Please help ASAP!! I mark brainliest.

Answer:

\(x=\dfrac{32}{15}\)

Answer:

25.4 miles

Step-by-step explanation:

added them all up

but if i just wants miles than tha answer is 25

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

Step-by-step explanation:

Note: the question did not provide the quantity to work with, so we will assume some values, say quantity Q= 30

Generally, it is normal for the revenue to decrease when the price of a commodity increase, this is so that buyer will have to react to adjust to the change in price.

When price increase from $50 to $60, the total revenue will decrease

let say the quantity Q1=30 , and the new quantity after price increase is Q2=20

1. The revenue PxQ before price change will be

PxQ= P1xQ1=50*30

PxQ= $1500

1. The revenue PxQ after price change will be

PxQ=P2xQ2= 60*20

P2xQ2= $1200

This clearly shows that based on the assumed data, the total revenue will drop from1500 to 1200, a total of $300 in a decrease

Answer:

3/9 = 1/3 of a minute or 20 seconds

Step-by-step explanation:

Answer:

1/3 of a minute

Step-by-step explanation:

1/3 x 3 = 1 bottle

1/9 x 3 = the time

1/9 x 3 = 3/9 or 1/3

The solutions to the system of equations 2x + y = 3 and y - 3 = 2x - 2 are (1,5) and (-2,-1).

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.

The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.

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Answer:

is there something suggested?

The volume of one of the containers that have dimensions of 2 1/2 feet by 4 2/3 feet by 3 1/2 feet is approximately 40.83 cubic feet.

To find the volume of the container, we need to multiply its three dimensions: length, width, and height.

First, we need to convert the mixed numbers into improper fractions for easier calculation.

2 1/2 feet = (2 × 2 + 1)/2 = 5/2 feet

4 2/3 feet = (4 × 3 + 2)/3 = 14/3 feet

3 1/2 feet = (3 × 2 + 1)/2 = 7/2 feet

Now we can use the formula for volume of a rectangular prism, which is:

Volume = length × width × height

Plugging in the values we have, we get:

Volume = (5/2) × (14/3) × (7/2) cubic feet

Volume = 122.5/3 cubic feet

Volume = 40.83 cubic feet (rounded to two decimal places)

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Answer:

7/8

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Divide common factors from both the numerator and denominator. Divide 5 from both top and bottom:

(35/40)/(5/5) = 7/8

7/8 is your answer.

~

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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The distance between point P and line L is 16/9√(13).

To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:

Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:

|ax1 + by1 + c|/√(a² + b²)

To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.

2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y

The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:

y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4

Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.

Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).

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Therefore, to calculate the scale factor of dilation, we need to know the coordinates of points A, B, C, M, and N or the lengths of AB and MN.

The scale factor of dilation is the ratio of the length of the image to the length of the pre-image.

In this case, MN is the image of AB after a dilation centered at point C. of the length of MN to the length of AB.

Let's denote the length of AB as "a" and the length of MN as "b". Then the scale factor of dilation, k, can be expressed as:

k = b/a

To find this ratio, we need to know the lengths of AB and MN. If those are given, we can simply divide them to find the scale factor. However, if the lengths are not given, we need additional information.

One way to find the lengths is to use the distance formula. Let's assume that the coordinates of points A, B, C, M, and N are known. Then we can use the distance formula to find the lengths of AB and MN, as follows:

\(Length of AB = \sqrt{[(xB-xA)^2 + (yB-yA)^2]\)

\(Length of MN = \sqrt{[(xN-xM)^2 + (yN-yM)^2]\)

Once we have the lengths, we can calculate the scale factor using the formula:

\(k = Length of MN / Length of AB\)

Therefore, to calculate the scale factor of dilation, we need to know the coordinates of points A, B, C, M, and N or the lengths of AB and MN.

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The interest amount is $622.85

The given parameters are:

The interest amount is calculated as:

I = P(1 + r/n)^(nt) - P

This gives

I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000

Evaluate the products and the quotient

I = 1000 * (1 + 0.045)^(11) - 1000

Evaluate the sum

I = 1000 * (1.045)^(11) - 1000

Solve

I = 622.85

Hence, the interest amount is $622.85

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Answer:

If you're moving the vehicle to the right, shoulder check by moving your head 90° to the right. Turn your head 90° degrees in the direction you're moving the vehicle. And, if you're moving the vehicle to the left, you shoulder check to the left by turning your head 90° to the left.

Answer: 49π square units

Step-by-step explanation:

Area of a circle = πr^2

Area = π x 7^2

Area = 49π

Answer:

9.8646 or I think 14 units 2

Answer:

Step-by-step explanation:

If the larger of 2 consecutive integers is 324, then 324-(2-1) = 323 is the smaller.

If the largest of 89 consecutive integers is 324, then 324 - (89-1) = 236 is the smallest.

Hence, the smallest consecutive integer is \(237\).

What is the smallest consecutive integer?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Here given that,

The largest of \(89\) consecutive integers is \(324\)

So, it is of the form

\(324-89=237\)

Hence, the smallest consecutive integer is \(237\).

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Answer:

8x-24

Step-by-step explanation:

First you do:

8×x which is 8x

Then you do:

8×-3 which is -24

Then you put it into 1 expression:

8x-24

Answer:

8−24

Thank You!

Answer:

option B: 15\(x^8 y^5 z^7\)

Step-by-step explanation:

we just calculate 5 x^4 y^2 z^2 multiplied by 3x^4 y^3 z^5

and that gives the answer

The probability that a marble drawn is red is 0.4286, marble is odd-numbered is 0.5, and marble drawn is red or blue is 1.

There are 6 red marbles and 8 blue marbles, for a total of 14 marbles. The probability of drawing a red marble is the number of red marbles divided by the total number of marbles

P(Red) = 6/14 = 0.4286 (rounded to four decimal places)

There are 6 red marbles and 8 blue marbles, and 7 of them are odd-numbered (1, 3, 5, 7). The probability of drawing an odd-numbered marble is the number of odd-numbered marbles divided by the total number of marbles:

P(Odd) = 7/14 = 0.5 (rounded to four decimal places)

The probability of drawing a red or blue marble is the sum of the probabilities of drawing a red marble and a blue marble:

P(Red or Blue) = P(Red) + P(Blue)

To find P(Blue), we note that there are 8 blue marbles and 14 total marbles. Therefore,

P(Blue) = 8/14 = 0.5714 (rounded to four decimal places)

Now we can find P(Red or Blue)

P(Red or Blue) = P(Red) + P(Blue) = 6/14 + 8/14 = 14/14 = 1

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Answer:

{ - 4, - 1, 2, 5 }

Step-by-step explanation:

the range is the values of y from the ordered pairs in the relation

range = { - 4, - 1, 2, 5 }

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

(a) Bako is 10 years old

(b) His mother was 30 years old when Bako was 5

(c) Bako will be 25 years old when his mother is 50

(d) Bako's mother was 25 years old when he was born

(e) The difference between Bako's age & his mother's is 25 years

Step-by-step explanation:

Let Bako's age five years ago be x years

Presently, Bako is 2x years old (according to the 1st statement)

Normal, Bako's present age should have been (x + 5) years; since he was x years old 5 years ago.

This simply means that Bako's present age is BOTH 2x years & (x + 5) years.

We have to equate them since they mean the same thing (Bako's present age)

x + 5 = 2x

2x - x = 5

Therefore x = 5 years

Remember that x signified Bako's age five years ago... This simply means that Bako's age five years ago was 5 years.

This simply means that Bako's age now is 10 years old.

His mother was then six times 5 years = 30 years old (from the 2nd statement).

If Bako was 5 years old five years ago and his mother was 30 years old... It simply means that Bako was born ten years ago when his mother was 25 years old.

This simply means that Bako's mother is older than him with 25 years.

Therefore, Bako will be 25 years old when his mother is 50 years old

The volume of the cube with side length 8 inches is 512 inches cube.

The cube with side length s has volume s³. Matt has a cube-shaped wooden box that he uses to store his marble collection. It has 8-inch sides.

The volume of the cube can be calculated as follows:

A cube has all side length equal to each other.

Therefore,

volume of the cube = s³

where

Therefore,

s = 8 inches

Hence,

volume of the cube = 8³

volume of the cube = 8 × 8 × 8

volume of the cube = 512 inches cube

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Kiran's age = x

Uncle's age = 54

Also,

Uncle's age = 8 + 3x

Now,

8 + 3x = 54

3x = 54 - 8

3x = 46

x = 46/3

x = 15.33

x = 15 (rounded)

The length of wall in real life is 4 feet.

Given that on an architect's blueprint, 1 inch corresponds to 4 feet.

In this architect's plan, a wall represented by a line 1 inches long on the blue print.

So, the length of wall in real life is = 4 feet.

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Answer:

4ft

Step-by-step explanation:

If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.

Answer:

8

Step-by-step explanation:

9: 9, 18, 27, 36, 45, 54, 63, 72

12: 12, 24, 36, 48, 60, 72

72 is the first number that can be divided (evenly) by both 9 and 12

Answer:

8

Step-by-step explanation:

9: 9, 18, 27, 36, 45, 54, 63, 72

12: 12, 24, 36, 48, 60, 72

72 is the first number that can be divided (evenly) by both 9 and 12

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

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