Please answer the following question on linear algebra.

Answer:

I belive it’s C

Step-by-step explanation:

I don’t know if it’s correct tell me if I’m wrong

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Solve Absolute Value.

|6x + 3| = 15

We know either 6x + 3 =15 or 6x + 3 = −15

================================================================

6x + 3 = 15 (Possibility 1)

6x + 3 - 3 = 15 − 3 (Subtract 3 from both sides)

6x = 12

\(\boldsymbol{\sf{\dfrac{6x}{6}=\dfrac{12}{6} \ \longmapsto \ (Divide \ both \ sides \ by \ 6) }}\)

x = 2

=================================================================

6x + 3 = −15 (Possibility 2)

6x + 3 - 3 = -15 - 3 (Subtract 3 from both sides)

6x = -18

\(\boldsymbol{\sf{\dfrac{6x}{6}=\dfrac{-18}{6} \ \longmapsto \ (Divide \ both \ sides \ by \ 6) }}\)

x = -3

Therefore, the answer is x = 2 or x = −3. The correct option is alternative "D".

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

To calculate the mean of a given set of data, you need to follow these steps:
1. Add up all the numbers in the data set.
2. Divide the sum by the number of items in the data set.

The mean is a measure of central tendency that represents the average value of a set of numerical data. It is also known as the arithmetic mean or simply the average. To calculate the mean, you add up all the values in a set of data and then divide by the number of values.

Here is an example:

Data set: 5, 8, 10, 12, 15

Step 1: Add up all the numbers: 5 + 8 + 10 + 12 + 15 = 50
Step 2: Divide the sum by the number of items in the data set: 50 ÷ 5 = 10

The mean of this data set is 10.

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Answer:

x=6

Step-by-step explanation:

Answer:

x-10=6 here is the right answer

Answer:

The correct equation for this situation is: 27 = j + 9, where j represents the number of shells Jamie has collected.

To find out how many shells Jamie has collected, we need to solve this equation for j:

27 = j + 9

Subtracting 9 from both sides of the equation:

27 - 9 = j + 9 - 9

18 = j

Therefore, Jamie has collected 18 shells.

So, the correct answer is A) 27 = j + 9; Jamie collected 18 shells.

Step-by-step explanation:

The solution of the expression \(\sqrt{z^4\times z^{\frac{-3}{2}}\) will be z⁵.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The expression will be solved as:-

\(E = \sqrt{z^4\times z^{\frac{-3}{2}}\)

\(E = \sqrt{(z)^{4- {\frac{3}{2}\)

E = z⁵

Therefore, the solution of the expression is z⁵.

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The ratio of dogs to cats at the

pet store is 2:5. If there are 6 more

cats than dogs, how many dogs are

at the pet store?

Dogs : 2

Cats : 5

-1

5 - 2 = 3,

-1, 0, 1, 2, 3, 4, 5

1 - 5 will give us a 6

Answer:

θ =  60 degrees

If needed in radians:

θ = π/3

Step-by-step explanation:

2cos(θ) = 1

We are solving for theta.

We can divide 2 on both sides.

2cos(θ) = 1

/2             /2

cos(θ) = 1/2

Now we can use Inverse of cosine to isolate theta.

θ \(= cos^-^1(1/2)\)

θ =  60 degrees

If needed in radians:

θ = π/3

To solve the question, we will apply the principle

If the sides are not equal, the sum of the two shortest sides must be greater than the longest sides

For option A

3 cm, 3cm, 3cm

All sides are equal so it satisfies the condition for a triangle

For option B

The sum of the two shorter sides (4cm and 8cm) = 12cm

while the longest side is 12cm

Since the sum of 12cm is not more than the longest side, then

the sides are NOT suitable for a triangle

For option C

5cm + 9cm = 14 cm

The longest side = 14cm

Since the sum 14cm is not greater than the longest side, then

the sides are NOT suitable for a triangle

For option D

Sum of the shorter sides = 6cm + 7cm = 13cm

longest side = 8cm

Since the sum of 13cm is greater than 8cm, then it is suitable for a triangle

For option E

Sum of shorter sides = 7cm + 7cm = 14cm

longer side = 10cm

Since the sum of 14cm is greater than 10cm, then it is suitable for a triangle

Subtract the difference form the total:

717 - 67 = 650

Divide the remaining amount by 2:

650/2 = 375

The bench cost$375

Answer:

d. The employer offers stock options, which require the employee to work for a specific amount of time before they vest.

Step-by-step explanation:

its right

Answer:

It is D

Step-by-step explanation:

Step-by-step explanation:

A. n is the number of persons excluding chaperones

B. The equation describes the situation where the total admission cost at orchard A is equal to that of B. (This happens at n=17 persons)

C. For which number of persons is orchard A cheaper than orchard B? (It will be for n is more than 17 persons, but there is no requirement to calculate this).

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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The restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.

Sale refers to the transfer of ownership of goods or services from one person to another in exchange for money or other consideration.

The total purchase price of the franchise naming rights and physical property was $1,250,000.

To calculate the amount paid for each individual element of the sale, the total purchase price must be divided by the two elements.

The total purchase price of $1,250,000 divided by two elements equals $625,000.

This means that the restaurant chain paid $625,000 for the franchise naming rights and $625,000 for the physical property.

The amount of money paid for the franchise naming rights (four times the cost of buying the physical property) can be calculated by multiplying the cost of the physical property, which is

$625,000/4 .

When the cost of the physical property is multiplied by four, the result is $2,500,000.

This means that the restaurant chain paid $2,500,000 for the franchise naming rights.

In summary, the restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.

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1) Gathering the data

Arranging 9 speakers in an array, and there's fewer than 40

Algebraically we could write

xy<40

2) Counting the 9 on the array. The other number that multiplied by 9 would be lesser than 40?

In other words, let's factor so x would be 9. The highest product between 9 and another whole number lesser than 40 is between 9 and 4

9y < 40

And y would be 4

36 < 40

2) So they have 36 speakers on the band.

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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Answer:

The smaller number is 40.

Step-by-step explanation:

The divisor is 5 + 6 = 11.

So one part = 88/11 = 8

So we need to find 5 parts and 6 parts.

The 2 numbers are:

5 * 8 = 40 and

6 * 8 = 48.

Answer:

The sample proportion of undergraduate students that used library books is 0.5286.

Step-by-step explanation:

The sample proportion is the number of desired outcomes divided by the size of the sample.

In this question:

Sample of 70 undergraduate students, 37 had used library books.

\(p = \frac{37}{70} = 0.5286\)

The sample proportion of undergraduate students that used library books is 0.5286.

Answer:

55 OZ

Step-by-step explanation:

If the length of the insect is 2.5 inches long, then the length of the insect in centimeter is 6.35 centimeter

Given,

The length of the insect = 2.5 inches

Convert inches to centimeter

We know,

1 inches = 2.54 centimeter

2.5 inches = 2.54× 2.5

=6.35 centimeter

Hence, if the length of the insect is 2.5 inches long, then the length of the insect in centimeter is 6.35 centimeter

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Considering the sequences given, the first number that appears in both sequences is given by: 45.

The rule is multiply by 3 starting from 5, hence the numbers are:

(5, 15, 45, 135, ...).

The rule is add 9 starting from 18, hence the numbers are:

(18, 27, 36, 45, ...).

45 is the first number that appeared in both sequences.

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Answer:

This is very unclear however if your miles are 214 and you need 1% of the miles you can multiply it by 0.01 and the answer would be 2.14 miles

Answer: The answer is D. the last option

Step-by-step explanation:

The correct answer is option d) The graph is the radical function, y = √x shifted right 1 unit and up 4 units.

The original function is y = √(x - 1) + 4, which represents a radical function.

This function involves taking the square root of the quantity (x - 1) and then adding 4 to the result.

By shifting the function right 1 unit, we are replacing x with (x - 1). This means that the graph will be shifted horizontally by 1 unit to the right compared to the standard square root function.

By shifting the function up 4 units, we are adding 4 to the output of the square root function.

This means that the graph will be shifted vertically by 4 units compared to the standard square root function.

Therefore, the graph of the function y = √(x - 1) + 4 is the radical function y = √x shifted right 1 unit and up 4 units.

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