What is the slope of the line on this graph?
6
5
4
3
2
1H
-7
-6 -5 -4 -3 -2 -1 9
23
-2
-3
14

If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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According to the question, therefore, the maximum number of grams of fat he should consume will be 76.3 grams.

Directly divide 687 by 9 as both are fat content. Therefore, by dividing them, we get to know about how grams of fat can be consumed.

✍️ By Benjemin ☺️

Answer:

4s

Step-by-step explanation:

s is the original number of stickers, and since she wants four times as many stickers, you just multiply by 4 so you get 4s

Answer:

Step-by-step explanation:

  x + 6 I x³ + 2x²  - 10x + 84   I   x² - 4x + 14

              x³ + 6x²

            -     -      

                     -4x² - 10x

                    -4x²  - 24x

                    +       +    

                               14x + 84

                                14x + 84

                                -      -      

                                     0

P(x)  =(x +6)* ( x² - 4x + 14) + 0

Answer:

100 cg

Step-by-step explanation:

Answer:

100 centigrams

Step-by-step explanation:

Answer:

the first and second one i think

Step-by-step explanation:

Answer:

126,300.

Step-by-step explanation:

Answer:

Your answer would be 126,350!

Step-by-step explanation: Since the ones place is directly beside the hundreds place to the right, you would use this number to determine whether you stay or round up. 9 is greater then 5, meaning you round up making the hundreds place a 5. Hope this helps! :)

The per capita emissions for each country is:

Using this formula to find the  Per capita emissions for each country

Per capita emissions = C02 Emission (tons of carbon dioxide ) /  Total emissions by population

China

Per capita emissions =8,782,000,000/1,359,750,000

Per capita emissions = 6.46

United States

Per capita emissions =5,144,000,000/316,597,000

Per capita emissions= 16.25

India

Per capita emissions = 2,185,000,000 /1,233,460,000

Per capita emissions = 1.77

Russia

Per capita emissions=1,646,000,000/143,400,000

Per capita emissions = 11.48

Japan

Per capita emissions = 1,232,000,000/127,310,000

Per capita emissions = 9.68

Germany

Per capita emissions = 733,000,000/80,523,700

Per capita emissions = 9.10

Iran

Per capita emissions = 583,000,000/76,876,000

Per capita emissions = 7.58

South Korea

Per capita emissions = 576,000,000/50,219,669

Per capita emissions = 11.47

Indonesia

Per capita emissions = 535,000,000/237,641,326

Per capita emissions = 2.25

Canada

Per capita emissions = 528,000,000/35,141,542

Per capita emissions =15.02

Therefore China per capita emissions is 6.46.

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1. Find the length of the segment AB, use the next formula:

x- difference:

y-difference:

2. Find the 2/5 of each difference:

3. Add the results you get in step 2 to the coordinates of point A:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.

Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.

Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.

Assuming that the basketball follows a parabolic path, we can use the formula:

y = ax² + bx + c,

where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.

To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.

Therefore, the points on the trajectory of the basketball are:

(0, 1.5), (8.5/2, h), and (8.5, 0),

where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,

we get:

1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)

Simplifying equations (1) and (2),

we get:

c = 1.5...(4)b = -a(8.5)²/8.5...(5)

Substituting equation (4) in equation (3), we get:

h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5

Substituting the value of a from equation (5) in the above equation,

we get:

h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5

Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,

we can use the formula:

x = ut + 0.5at²,

where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.

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Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

B) The cost of milk by the gallon.

C) The price of pears by the pound.

Step-by-step explanation:

A linear function is one that both the dependent and independent variables increases or decreases proportionally.

Thus from the given options:

i. If the gallons of milk increase, then the cost of milk also would increase proportionally. A decrease in the gallons of milk would also reduce the cost of milk.

ii. An increase in the pounds of the pearls would cause an increase in the price of the pearls. Also, a decrease in the pounds of pearls would reduce the price of the pearls.

Thus, the answers to the question are options B and C.

Answer:

The other guy is correct however he missed one

The Answer is actually A, B, C

Step-by-step explanation:

I took the test on Usa test prep.

Answer:

I would say, A. y < 3.

Step-by-step explanation:

I hope this is right and i hope this helps! ;)

Answer:

c

Step-by-step explanation:

i haven't done this in over a year so my explanation wont be good but i know the answer is right

Answer:

12.68

Step-by-step explanation:

Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

Holden drinks 1/8 gallon of water every 2 miles, so after hiking 14 miles, he would have drank (14/2) * (1/8) = 7/16 gallons of water.

Melissa drinks 3/8 gallon of water every 2 miles, so after hiking 14 miles, she would have drank (14/2) * (3/8) = 21/32 gallons of water.

The difference in the amount of water they drink is:

21/32 - 7/16 = 21/32 - 14/32 = 7/32 gallons

Therefore, Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

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The area of the sector OPR is approximately 5.20 cm².

What is an area?

First, we need to find the length of PR. Since O is the center of the circle, we know that OP and OR are both 6 cm long (the radius of the circle). By the triangle inequality, we have:

PR < OP + OR = 6 + 6 = 12

Since QR = 14, we have:

PR > QR - OP - OR = 14 - 6 - 6 = 2

Therefore, 2 cm < PR < 12 cm.

Next, we can use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

To find the central angle θ, we can use the law of cosines:

(PR)² = (OP)² + (OR)² - 2(OP)(OR)cos(θ)

Substituting in the known values, we get:

(PR)² = 6² + 6² - 2(6)(6)cos(θ)

(PR)² = 72 - 72cos(θ)

cos(θ) = (72 - (PR)²)/72

Using the known values, we have:

cos(θ) = (72 - (PR)²)/72 = (72 - x²)/72

where x is the length of PR.

Since OPQ is a triangle, we know its area:

25 = (1/2) base × height

25 = (1/2) QR × OP

25 = (1/2) (14) × 6

25 = 42

Therefore, the height of triangle OPQ is:

height = (2)(25)/QR = (2)(25)/14 = 25/7

The height of the triangle is also the distance from O to the line PQ, which is also the distance from O to the chord PR. Therefore, the area of sector OPR can be calculated as follows:

A = (θ/360)πr² = (θ/360)π(6)²

A = (θ/360)(36π) = (θ/10)π

where θ is the central angle of the sector in degrees. To find θ, we can use the formula:

sin(θ/2) = (PR/2)/r = x/6

Substituting in the known values, we get:

sin(θ/2) = x/6

θ/2 = \(sin^{-1}\)(x/6)

θ = 2\(sin^{-1}\)(x/6)

Finally, substituting this value of θ into the formula for the area of the sector, we get:

A = (θ/10)π = [2\(sin^{-1}\)(x/6)]/10 * π

To find the value of x that gives the area of the sector, we can use trial and error or a numerical solver. Using a calculator, we find that x ≈ 5.5 cm gives an area of the sector of:

A ≈ 5.20 cm²

Therefore, the area of the sector OPR is approximately 5.20 cm².

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The function h(x) = (x + 9)(x² - 10x+25) has two distinct real zeros. so the option D is correct .

The values of the variable in a function that cause the function to equal zero are known as the zeros of the function. The places on the x-axis where the graph crosses the x-axis are known as a function's zeros graphically. In other words, we can say that a function's zeros are the graph's x-intercepts.

We have been given that

h(x) = (x + 9)(x² - 10x+25)

(x² - 10x+25) is also write as in the square form

(x - 5)²

Then

h(x) = (x + 9)(x - 5)²

When h(x) = 0,

(x + 9) = 0

x = -9

or

(x - 5)² = 0.

(x-5) = 0

x = 5

x = -9 or x = 5.

Hence , the real zeros of the function h(x) = (x + 9)(x2 - 10x+25) are two separate values.

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Answer:

72\(\sqrt{3}\) units²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here b = ST = a = 12 and h = RS

To calculate RS use the tangent ratio in the right triangle and the exact value

tan60° = \(\sqrt{3}\) , thus

tan60° = \(\frac{opposite}{adjacent}\) = \(\frac{RS}{ST}\) = \(\frac{RS}{12}\) = \(\sqrt{3}\) ( multiply both sides by 12 )

RS = 12\(\sqrt{3}\)

Thus

A = \(\frac{1}{2}\) × 12 × 12\(\sqrt{3}\) = 6 × 12\(\sqrt{3}\) = 72\(\sqrt{3}\) units²

Answer:

She was there for 3 hours.

Step-by-step explanation:

7.25-5= 2.25

2.25÷0.75=3

The fine to be paid for the overdue book as given by the function is $4.50

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

To solve this, we simply need to find the value of n and then substitute it into the function.

Given that;f(n) = 1.5 + 0.5(n -1), find f(10 - 3). This becomes f(7)

Substitute 7 in place of nf(7) = 1.5 + 0.5(7 - 1)f(7)

= 1.5 + 0.5(6)f(7) = 1.5 + 3f(7)

= 4.5

The fine for the overdue book is $4.50

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Answer:

4.5

Step-by-step explanation:

God bless u all

The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:

Volume = π * r^2 * h

Given:

Radius (r) = 20 inches

Height (h) = 0.7 feet

First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:

Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches

Now, we can substitute the values into the volume formula:

Volume = π * (20 inches)^2 * 8.4 inches

Calculating the volume:

Volume = 3.14159 * (20 inches)^2 * 8.4 inches

≈ 3.14159 * 400 inches^2 * 8.4 inches

≈ 1005.3096 cubic inches

Rounding the volume to the nearest tenth:

Volume ≈ 1005.3 cubic inches

Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

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To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

Answer:

I think its J, but I'm not 100% posative

Answer:

20%

Step-by-step explanation:

The theoretical probability of drawing a red marble can be found by dividing the number of red marbles by the total number of marbles in the bag:

P(red) = number of red marbles / total number of marbles

P(red) = 5 / (5 + 8 + 12)

P(red) = 5 / 25

P(red) = 0.2

So the theoretical probability of randomly drawing a red marble is 20%, which corresponds to option (C).

Answer:

B

Step-by-step explanation:

I'am sure

Answer:

5

Step-by-step explanation:

3/12=x/20

cross multiply

12x=3(20)

12x=60

x=60/12

x=5