Determine the cubic function obtained from the parent function y=x³ after each sequence of transformations.

a vertical stretch by a factor of 6 ; and a translation 3 units left.

Answer:

3 to the power of 7 is 2,187.

Step-by-step explanation:

3x3x3x3x3x3x3=2,187

The correct value by using calculator to evaluate sin(91°), sin(91°) is approximately 0.99., sin(91°) ≈ 0.99.sec(pi/5), we find that sec(pi/5) is approximately 1.38.Therefore, sec(pi/5) ≈ 1.38.

Evaluating sin(91°):

The sine function (sin) relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. When we input 91° into the sine function, we get sin(91°). Using a calculator, we find that sin(91°) is approximately 0.99, rounded to two decimal places.

Evaluating sec(pi/5):

The secant function (sec) represents the reciprocal of the cosine function. In this case, we have sec(pi/5), which means we need to find the value of the cosine of pi/5 first. The value of pi/5 represents an angle in radians. Using a calculator, we find that cos(pi/5) is approximately 0.81, rounded to two decimal places. Taking the reciprocal of this value, we get 1/cos(pi/5), which is equal to sec(pi/5). Evaluating it using a calculator, we find that sec(pi/5) is approximately 1.38, rounded to two decimal places.Therefore, sin(91°) is approximately 0.99, and sec(pi/5) is approximately 1.38.

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Answer:

y+2=1/6x(x-4)

Step-by-step explanation:

An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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\(\large \mathfrak{Solution : }\)

let's solve for b :

Answer:

B

Step-by-step explanation:

because 10 and 11 are not equal, therefore, when you add 10 then subtract 11, you will not end up with your original number

Answer:

Deposit $10, then withdraw $11.

Step-by-step explanation:

If you have $10 and you take away $11. You balance a of -1. Which is not zero.

It's (8,-2), (5,-1), (2,0), (-1,1), (-4,2).  Just took it and suffered the fate of the wrong answer.

Answer:

C

Step-by-step explanation:

The numbers in this problem are classified as follows:

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The amount of titanium in 1508 grams of alloy will be 527.8 grams.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The alloy is 35% titanium.

If there are 1508 grams of other elements in the alloy.

Then the amount of titanium in 1508 grams of alloy will be

⇒ 35% of 1508

⇒ 0.35 x 1508

⇒ 527.8 grams

The amount of titanium in 1508 grams of alloy will be 527.8 grams.

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At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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The expression in terms of k, m, and n that represents the amount of data needed to represent the rank-k approximation is:

Data needed = (m + n) * k + k

What is expression?

In mathematics, an expression is a combination of numbers, variables, operators, and mathematical symbols that represents a mathematical relationship or computation.

To represent a rank-k approximation of a matrix, we need to determine how much data is needed.

Let's consider a matrix A of size m x n, where m represents the number of rows and n represents the number of columns. The rank-k approximation of matrix A can be obtained by decomposing it using a technique such as Singular Value Decomposition (SVD) and then truncating the decomposition to keep only the k largest singular values and corresponding singular vectors.

In SVD, matrix A is decomposed as \(A = U\sum V^T\), where U is an m x k matrix, Σ is a k x k diagonal matrix containing the singular values, and \(V^T\) is the transpose of an n x k matrix.

To represent the rank-k approximation, we need to store the matrices U, Σ, and \(V^T\).

The storage requirements for each of these matrices are as follows:

Matrix U: m x k matrix, which requires m * k data elements.

Matrix Σ: k x k diagonal matrix, which requires k data elements on the diagonal and zero elements elsewhere. Therefore, Σ requires k data elements.

Matrix \(V^T\): n x k matrix, which requires n * k data elements.

Therefore, the total amount of data needed to represent the rank-k approximation is given by:

Data needed = Data for U + Data for Σ + Data for \(V^T\)

Data needed = m * k + k + n * k

Hence, the expression in terms of k, m, and n that represents the amount of data needed to represent the rank-k approximation is:

Data needed = (m + n) * k + k

Please note that this expression assumes that the data elements are represented in a standard numerical format that requires a fixed amount of memory per element. Actual storage requirements may vary depending on the specific implementation or data representation used.

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As per direct variation,

Part A) Decorators fee is $198.132

Part B) Tax for the purchase is $71.10

Part C) The total amount spend by the family is $1849.232.

Direct variation:

Direct variation depicts a simple relationship between two variables . We say y varies directly with x if:

y=kx

for some constant kk , called the constant of variation or constant of proportionality. Which means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

Given,

A family used a professional decorator to furnish their new home.

The decorator selected $1,580 worth of furnishings for their home.

The payment will be made by the family for the furnishings, plus 4.5% tax on the purchases.

The decorator’s fee was 12% of the furnishings , excluding the tax.

Here we need to find the following:

Part A) Decorator's fee

Part B) Tax amount

Part C) Total cost.

We know that, the decorator’s fee was 12% of the purchases.

So, the equation is then be calculated as:

y = kx

where,

y = decorators fee

k = percentage of decorators fee for the purchases

x = amount paid

y = 12% × $1651.10

= 0.12 × $1651.10

Therefore, the decorators fee is $198.132

Decorator selected furnishings cost = $1,580.

Tax = 4.5%

Decorator’s fee = 12% of the purchases.

So, it can be calculated as,

Tax = 4.5% × 1580

Tax = 0.045 × 1580

Therefore, the tax for the purchase is $71.10

Amount paid = 1580 + 71.10 = 1651.10

Now, the total amount paid by the family is,

=> purchase amount + decorator fee

=> 1651.10 + 198.132

=> 1849.232

Therefore, the total amount spend by the family is $1849.232.

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Answer: Tiffany can be certain the trapezoids are congruent.

Step-by-step explanation: Two figures are congruent when their corresponding angles are equal and they have the same shape and size.

A figure can go thorugh 3 types of transformations:

As long the figure doesn't change its size or shape, it doesn't matter if it's rotated, reflected or translated, they will be congruent.

When the trapezoid was rotated creating another one, the two shapes didn't change its size or shape, so Tiffany can be certain they are congruent.

Answer:

Looks to confusing for me sorry tho

Step-by-step explanation:

Bisect each angle of the triangle using a compass then where the lines the have been bisected meet up, from there, put the the compass and then your pencil tip on the perimeter of the triangle and draw a circle

Estimation involves using a convenient value, close to the actual value, for calculations; especially in the absence of a calculator. The estimated number of gallons she needs to get to the station is 3 gallons.

Given that:

\(Speed= 70mph\)

\(Time = 1.25hr\) ---- equivalent of 1hr 15mins

\(Rate = 30 m/gallon\)

First, she will need to estimate the distance she can cover using:

\(Distance= Speed \times Time\)

An estimate of the calculation is:

\(Distance= 70mph \times 1.5 = 105m\)

The number of gallons is then estimated as follows:

\(Gallons = D ista nce\div Rate\)

Because the estimated distance is 105 m; she can use 35 as an estimate the rate of miles per gallon; instead of 30

\(Gallons = 105m \div 35m/gallon\)

\(Gallons = 3gallon\)

So, the estimated number of gallons she needs is 3 gallons.

We can check if the estimate is true or close by calculating the actual values.

\(Distance= Speed \times Time\)

\(D i s t a n c e= 70mph \times 1.25hr=87.5m\)

\(Gallons = D ista nce\div Rate\)

\(Gallons = 87.5m \div 30m/gallon =2.92m\)

Hence, the estimated number of gallons she needs to get to the station is 3 gallons.

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The first five terms of the sequence are {-9, 54, -324, 1944, -11664}.Hence, the first five terms of the sequence are {-9, 54, -324, 1944, -11664}.

Given that a1 = -9 and an = -6an-1 to find the first five terms of an: {a1, a2, a3, a4, a5}

We have to use the formula an = -6 an-1 to find the next terms.

The first term a1 is given to us. So, a1 = -9

We can use the formula an = -6an-1 to find the next term using a1= -9 an1 = -6 * a1 = -6 * (-9) = 54

Thus the first two terms of the sequence are {-9, 54}.

We can use the formula an = -6an-1 to find the third term an2 = -6 * an1= -6 * 54 = -324

Thus the first three terms of the sequence are {-9, 54, -324}.

We can use the formula an = -6an-1 to find the fourth term an3 = -6 * an2= -6 * (-324) = 1944

Thus the first four terms of the sequence are {-9, 54, -324, 1944}.

We can use the formula an = -6an-1 to find the fifth term an4 = -6 * an3= -6 * (1944) = -11664

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The number of students age 15 and above take a bus to school are 50. Therefore, the correct answer is option B.

Total number of students Age 15 and above are 195.

Number of students who travel in bike or walk of Age 15 and above are 65.

Total number of students who travel in bus are 110.

The number of students under the Age 15 who travel in bus are 60.

The number of students above the Age 15 travel in bus = 110-60

= 50

Therefore, the correct answer is option B.

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6(x-3)=3x+9

6x-18=3x+9

6x-3x=18+9

3x=27

x=27 ÷3

x=9

Hope this will help you

The solution is x = 9, which is an option (B).

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Let's simplify the equation by distributing 6 on the left-hand side:

6x - 18 = 3x + 9

Now, let's isolate the x terms on one side and the constant terms on the other side:

6x - 3x = 9 + 18

3x = 27

x = 9

Therefore, the solution to the equation 6(x - 3) = 3x + 9 is x = 9, which is option B.

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Answer: 0.69

Step-by-step explanation:

0.44 + 0.25 = 0.69

The correct answer is \(\boxed{0.69}\)

For this question we will be adding the numbers given.

Given:

\(0.44\\0.25\)

Therefore, the equation is:

\(\boxed{0.44 +0.25}\)

Therefore, the correct answer is \(\boxed{0.69}\)

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

Rs 1400

Step-by-step explanation:

Let us take the required number be x. According to question ,

=> 25% of x = Rs 350

=> 25/100 × x = Rs 350

=> x = Rs 350 × 100 / 25

=> x = Rs 1400

Answer:

2x - 3y + 9 = 0 which is the first option

Step-by-step explanation:

We make use of the fact that the diagonals of a square bisect each other at right angles

In other words, diagonal BD is perpendicular to diagonal AC

Equation of AC = 3x + 2y - 7 = 0

Convert this standard form to slope-intercept form

3x + 2y - 7 = 0

Answer
2x - 3y + 9 = 0 which is the first option

Answer:

Step-by-step explanation:

x       - the first of consecutive integers

x+1   - the second of consecutive integers

x+2  - the third of consecutive integers

x+x+2  - sum of the first and third integers

3(x+x+2)  - three times the sum of the first and third integers

3(x+x+2) = -342

  ÷3             ÷3

2x + 2 = -114

  -2            -2

 2x = -116

 ÷2     ÷2

   x = -58

x+1 = -58 + 1 = -57

x+2 = -58 + 2 = -56

If "water-sprinkler" sends out water 21 feet in any direction in circular pattern, then the area formed by water pattern is 1384.74 feet².

If the sprinkler can spray water out 21 feet in any direction, then the radius of the circular pattern formed by the water is 21 feet.

The formula for area of circular pattern is : A = πr², where 'r" is = radius of the circle.

Substituting the radius of circular pattern as 21 feet,

We get,

⇒A = πr² = 3.14 × 21 × 21 = 1384.74 ft².

Therefore, the area formed by the water pattern is 1384.74 square feet.

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Suppose that the number u were thinking about is x thus :

\( \frac{1}{4} x + \frac{1}{2} x = 12 \\ \)

Multiply both sides by 4

\(4 \times ( \frac{1}{4} x + \frac{1}{2} x) = 4 \times 12 \\ \)

\(x + 2x = 48\)

\(3x = 48\)

Divide both sides by 3

\( \frac{3x}{3} = \frac{48}{3 } \\ \)

\(x = 16\)

False, The eigenvalues of a matrix A are not same as the eigenvalues of the reduced row echelon form of A.

A matrix's eigenvalues are not the same as those of the matrix's reduced row echelon form, contrary to what is claimed.

This is due to the fact that when a matrix is reduced to its echelon form via row operations, its eigenvalues may not always stay the same. The eigenvalues of a matrix may be different in the reduced row echelon form than they are in the original matrix as a result.

Think about these matrices as an illustration:

Likewise, B's reduced row echelon form is B, and B's eigenvalues are both 1.

A = [1 2; 2 1]

and

B = [1 0; 0 1].

The eigenvalues of a matrix and its reduced row echelon form are thus typically not the same.

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FALSE. The eigenvalues of a matrix A are NOT the same as the eigenvalues of the reduced row echelon form of A.

Explanation:

Eigenvalues are scalar values that, when multiplied by an eigenvector, produce the same effect as the original matrix A on that eigenvector. Mathematically, for a matrix A and its eigenvector v, Av = λv, where λ is the eigenvalue.

Row echelon form is a matrix transformation using elementary row operations to obtain a triangular form. The reduced row echelon form (RREF) is a further simplified version of the row echelon form.

However, transforming a matrix A to its RREF changes the properties of the matrix, and therefore the eigenvalues of matrix A and its RREF are generally not the same. The eigenvalues are preserved only under specific matrix transformations, such as similarity transformations, which row echelon form is not one of them.

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Answer:

TN/TS=NM/RS

\( \frac{240}{120} = \frac{x}{70 } \\ 120x = 16800 \\ x = 140\)