The matrix A eigenvalues and eigenvectors are as follows:
Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]
Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]
Using the equation (A - λI)v = 0, where is an eigenvalue of A, I am the 2x2 identity matrix, and v is the associated eigenvector, we can determine the eigenvalues and eigenvectors of the matrix A = [[5, 4], [1, 2]].
First, we calculate the (A - λI) matrix's determinant:
det(A - λI) = |5-λ 4| = (5-λ)(2-λ) - 4 = λ^2 - 7λ + 6
|1 2-λ|
We obtain the characteristic equation by setting the determinant to zero:
λ^2 - 7λ + 6 = 0
We obtain two eigenvalues after solving for λ :
λ = 1 and λ = 6
Next, For each eigenvalue, we identify the appropriate eigenvectors:
For λ = 1, We solve the system of linear equations represented by the equation(A - λI)v = 0:
4v1 + 4v2 = 0
v1 + v2 = 0
The second equation is evidently as straightforward as v1 = -v2. When we enter this into the initial equation, we get:
4v2 - 4v2 = 0
Thus, the eigenvector for λ = 1 is v = [1, -1].
For λ = 6, We solve the system of linear equations represented by the equation(A - λI)v = 0:
-v1 + 4v2 = 0
-v1 + 4v2 = 0
v1 - 4v2 = 0
It is evident that the first equation is just v1 = 4v2. When we enter this into the second equation, we get:
4v2 - 4v2 = 0
Thus, the eigenvector for λ = 6 is v = [4, 1].
Therefore, The matrix A eigenvalues and eigenvectors are as follows:
Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]
Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]
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line 1 is y=2x line 2 is y=2x-3 how many solutions are there and whats the coordinates.
Answer:
no solutions
Step-by-step explanation:
y = 2x → (1)
y = 2x - 3 → (2)
since both equations express y in terms of . equate the right sides to find any solutions.
2x - 3 = 2x ( add 3 to both sides )
2x = 2x + 3 ( subtract 2x from both sides )
0 = 3 ← false statement
this indicates there are no solutions
Mathematics Grade 11 Capricom Sou SECTION A Part 1 Solve for x in the following equation by using exponential rules 1. 27**** = 3³x² x 9
The solution to the expression is x = 1/9
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
27**** = 3³x² x 9
Express properly
27 = 3³x² * 9
We can start solving this equation by rearranging it to isolate the variable x:
27 = 243x
Now we divide both sides by 243 to find x
x = 27/243
Evaluate
x = 1/9
Hence, the solution is 1/9
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what kind of slope is x = -5
Answer:
undefined slope
Step-by-step explanation:
The graph of the equation x = -5 is a vertical line That passes through point (-5, 0).
The slope of a vertical line is undefined.
5. Name the angle that is supplementary to COD.
A
F
OZCOA
O ZBOC
OLCOB
O ZBOA
B
O
۶,
D
(1 point)
Answer:
Example 2:
Find m∠P and m∠Q
if ∠P and ∠Q
are supplementary, m∠P=2x+15
, and m∠Q=5x−38
.
The sum of the measures of two supplementary angles is 180°
.
So, m∠P+m∠Q=180°
Substitute 2x+15
for m∠P
and 5x−38
for m∠Q
.
2x+15+5x−38=180°
Combine the like terms. We get:
7x−23=180°
Add 23
to both the sides. We get:
7x=203°
Divide both the sides by 7
.
7x7=203°7
Simplify.
x=29°
To find m∠P
, substitute 29
for x
in 2x+15
.
2(29)+15=58+15
Simplify.
58+15=73
So, m∠P=73°
.
To find m∠Q
, substitute 29
for x
in 5x−38
.
5(29)−38=145−38
Simplify.
145−38=107
So, m∠Q=107°
.Example 2:
Find m∠P and m∠Q
if ∠P and ∠Q
are supplementary, m∠P=2x+15
, and m∠Q=5x−38
.
The sum of the measures of two supplementary angles is 180°
.
So, m∠P+m∠Q=180°
Substitute 2x+15
for m∠P
and 5x−38
for m∠Q
.
2x+15+5x−38=180°
Combine the like terms. We get:
7x−23=180°
Add 23
to both the sides. We get:
7x=203°
Divide both the sides by 7
.
7x7=203°7
Simplify.
x=29°
To find m∠P
, substitute 29
for x
in 2x+15
.
2(29)+15=58+15
Simplify.
58+15=73
So, m∠P=73°
.
To find m∠Q
, substitute 29
for x
in 5x−38
.
5(29)−38=145−38
Simplify.
145−38=107
So, m∠Q=107°
.
3 pounds of apples cost 5.52 how much for 10 pounds?
Answer:
OUT OF BUSINESS
Step-by-step explanation:
you cant afford it on food stamps my guy
In the figure below, points E, G, A, B, and C lie in plane X.
Points D and F do not lie in plane X.
For each part below, fill in the blanks to write a true statement.
Following are the given complete statements:
(a) Another name for plane X is plane EABC.
(b) F, D, and C are distinct points that are collinear.
(c) A, B, C and G are distinct points that are coplanar.
What is plane ?A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is a mathematical concept used in geometry and is often represented as a flat sheet or a graph on a coordinate system. In the real world, a plane can be thought of as a flat surface such as a tabletop, a piece of paper or a wall.
According to the given information :(a) Another name for plane X is plane EABC.
(b) F, D, and C are distinct points that are collinear.
(c) A, B, C and G are distinct points that are coplanar.
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True or False? These figures are similar
True. Because they have comparable angles, the offered figures are comparable figures.
What are similar figures?Similar figures are described as two shapes that share the same shape but differ in size. For instance, similar objects are depicted but are not consistent in different-sized images of a person, such as passport size, stamp size, etc. In geometry, two comparable shapes with different side lengths or sizes are those whose dimensions are equal or have a common ratio. Examples of these shapes are similar triangles, similar rectangles, and similar squares. Scale factor is the name given to the common ratio. The matching angles are also of equal measure.
If two figures are similar, then they are represented by the symbol ‘∼’. Let us say there are two triangles, ABC and PQR, which are similar, then they are represented as;
∆ABC ~ ∆ PQR
Now if the two triangles are similar to each then their corresponding sides should be in proportion. Hence,
AB/PQ = BC/QR = AC/PR
∠A = ∠P, ∠B = ∠Q, ∠C = ∠R
Since, we can see that the angles in both the given figures are exactly the same. Thus, the given figures are similar figures.
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a negative divided by a positive become?
When a negative number is divided by a positive number, the result is always negative.
Let's use the example (-6) / 2 again. We can write this expression as:
(-6) / 2 = (-1) * 6 / 2
We can then simplify the expression on the right-hand side by multiplying -1 and 6, which gives us:
(-1) * 6 / 2 = -6 / 2
Now, we can divide 6 by 2, which gives us:
-6 / 2 = -3
So we see that the quotient is negative.
We can generalize this to any negative number divided by a positive number. Let's say we have a negative number -a and a positive number b. We can write the expression as:
(-a) / b = (-1) * a / b
Multiplying -1 and a gives us:
(-1) * a / b = -a / b
So we see that the quotient is negative, since -1 times a is negative, and dividing a negative number by a positive number results in a negative quotient.
Therefore, we can conclude that when a negative number is divided by a positive number, the result is always negative.
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Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution?
Answer:Y = 7x – 16,
y = 2(2x – 5)
Step-by-step explanation:
he answer to the system of equations is (2,-2)
First, we can substitute in for y in the other equation
This will give us
Next, we distribute the 2 throughout the parenthesis
Now we can solve for x. Begin by adding 16 to each side
Now we can subtract 4x from each side
Lastly, we can divide each side by 3
Now, we need to substitute in the value that we got for x into one of the equations to find the y value.
This becomes
So
This means that the solution to the system of equations is (2,-2)
what is 73kg to lbs?
73 kg is equivalent to approximately 160.937 pound (lbs).
Kilogram (kg) and pound (lb) are both units of mass commonly used in different parts of the world. Kilogram is the base unit of mass in the International System of Units (SI) and is defined as the mass of the International Prototype of the Kilogram, which is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.
Pound, on the other hand, is a unit of mass commonly used in the United States, the United Kingdom, and other countries, which is defined as exactly 0.45359237 kilograms. This value is based on the international avoirdupois pound, which is defined as exactly 0.45359237 kg.
To convert kilograms to pounds, you can use the conversion factor of 2.20462 lbs/kg. To convert pounds to kilograms, you can use the conversion factor of 0.45359237 kg/lb.
To convert 73 kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462.
So,
73 kg * 2.20462 lbs/kg = 160.937 lbs (rounded to three decimal places)
Therefore, 73 kg is equivalent to approximately 160.937 lbs.
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What are tables in a research paper?
Tables and figures area way of presenting data in an organized form or more in a presentable way to attract more audience.
With tables and figures, it arranges your data to a simplified form and also it makes the content easy to understand for the front person.
Tables and figures in scientific papers are wonderful ways of presenting data. Effective data presentation in research papers requires understanding your reader and the elements that comprise a table.
It also several elements, including the legend, column titles, and body.
With all this tables in a research paper helps the reader understand the content for the data more effectively and efficiently.
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Please hurry, and I will give brainiest
Describe what your first step would be in solving the system of equations:
4x + 2y = 11
3x - y = 9
The first step is to describe the method to take
How to determine the first stepTo solve the system of equations 4x + 2y = 11 and 3x - y = 9, the first step would be to choose a method to solve the system.
There are several methods for solving systems of equations, including:
Substitution methodElimination methodGraphing methodOne common method is the substitution method, which involves solving one equation for one variable and then substituting the expression for that variable into the other equation.
For example, we could solve the second equation 3x - y = 9 for y to get:
y = 3x + 9
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what is errors in calculations?
Errors in calculations are mistakes or inaccuracies that occur when performing mathematical calculations. They can be caused by a variety of factors, including human error, equipment malfunction, incorrect assumptions or data, and flawed methodology.
There are several types of errors that can occur in calculations, including:
Transcription errors: These occur when a number or a calculation is copied down incorrectly from one place to another, such as from a calculator to a piece of paper.
Calculation errors: These occur when the wrong calculation is used, or when a mistake is made in performing a calculation, such as forgetting to carry a digit when doing long division.
Rounding errors: These occur when numbers are rounded to a certain number of decimal places, and the resulting calculation is not as precise as it could be.
Measurement errors: These occur when the instruments used to measure quantities are not accurate, or when the measurements are not taken correctly.
Conceptual errors: These occur when the underlying concepts or principles of the problem are not fully understood, leading to incorrect calculations.
It is important to identify and correct errors in calculations to ensure the accuracy and validity of the results. Checking calculations multiple times and using multiple methods of verification can help to reduce the risk of errors.
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find the measure of CDE,BC,AB, and CAB.
The measure of arc CDE is, 154°
The measure of arc BC is, 26°
The measure of arc AB is, 90°
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Now, By the figure, we have;
⇒ ∠APE + ∠EPD = 180°
⇒ (25x + 15)° + (33x - 9)° = 180°
⇒ 58x + 6 = 180
⇒ 58x = 180 - 6
⇒ 58x = 174
⇒ x = 3
Hence, The measure of arc CDE is,
⇒ (20x + 4)° + (33x - 9)°
⇒ (20×3 + 4)° + (33×3 - 9)°
⇒ 64° + 90°
⇒ 154°
And, The measure of arc BC is,
⇒ 90° - (20x + 4)°
⇒ 90° - (20×3 + 4)°
⇒ 90° - 64°
⇒ 26°
The measure of arc AB is,
⇒ arc AB + 90° = 180°
⇒ arc AB = 90°
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please help out with geometry answers
The area of the left over wood is
28.54 square cmArea of the kite
786.72 square cmperimeter of the kite
81.94 cmHow to find the area of the left over woodThe area of the left over wood is given by
= area of the circle - area of the pentagon
area of the circle
= pi * r^2
= pi * 5^2
= 78.54 square cm
area of the pentagon
= 5/2 * a * 5
solving for a
360 / 5 = 72
72 / 2 = 36
cos 36 = a / 5
a = 5 cos 36 = 4
area of the pentagon = 5/2 * 4 * 5 = 50 sq cm
left over wood = 78.54 - 50 = 28.54 square cm
Area and perimeter of kite
area of kite = product of the two diagonals
length of one of the diagonals = 2 * KT = 2 * 12 = 24 cm.
The second diagonal
tan 30 = KT / x
x = 12 / tan30 = 20.78
the length = 12 + 20.78 = 32.78
area of the kite = 32.78 * 24 = 786.72 square cm
perimeter of the kite
= addition of the sides = 2(shorter side + longer side)
Using Pythagoras rule
shorter side = √(12² + 12²) = 16.97
longer side = √(20.78² + 12²) = 24
perimeter = 2 (16.97 + 24) = 81.94 cm
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Need some help please
x+6y+10
llllllllllllllllllllllllllllllllllllllllllllllllll
Qualitative data contribute to analysis and should aid the explanation of a process that may otherwise be unclear if explained by quantitative data only. (T/F)
The given statement "Qualitative data contribute to analysis and should aid the explanation of a process that may otherwise be unclear if explained by quantitative data only." is true.
Qualitative data is non-numeric information that provides insight into attitudes, behaviors, motivations, and perceptions. It is typically collected through open-ended questions, observation, and interviews. Qualitative data can provide a rich and nuanced understanding of a process or phenomenon that may not be possible to obtain through quantitative data alone. This is because qualitative data can help to uncover the underlying reasons behind a process, how people experience it, and how it is perceived by different groups. As a result, qualitative data can provide valuable context and insight into a process that may otherwise be unclear if explained by quantitative data alone.
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In 2015 the highest tower in the world is the tower Burj Khalifa in Dubai.
It measures 828 meters of height
Alex have represented this tower at the scale 1=4000
What is the height of the tower in his draw ?
The height of the tower in Alex's drawing is 20.7 centimeters.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We need to find the height of the tower in Alex's drawing.
Let us multiply the actual height of the tower by the scale factor.
Scale factor = 1 : 4000
Height of the actual tower = 828 meters
Height of the tower in Alex's drawing = 828 meters x (1/4000) = 0.207 meters or 20.7 centimeters.
Therefore, the height of the tower in Alex's drawing is 20.7 centimeters.
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How many cg are in g?
Answer:
there are 100 centigrams in a gram
Step-by-step explanation:
how to use calculus cheat sheet?
A calculus cheat sheet can be a helpful tool to assist you in studying and reviewing calculus concepts.
Here are some tips for how to use a calculus cheat sheet effectively:
1. Familiarize yourself with the content: Take the time to read through the entire cheat sheet to get a sense of what topics are covered and how the information is organized.
2. Use it as a study aid: A calculus cheat sheet can be a helpful study aid to review concepts and formulas before a test or exam. Work through practice problems and apply the concepts you have learned.
3. Keep it handy: Print out the cheat sheet or save it to your phone or computer so that you can refer to it whenever you need to.
4. Use it as a reference: As you work on calculus problems, use the cheat sheet to remind yourself of key concepts, formulas, and rules.
5. Customize it: You can create your own cheat sheet, which includes the formulas and concepts that you find most challenging. This will help you focus on the areas that you need to improve upon.
Remember that while a calculus cheat sheet can be a helpful tool, it is important to develop a deep understanding of calculus concepts through practice, problem-solving, and building intuition. The cheat sheet should be used as a supplement to your learning, not a replacement for it.
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Heidi earned $1130 a week last year. What was her yearly salary ?
A. $52,800
B. $54,240
C. $57,200
D. $58,760
Answer:
Its D
Step-by-step explanation:
1130 / 7 = 161
161 x 365 = 58 765
Answer: D
Step-by-step explanation:
According to the yearly compound interest, a sum of money amounts to Rs. 6050 in 2 year and Rs. 6655 in 3 years. What was the sum? Ans: Rs. 5000
The principal sum of the given compound interest is Rs 5000.
What is principal amount?The total amount of money borrowed (or invested), not including any interest or dividends, also called sum.
Given that, a sum of money amounts to Rs. 6050 in 2 year and Rs. 6655 in 3 years. we are asked to find the principal amount or sum,
CI = P(1+r/100)ⁿ
P = principal amount, CI = compound interest, r = rate, n = time
Therefore,
CI = 6050(1+r/100)²....(i)
CI = 6655(1+r/100)³....(ii)
Diving eq(ii) by eq(i)
6655 / 6050 = (1+r/100)
1+r/100 = 1.1
r/100 = 1.1-1
r/100 = 0.1
r = 10%
Put r = 10% in eq(i)
6050 = p(1.1)²
p = 5000
Hence, the principal sum of the given compound interest is Rs 5000.
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The height of a triangle is 2cm more than base the area of the triangle is 10cm^2 find the height
If the height of a triangle is 2 cm more than base and the area of the triangle is 10 cm then the height is, 7 cm
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
The area of a triangle is given by the formula:
Area = (base x height) / 2
We are given that the area is 10 cm² and that the height is 2 cm more than the base.
Let's call the base "b".
Then, the height is "b + 2".
We can substitute these values into the area formula:
10 = (b x (b + 2)) / 2
Expanding the right side:
10 = (b² + 2b) / 2
Multiplying both sides by 2:
20 = b² + 2b
Subtracting b² from both sides:
20 - b² = 2b
Factoring the left side:
(10 - b)^2 = b²
Taking the square root of both sides:
|10 - b| = b
Adding b to both sides:
10 = 2b
Dividing both sides by 2:
5 = b
So, the base of the triangle is 5 cm and the height is b + 2 = 5 + 2 = 7 cm.
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If Figure 1 is similar to Figure 2, which of the following must be true?
there just reflected because the shape is just refected to the other side it the same but smaller
Find the value of p for which the polynomial x3 + 4x²-px-18 is exactly divisible by x-2. Hence factories the polynomial
Solution in da attachment!! :)
A sensor on a boat notices buried treasure 200 meters away diagonally with an angle of depression of 25 degrees. How deep is the treasure beneath the water rounded to the nearest tenth of a meter?
Answer: To solve this problem, we can use the Pythagorean theorem. Let's call the depth of the treasure "d".
We can create a right triangle with the following sides:
The sensor on the boat is at the top of the triangle and is 200 meters away from the treasure diagonally.
The line from the sensor to the treasure, which we can call "x", is at a 25-degree angle from the surface of the water.
The line from the treasure to the ocean floor, which we can call "d", is perpendicular to the surface of the water.
Since we know that the angle of depression is 25 degrees, we can use tangent to find the length of x.
tan(25) = x/d
x = d * tan(25)
Now, we have two sides of a right triangle and can use the Pythagorean theorem to find d:
x^2 + d^2 = 200^2
d^2 = 200^2 - x^2
d^2 = 200^2 - (d * tan(25))^2
Solving for d, we find that d = 174.59 meters. Rounding to the nearest tenth of a meter, we get d = 174.6 meters.
Step-by-step explanation:
In the diagram, segment AD bisects angle BAC.
Given the following segment lengths, find the value of x.
Round to the nearest tenth.
AB = 23
AC = 18
The value of x is 77.5. In order to solve for x, we need to use the Triangle Angle Sum Theorem.
What is value?Value is a subjective concept that referred to the word of importance that an individual group of people places on something it is often associated with principal beliefs and standard that are accepted by society when you can be seen as a measure of how important something is true person of organization it is often seen as a reflection of ones worldview and can help to save attitudes decision and behaviors believe is not an absolute and very depending on the context of the looks like commands.
In order to solve for x, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180°. Since angle BAC is bisected by segment AD, the two angles must be equal. Therefore, we can set up the following equation to solve for x:
180° = angle BAC = (x + 7) + (x + 18)
We can solve this equation by combining like terms and isolating the variable x.
180° = 2x + 25
2x = 155
x = 77.5
Therefore, the value of x is 77.5.
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(Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 8 inches and height of 6 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold?
Approximate using pi equals 355 over 113. )
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 6 squared times 4
V equals 355 over 113 times 4 squared times 6
The method that is used to calculate the cubic units of cake batter needed to fill the mold is V equals 355 over 113 times 4 squared times 6. (third option)
How much cake batter is needed to fill the mold?A cylinder is a three-dimensional object. It is a prism with a circular base. The amount of cake batter that is needed to fill the mold is equal to the volume of the cylinder.
Volume of a cylinder = πr²h
Where:
π = 355 / 113 = pir = radius = diameter / 2 = 8 / 2 = 4 inchesh = height= 355/133 x 4² x 6
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The answer is V equals 355 over 113 times 4 squared times 6, thus, option (d)
The formula for volume of a cylinder is: V= πr2h, so if pi = 355/113 then
V= (355/113)(4)2(6)
Goodluck! ~izzy~
can anyone help me with this
Sixty percent of the students preferred raisins to banana chips. If there
were 95 students in all, how many preferred banana chips
The number of students who preferred banana chips are 57.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that sixty per cent of the students preferred raisins to banana chips. If there were 95 students in all, the number of the students will be calculated as:-
Number = 95 x 60%
Number = 95 x 60 / 100
Number = 95 x 0.6
Number = 57
Therefore, the number of students who choose banana chips is 57.
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