b since we are multiplying a positive U times -5, therefore making it negative
-5(15)
-75
then, to find the answer u need to find the right formula
tan(v2/v1) or tan^-1(v2/v1)
for this it is the inverse tangent (tan^-1)
so you have to plug the values in
=tan^-1(sin45/cos45)
which then would equal 45
if two similar polygons have corresponding sides that measure 6 and 8 inches respectively and the are of the smaller one si 36 sq. inches what would be the area of hte larger polygon.
Answers
Answer:
48 sq inches
Step-by-step explanation:
The ratio of the smaller polygon to the larger one is 6:8, which can be simplified to 3:4.
36:48 is equivalent to 3:4 (both sides multiplied by 12)
C. Part A
Let BE = x² - 48 and let DE = 2x. What are the lengths of BE and DE?
Justify your answer.
Enter your answer and your justification in the space provided.
Answers
Answer:
A. BE = DE = 16
B. rectangle
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. The diagonals of a rectangle are the same length.
__
A. diagonal BDPoint E is the midpoint of diagonal BD of the parallelogram, so we have ...
BE = DE
x² -48 = 2x
x² -2x -48 = 0 . . . . . put in standard form
(x -8)(x +6) = 0 . . . . factor
x = 8 or -6 . . . . . . values that satisfy the equation
We know the lengths have positive values, so the only value of x that works in this problem is x=8. Then the halves of diagonal BD are ...
BE = DE = 2x = 2(8)
BE = DE = 16
__
B. comparison of diagonalsWe know also that E is the midpoint of diagonal AC, so its length is ...
AC = 2×AE = 2×16 = 32
From the above, we know that ...
BD = BE +DE = 16 +16 = 32
The two diagonals are the same length, so the figure is a rectangle.
_____
Additional comment
If we knew something about the side lengths or the angle at which the diagonals cross, we could further classify the figure. Congruent adjacent sides, or perpendicular diagonals would mean this rectangle is a square.
Use a unit multiplier to convert
$15.00 per hour to dollars per
minute. Show your work.
Answers
Solve for xx. Round to the nearest tenth of a degree, if necessary.
Answers
Answer:
56.6 °
Step-by-step explanation:
For a RIGHT triangle cos (x ) = adjacent leg / hypotenuse
cos (x) = 4.4 / 8
arc cos (4.4/8) = 56.63 ° = ~ 56.6°
if a pupil has a score of 60% how many marks out of 150 did he obtain
Answers
Answer:
90
Step-by-step explanation:
60 % = .60 in decimal
.60 (150) = 90
p
Line m has a y-intercept of cand a slope of 9, where p>0, q> 0, and p + q.
What is the slope of a line that is perpendicular to line m?
-q/p
P/q
q/p
-p/q
Answers
So slope of the line m is 9
We know perpendicular lines have slopes negative reciprocal to each other and their product of slopes is -1
9m2=-1m2=-1/9If slope of m is p/q then slope of perpendicular line is -q/p and vice versa
Answer:
[tex]-\dfrac{q}{p}[/tex]
Step-by-step explanation:
Slope-intercept form of a Linear Equation:
[tex]y = mx + b[/tex]
where:
m is the slopeb is the y-interceptIf line m has a y-intercept of c and a slope of p/q, then:
[tex]\textsf{Equation of line m}: \quad y = \dfrac{p}{q}x + c[/tex]
If two lines are perpendicular to each other, the product of their slopes will be -1.
Let a = slope of the line perpendicular to line m.
[tex]\implies a \times \dfrac{p}{q}=-1[/tex]
[tex]\implies a=-\dfrac{q}{p}[/tex]
Therefore, the slope of the a line that is perpendicular to line m is:
[tex]-\dfrac{q}{p}[/tex]
Which relationships could have a negative correlation? Select three options. number of hours worked and free time speed of a car and minimum stopping distance the speed of a train and the length of time to reach the destination adult’s head circumference and age a tadpole’s age and the length of it’s tail
Answers
Answer:
hope you can understand
Answer
- number of hours worked and free time
- a tadpole’s age and the length of its tail
- the speed of a train and the length of time to reach the destination
Step-by-step explanation:
The more hours worked, the less free time they will have
The older a tadpole gets, the shorter its tail gets because it is turning into a frog
The faster a train. the shorter time it takes to get to a place
Question 5 of 10
Which of the following describes the non-rigid transformation in the function
shown below?
y+ 5 = − 2(x − 1)²2
-
OA. The graph is stretched vertically by a factor of 2.
OB. The graph is shifted 5 units down.
OC. The graph is reflected across the x-axis.
OD. The graph is shifted 1 unit right.
Answers
Answer:
the answer is B. because I had the same problem
The lines of the equations are parallel, perpendicular, or neither. y = 2x + 3 y = 2x 1)parallel
2)perpendicular
3)neither
Answers
Answer:
Parallel
Step-by-step explanation:
Parallel lines:
The parallel lines have same slope.
y = 2x + 3
Compare with slope y-intercept form of the line: y = mx +b
m is slope and b is the y-intercept.
slope of this line = 2
y = 2x
Slope = 2
These lines have same slope. So, they are parallel.
the diameter of a circle is 14 inches.Fund the circumference and area.Use 22/7 for pie
Answers
Answer:
[tex]area = 154 {in}^{2} \\ circumference = 44inches[/tex]
Step-by-step explanation:
The solution is in the image
If the nurse to patient ratio is 3:15, how many nurses would you expect to see in a unit with 37 patients?
Answers
in order to find how many nurses would care for 37 patients, we can divide by 5.
37/5 = 7.4 nurses.
however, we cannot have .4 of a nurse, so you can either say 7 nurses or 8 nurses, but 7.4 rounds down to 7.
Which of the following rational functions is graphed below
Answers
The correct answer is option A which is [tex]f(x) =\dfrac{1}{(x+3)(x+5)}[/tex] this expression is showing the graph given in the question.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In the given question we can see the graph. The function [tex]f(x) =\dfrac{1}{(x+3)(x+5)}[/tex] is showing the graph given in the question.
As we put the values of x in the function we will get this type of symmetric graph shown. I also attached the graph I made on the graphing tool in the answer below.
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PLSSS HELPP ME ASAPP!!!!
Answers
Answer:
<HLI = 123
Step-by-step explanation:
Angles <KLG, <KLJ, and JLI are on a straight line and that so their sum is 180
KLJ is a right angle so its value is 90
90 + 5x - 7 + 10x + 7 = 180 add like terms
90 + 15x = 180 subtract 90 from both sides
15x = 90 divide both sides by 15
x = 6
angles <JLI and <HLI are also on a straight line and supplementary so their sum is also equal to 180
the measure of angle <JLI:
10*6 + 7 = 53 (we found x = 6 earlier)
53 + <HLI = 180 subtract 53 from both sides
<HLI = 123
3.5x-10>-3and8x-9<39
Answers
The solutions to the given inequalities are x > 3.5 and x < 6 respectively
Linear inequalitiesFrom the question, we are to determine values of x that satisfy the given inequalities
The given inequalities are
3.5x-10 > -3 and 8x-9 < 39
First,
3.5x - 10 > -3
Add 10 to both sides
3.5x - 10 + 10 > -3 + 10
3.5x > 7
∴ x > 7/3.5
x > 3.5
For 8x-9 < 39
Add 9 to both sides
8x -9 +9 < 39 +9
8x < 48
x < 48/8
x < 6
Hence, the solutions to the given inequalities are x > 3.5 and x < 6 respectively
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Approximate the population mean and standard deviation of age for males.
Age Lower Limit Upper Limit Males Females
0-9 0 9 11 9
10-19 10 19 10 9
20-29 20 29 12 13
30-39 30 39 16 16
40-49 40 49 20 24
50-59 50 59 25 24
60-69 60 69 17 18
70-79 70 79 13 12
Answers
The population mean and standard deviation of age for males are 43.21 and 20.83, respectively
How to determine the population mean and the standard deviation?The frequency table is given as:
Age Lower Limit Upper Limit Males Females
0-9 0 9 11 9
10-19 10 19 10 9
20-29 20 29 12 13
30-39 30 39 16 16
40-49 40 49 20 24
50-59 50 59 25 24
60-69 60 69 17 18
70-79 70 79 13 12
Rewrite the frequency table to show the class midpoints and the male frequency, only.
Midpoint (x) Male Frequency (f)
4.5 11
14.5 10
24.5 12
34.5 16
44.5 20
54.5 25
64.5 17
74.5 13
The population mean is then calculated using:
[tex]\mu =\frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\mu = \frac{11 * 4.5 + 10 * 14.5 + 12 * 24.5 + 16 * 34.5 + 20 * 44.5 + 25* 54.5 + 17 * 64.5 + 13 * 74.5}{11 + 10 + 12 + 16 + 20 + 25 + 17 + 13}[/tex]
Evaluate
[tex]\mu = 43.21[/tex]
The standard deviation is calculated using:
[tex]\sigma = \sqrt{\frac{\sum f(x - \mu)^2}{\sum f}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{11 * (4.5 -43.21)^2+....................+ 13 * (74.5-43.21)^2}{11 + 10 + 12 + 16 + 20 + 25 + 17 + 13}}[/tex]
Evaluate the expression
[tex]\sigma = 20.83[/tex]
Hence, the population mean and standard deviation of age for males are 43.21 and 20.83, respectively
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During a school event, there were 8 times as many pupils as teachers and there were three times as many boys as girls. There were 70 fewer teachers than boys. How many people were there at the school event?
Answers
Students = S
boys = B
Teachers = T
So....
S = 8T
Boys = 3G
T = B - 70
Since there is 8x students than teachers, I did Boys = 6x and girls = 2x
I'm going to use this next: S = 8T
8x = 8(B -70)
8x = 8(6x - 70)
8x = 4x - 560
x = 14
We know there is 8x students, so there are 112 students and we know that there is 1/8 of teachers, so there are 14 teachers.
Answer = 126.
