Please help I'm stuck.

The orthonormal basis of p is {N1, N2, N3} = {(1/3, -2/3, 2/3), (1/√15, 3/√15, -1/√15), (-2/√33, -1/√33, 4/√33)}.

Let {v1, v2, v3} be the given basis of p.

Apply Gram-Schmidt orthonormalization process to B = {(1, -2, 2), (2, 2, 1), (-2, 1, 3)} as follows:v1 = (1, -2, 2)N1 = v1/‖v1‖ = (1/3, -2/3, 2/3)v2 = (2, 2, 1) - (v2 ⋅ N1) N1= (2, 2, 1) - (5/3, -4/3, 4/3)= (1/3, 10/3, -1/3)N2 = v2/‖v2‖ = (1/√15, 3/√15, -1/√15)v3 = (-2, 1, 3) - (v3 ⋅ N1) N1 - (v3 ⋅ N2) N2= (-2, 1, 3) - (-4/3, 8/3, -4/3) - (-2/√15, -4/√15, 7/√15)= (-2/3, -2/3, 10/3)N3 = v3/‖v3‖ = (-2/√33, -1/√33, 4/√33)

Therefore the orthonormal basis of p is {N1, N2, N3} = {(1/3, -2/3, 2/3), (1/√15, 3/√15, -1/√15), (-2/√33, -1/√33, 4/√33)}.Answer: {(1/3, -2/3, 2/3), (1/√15, 3/√15, -1/√15), (-2/√33, -1/√33, 4/√33)}.

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The orthonormal basis for the given basis isB = {B₁, B₂, B₃} = {(1, -2, 2)/3, (1, 3, 0)/√10, (-1/√10)(1, 1, -3)}Given basis is B = {(1, -2, 2), (2, 2, 1), (-2, 1, -2)}

Let’s begin the Gram-Schmidt orthonormalization process for the given basis and transform it into an orthonormal basis.

Step 1: Normalize the first vector of the basis.B₁ = (1, -2, 2)

Step 2: Project the second vector of the basis onto the first vector and subtract it from the second vector of the basis.

B₂ = (2, 2, 1) - projB₁B₂= (2, 2, 1) - [(2+(-4)+2)/[(1+4+4)] B₁]B₂ = (2, 2, 1) - (0.5)(1, -2, 2)B₂ = (1, 3, 0)

Step 3: Normalize the vector obtained in step 2.B₂ = (1, 3, 0)/ √10

Step 4: Project the third vector of the basis onto the orthonormalized first and second vectors and subtract it from the third vector.

B₃ = (-2, 1, -2) - projB₁B₃ - projB₂B₃ = (-2, 1, -2) - [(2+(-4)+2)/[(1+4+4)] B₁] - [(1+9+0)/10 B₂]

B₃ = (-2, 1, -2) - (0.5)(1, -2, 2) - (1.0)(1/ √10)(1, 3, 0)B₃ = (-2, 1, -2) - (0.5)(1, -2, 2) - (1/√10)(1, 3, 0)

B₃ = (-1/√10)(1, 1, -3)

Therefore, the orthonormal basis for the given basis isB = {B₁, B₂, B₃} = {(1, -2, 2)/3, (1, 3, 0)/√10, (-1/√10)(1, 1, -3)}

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Answer:

Step-by-step explanation:

Each equation is in vertex form, so you can easily determine the number of real roots. The leading coefficient tells you whether the parabola opens upward (positive) or downward (negative).

  y = a(x -h)^2 +k

has leading coefficient "a" and vertex (h, k).

__

f(x) = 1/3(x +5)^2 +7

  vertex: (-5, 7), opens downward

The vertex is above the x-axis, so there are two real roots.

__

f(x) = -5(x -3)^2

  vertex: (3, 0), opens downward

The vertex is on the x-axis, so there is one real root.

Rounding up to the nearest unit, it would take Calvin approximately 27 months to pay off his credit card with a monthly payment of $165.

To determine how long it would take Calvin to pay off his credit card, we need to consider the monthly payment amount and the interest rate. Let's calculate the time it would take for two different monthly payment amounts: $220 and $165.

a. Monthly payment of $220:

Let's assume the initial balance on Calvin's credit card is $3,000, and the annual interest rate is 4 percent. To calculate the monthly interest rate, we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate = 4% / 12 = 0.3333%

Now, we can calculate the time it would take to pay off the credit card using the monthly payment of $220 and the monthly interest rate. We'll use a formula for the number of months required to pay off a loan with fixed monthly payments:

n = -(log(1 - (r * P) / A) / log(1 + r))

Where:

n = number of months

r = monthly interest rate (as a decimal)

P = initial balance

A = monthly payment

Plugging in the values:

n = -(log(1 - (0.003333 * 3000) / 220) / log(1 + 0.003333))

Using a calculator, we can find:

n ≈ 15.34

Rounding up to the nearest unit, it would take Calvin approximately 16 months to pay off his credit card with a monthly payment of $220.

b. Monthly payment of $165:

We can repeat the same calculation using a monthly payment of $165:

n = -(log(1 - (0.003333 * 3000) / 165) / log(1 + 0.003333))

Using a calculator, we find:

n ≈ 26.39

Please note that these calculations assume that Calvin does not make any additional charges on his credit card during the repayment period. Additionally, the interest rate and the balance are assumed to remain constant. In practice, these factors may vary and could affect the actual time required to pay off the credit card balance.

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Answer:

Step-by-step explanation:

n = -14

(x^3)(x^−17) =

x^(3 - 17) =

x^-14

Answer:

Step-by-step explanation:

Congruent quadrilateral related parts are congruent.

The true statements are:

Statements 2, 4, and 6 are Not Congruent

Statements 1, 3, and 5 are Congruent

Two triangles are said to be congruent if their corresponding sides and angles are equal.

From the given figure:

Quadrilaterals 1, 2 and 4 are congruent

Quadrilateral 3 is not congruent to any of the other quadrilaterals.

The true statements are:

Quadrilateral 1 and quadrilateral 2 Congruent

Quadrilateral 1 and quadrilateral 3 Not Congruent

Quadrilateral 1 and quadrilateral 4 Congruent

Quadrilateral 2 and quadrilateral 3 Not Congruent

Quadrilateral 2 and quadrilateral 4 Congruent

Quadrilateral 3 and quadrilateral 4 Not Congruent

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The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

7.9

Step-by-step explanation:

the first thing to do is find the second projection.

16-7 = 9

than we can use a proportion to find BD

7 : BD = BD : 9

BD = √9 x 7 = √63 = 7.9

we have to use the square root because in the proportion BD Is repeated two times. If we don’t use it, we find BD^2

Answer:

ok

Step-by-step explanation:

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

Answer: A. the total kinetic energy of all particles in a substance

Step-by-step explanation:

Answer:

A. The total kinetic energy of moving particles of matter is called thermal energy.

Step-by-step explanation:

Thermal energy refers to the energy contained within a system that is responsible for its temperature. Heat is the flow of thermal energy. A whole branch of physics, thermodynamics, deals with how heat is transferred between different systems and how work is done in the process (see the 1ˢᵗ law of thermodynamics).

In the context of mechanics problems, we are usually interested in the role thermal energy plays in ensuring conservation of energy. Almost every transfer of energy that takes place in real-world physical systems does so with efficiency less than 100% and results in some thermal energy. This energy is usually in the form of low-level thermal energy. Here, low-level means that the temperature associated with the thermal energy is close to that of the environment. It is only possible to extract work when there is a temperature difference, so low-level thermal energy represents 'the end of the road' of energy transfer. No further useful work is possible; the energy is now 'lost to the environment'.

\(X = B(C^{-1})^2 - A\) is a solution to the invertible matrices equation \(C^{-1}(A+X)B^{-1}=I_n\).

We can begin by multiplying both sides of the equation by\((A+X)B^{-1}\):

\(C^{-1}(A+X)B^{-1}(A+X)B^{-1} = I_n(A+X)B^{-1}\)

Simplifying the left-hand side, we get:

\(C^{-1}(A+X)B^{-1}(A+X)B^{-1} = C^{-1}(A+X)(A+X)^{-1}C^{-1} = C^{-1}C^{-1} = (C^{-1})^2\)

Simplifying the right-hand side, we get:

\(I_n(A+X)B^{-1} = (A+X)B^{-1}\)

When we plug these values back into the original equation, we get:

\((C^{-1})^2 = (A+X)B^{-1}\)

Multiplying both sides by B, we get:

\(B(C^{-1})^2 = A+X\)

When we return to the original equation, we get:

\(C^{-1}(B(C^{-1})^2)B^{-1} = I_n\)

Simplifying, we get:

\((C^{-1})^2 = (C^{-1})^2\)

This is a true statement, so the equation has a solution,\(X = B(C^{-1})^2 - A\).

To solve the equation C^{-1}(A+X)B^{-1}=I_n, we first multiplied both sides by \((A+X)B^{-1}\) and simplified the equation to get \((C^{-1})^2 = (A+X)B^{-1}\). We then multiplied both sides by B and substituted the result back into the original equation to get \(C^{-1}(B(C^{-1})^2)B^{-1} = I_n\). Simplifying this equation, we got \((C^{-1})^2 = (C^{-1})^2\), which is a true statement. Therefore, the equation has a solution, X = \(B(C^{-1})^2 - A\).

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The smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

The nullity of a matrix is the dimension of its null space, which represents the set of vectors that satisfy the equation A * x = 0, where A is the matrix and x is a vector.

The nullity of a matrix can range from 0 to the number of columns in the matrix. In this case, since A is a 3 x 8 matrix, the minimum possible value of nullity(A) is 0, indicating that the null space is trivial and contains only the zero vector. This occurs when the matrix is full rank, meaning that its columns are linearly independent.

On the other hand, the maximum possible value of nullity(A) is 8, which would occur if the matrix has rank 0. In this case, all the columns of the matrix are linearly dependent, and the null space spans the entire vector space of size 8.

Therefore, the smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

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Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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Answer:

Step-by-step explanation:

perp. 1/4

y + 4 = -1/4(x - 4)

y + 4 = -1/4x + 1

y = -1/4x - 3

Answer:

Step-by-step explanation:

(-5 + 2)/(4 + 2) = -3/6 = -1/2

y + 2 = -1/2(x + 2)

y + 2 = -1/2x - 1

y = -1/2x - 3

Answer: y= -1/2x -3

Step-by-step explanation: you just have to do -5- (-2) over 4-(-2) when u divide these two you should get the slope. When you get the slope pick one of the coordinates in your questions and plug them in as Mx + b form.

Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

To find the probability that an individual's systolic blood pressure will be between 118.2 and 120 mmHg, we need to calculate the z-scores for these values

Then find the corresponding probabilities using the standard normal distribution. Step 1: Calculate the z-scores for the given values. The z-score formula is: z = (x - μ) / σ. where: z = z-score.  x = individual's blood pressure. μ = mean systolic blood pressure (120 mmHg). σ = standard deviation (5.6). For 118.2 mmHg: z1 = (118.2 - 120) / 5.6.  For 120 mmHg: z2 = (120 - 120) / 5.6. Step 2: Find the probabilities corresponding to the z-scores. Using a standard normal distribution table or calculator, we can find the probabilities corresponding to the z-scores calculated in Step 1. P(118.2 < x < 120) = P(z1 < z < z2). Please note that in this case, since z1 and z2 are both 0, the probability will be zero.

Therefore, the probability that an individual's systolic blood pressure will be between 118.2 and 120 mmHg is approximately 0.

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The number 2 in 239 is replaced by 5 and we get the greatest product as 539 x 86 = 46354

Given,

239 x 86

We have to replace one digit with 5 to create the greatest possible product.

Lets see;-

239 x 86 = 20554

Now change numbers

539 by replacing 2.

259 by replacing 3

235 by replacing 9.

56 by replacing 8

85 by replacing 6.

Now,

The largest number among this is 539.

And probably it will create a greatest product.

So,

The number 2 in 239 is replaced by 5 and we get the greatest product as 539 x 86 = 46354

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Answer:

A. 1.99 ounces

Step-by-step explanation:

Ramsey's weights is less than gerbil so if gerbil weights is 2.04 so  B is 2.3 is not correct C and D are not less than Ramsey's weights so the answer is A

The equivalent equation after combining like terms is x-7=1. To solve this equation, simply add 7 to both sides of the equation and you will get x=8.

An equivalent equation is an equation that is mathematically equal to another equation, meaning that both equations have the same solutions. For example, the equation "2x + 5 = 11" is equivalent to the equation "2x = 6". Both equations have the same solution, x = 3.

This is done by subtracting 2x from both sides, and then adding 9 to both sides. Doing so eliminates the -2x and -9 terms, leaving just x on one side, and 7 on the other. Combining like terms is a useful way to simplify equations, and it is important to understand how to do it in order to solve more complex equations.

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Answer:

c.

Step-by-step explanation:

it's been a while since I've done this but I'm about 90% sure

Answer:

C)

Step-by-step explanation:

one is zero and one is positive. The addition symbol indicates that you are adding a positive number

Answer:

A base

Step-by-step explanation:

its not an acid bc a ph level of 14 means is has a strong base.

a) The size of angle c is 128°

b) The angle fact shows that angle c and angle d are equal is "alternate angles are equal".

In geometry, an angle is the figure formed by two rays (i.e. the sides of the angle) sharing a common endpoint (i.e. vertex).

Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.

a) The size of the angle can be determined as follow:

52° + c = 180° (The sum of angles on a straight line is 180°)

c = 180 - 52

c = 128°

b) The angle fact shows that angle c and angle d are equal is "alternate angles are equal".

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Complete Question

Check image

Answer:

No they are not equivalent.

Step-by-step explanation:

2(x - 2) + 3

First distribute the 2. It goes to both the x and also to the - 2

= 2x - 4 + 3

Add - 4 + 3

= 2x - 1

This is not equal to 2x - 7

The request is to download a document and complete the proof of the Triangle Sum Theorem. After finishing the proof, the completed file should be saved for upload on a webpage.

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. To complete the proof, it is necessary to provide a logical and coherent argument that supports this theorem. The document provided likely contains a partially completed proof, and the task is to finish it.

The proof of the Triangle Sum Theorem typically involves using the properties of parallel lines and alternate interior angles. By extending one side of the triangle, parallel lines can be created that intersect with the other sides. This forms interior and exterior angles that can be related to the interior angles of the triangle. Through geometric reasoning and the use of angle relationships, the proof should demonstrate that the sum of the interior angles of a triangle equals 180 degrees.

Once the proof is completed, the document should be saved for upload on the webpage specified, most likely for evaluation or further review. It is important to follow any instructions provided regarding the file format or naming conventions for the upload.

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Answer:

Add a three more zeros at the end

Step-by-step explanation: 34.624*1000=34,624

This is scientific notation. . .

In other words, you would move the decimal point of the term being mutliplied by 10^3 to the right three times.