Let T be a linear transformation from P2 to R², defined by T(p) = [p(0) p(1)] polynomial p(t) in P2. Find bases for kernel of T and range of T.

The stack grows downwards in memory, meaning that as new variables are added, they are allocated at lower memory addresses compared to previously allocated variables.

Regarding whether variables stored on the stack can have the same address as other variables, it is possible but highly unlikely. Each variable on the stack is typically allocated a unique memory address. The compiler and the underlying system manage the allocation of memory for variables on the stack to ensure that they do not overlap or share the same address.

However, it's worth noting that certain scenarios, such as when using recursion or nested function calls, may lead to temporary overlapping of stack frames. In such cases, variables within different stack frames may have the same relative addresses, but they still have distinct absolute addresses within their respective stack frames.

In general, the stack is organized in a way that ensures variables have distinct addresses to maintain proper memory isolation and prevent unintended data corruption.

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Answer:

  1856 ft²

Step-by-step explanation:

You want the surface area of an isosceles triangular prism 23 ft long with a triangle base of 24 ft and a height of 16 ft.

The area of the two triangles is ...

  A = 2 × 1/2bh = bh

  A = (24 ft)(16 ft) = 384 ft²

The area of the three rectangular sides is ...

  A = LW

  A = (24 ft + 20 ft + 20 ft)(23 ft) = 64·23 ft² = 1472 ft²

The surface area of the prism is the sum of the base area and the lateral area:

  A = 384 ft² +1472 ft² = 1856 ft²

The surface area of the prism is 1856 square feet.

__

Additional comment

We recognize each of the smaller right triangles that make up one base is a 3-4-5 right triangle with a scale factor of 4 ft. That makes the hypotenuse exactly 20 ft, as shown in the diagram.

The lateral area is effectively the product of the prism length (23 ft) and the perimeter of the triangular base.

<95141404393>

9514 1404 393

Answer:

  16.4

Step-by-step explanation:

The law of cosines is useful here. It tells you ...

  b^2 = a^2 + c^2 -2ac·cos(B)

  b^2 = 22^2 +10^2 -2·22·10·cos(44°)

  b^2 ≈ 267.49

  b ≈ √267.49 ≈ 16.35514

  b ≈ 16.4

Answer:

give me the rest of the question/ a picture or something then i can answer

Step-by-step explanation:

Una caja de ahorros ofrece a sus clientes un interés simple del 8% anual por una imposición de 18.000 € durante 5 años. de los Interés es = 7,200 €

Interés = Principal × Tasa de interés × Tiempo

Dado que el principal es de 18.000 €, la tasa de interés es del 8% anual y el tiempo es de 5 años, podemos sustituir estos valores en la fórmula:

Interés = 18,000 € × 0.08 × 5

Interés = 7,200 €

Por lo tanto, el importe de los intereses generados en ese tiempo es de 7.200 €. Esto significa que al finalizar los 5 años, el cliente habrá obtenido 7.200 € adicionales como resultado de la imposición de 18.000 € con una tasa de interés del 8% anual. Es importante tener en cuenta que este cálculo se basa en la suposición de que el interés es simple y no se acumula ni se reinvierte.

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\(\text{If the number is x,}\\\\~~~~10\% \cdot x = 16\\\\\implies \dfrac{10x}{100} = 16\\\\\implies \dfrac x{10} = 16\\\\\implies x = 160\\\\\text{Hence,}~ 5\% \text{ of}~ 160 = \dfrac{5 \times 160}{100}=8\)

Answer:

y=3x-6

Step-by-step explanation:

formula for alope intercept for is

y=mx+b

m is slope

b is y-intercept

The value that is a solution to f(x) = g(x) is x = 4.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: f(x) = −x² + 4x + 12

g(x) = x + 8,  x = 1 x = 2 x = 3 x = 4 x = 5 x = 6

We have to find the value that is a solution to f(x) = g(x).

When x = 1

f(1) = −(1)² + 4(1) + 12

f(1) = -1 + 4 + 12

f(1) = 15

g(1) =  1 + 8

g(1) = 9

f(1) ≠ g(1)

When x = 2

f(2) = −(2)² + 4(2) + 12

f(2) = -4 + 8 + 12

f(2) = 16

g(2) = 2 + 8

g(2) = 10

f(2) ≠ g(2)

When x =3

f(3) = −(3)² + 4(3) + 12

f(3) = -9 + 12 + 12

f(3) = 15

g(3) = 3 + 8

g(3) = 11

f(3) ≠ g(3)

When x = 4

f(4) = −(4)² + 4(4) + 12

f(4) = -16 + 16 + 12

f(4) = 12

g(4) = 4 + 8

g(4) = 12

f(4) = g(4)

When x = 5

f(5) = −(5)² + 4(5) + 12

f(5) = -25 + 20 + 12

f(5) = -5 + 12

f(5) = 7

g(5) = 5 + 8

g(5) = 13

f(5) ≠ g(5)

When x = 6

f(6) = −(6)² + 4(6) + 12

f(6) = -36 + 24 + 12

f(6) = 0

g(6) = 6 + 8

g(6) = 14

f(6) ≠ g(6)

Hence, the value that is a solution to f(x) = g(x) is x = 4.

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Answer:

Solution:

x + 2y = 5

Put the value of x = 0 in the equation x + 2y = 5

0 + 2y = 5

2y = 5

2y/2 = 5/2

y = 5/2

(0, 5/2)

Put the value of y = 0,

x + 2 × 0 = 5

x = 5

(5, 0)

Put the value of x = 2,

2 + 2y = 5

2 – 2 + 2y = 5 - 2

2y = 3

2y/2 = 3/2

y = 3/2

(2, 3/2)

Put the value of y = 2,

x + 2 × 2 = 5

x + 4 = 5

x + 4 – 4 = 5 – 4

x = 1

(1, 2)

Table Value

6Save

Step-by-step explanation:

Answer:

22x2 -  9x) -  9

Trying to factor by splitting the middle term

   Factoring  4x2-9x-9  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -9  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -9 = -36  

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -9 .

     -36    +   1  =  -35  

     -18    +   2  =  -16  

     -12    +   3  =  -9  

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  3  

                    4x2 - 12x + 3x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4x • (x-3)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-3)

Step-5 : Add up the four terms of step 4 :

                   (4x+3)  •  (x-3)

                                 Hope this helps!

The distance between the trees is 48 cm.

To determine the distance between the trees, we need to consider the lengths of the footsteps and the dad. Let's assume that the person takes one step with each foot, resulting in a total stride length equal to the sum of the lengths of both footsteps.

Given:

Length of each footstep = 60 cm

Length of the dad = 72 cm

The total stride length would be:

Total stride length = 2 * length of each footstep

= 2 * 60 cm

= 120 cm

To calculate the distance between the trees, we subtract the length of the dad from the total stride length:

Distance between the trees = Total stride length - Length of the dad

= 120 cm - 72 cm

= 48 cm

Therefore, the distance between the trees is 48 cm.

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Answer: y = \(\frac{5}{3}\)x + 14 \(\frac{5}{3}\)

Step-by-step explanation:

      First, we will transform the given equation into slope-intercept form. To do this, we will isolate the y-variable.

             -5x + 3y = 6

             3y = 5x + 6

             y = \(\frac{5}{3}\)x + 2

      A parallel line will have the same slope as the given line. To solve for the y-intercept, we will input the given coordinate point and solve.

             y = \(\frac{5}{3}\)x + b

             (14) = \(\frac{5}{3}\)(-1) + b

             (14) = -\(\frac{5}{3}\) + b

             14 \(\frac{5}{3}\) = b

             y = \(\frac{5}{3}\)x + 14 \(\frac{5}{3}\)

      We can also graph the two lines and the given coordinate point. You can see the equation we wrote goes through the coordinate point (-1, 14) and is parallel to -5x + 3y = 6.

Answer:

  5x -3y = -47

Step-by-step explanation:

You want the equation of the line through point (-1, 14) that is parallel to -5x +3y = 6.

The equation of a parallel line can be found by leaving the x- and y-coefficients alone, and finding the constant that makes the equation be true at the given point. Substituting the point coordinates for x and y, we have ...

  -5(-1) +3(14) = 5 +42 = 47

Making the constant be 47 will give the desired equation:

  -5x +3y = 47

The equation is written in standard form when the leading coefficient is positive:

  5x -3y = -47 . . . . . . multiply the above equation by -1

<95141404393>

Step-by-step explanation:

Using cosine rule,

f² = g² + e² - 2(g)(e)(cosF) = 6.7² + 5.9² - 2(6.7)(5.9)(cos70°)

= 52.6598 in²

Hence f = 7.3 in.

The length of f in the triangle EFG is 7.3 inches.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Given that, in ΔEFG, g = 6.7 inches, e = 5.9 inches and ∠F=70°.

By using cosine rule in ΔEFG, we get

f² = e² + g² − 2eg·cos70°

= 5.9²+6.7²-2×5.9×6.7×0.342

= 79.7-27.03852

f² = 52.66148

f = 7.3 inches

Therefore, the length of f is 7.3 inches.

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Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

Answer: here it is

Step-by-step explanation:

Statement A is an example of inductive statement, whereas, statement B is a example of deductive statement.

Inductive reasoning is a method of reasoning in which a body of observations is considered to derive a general principle. It consists of making broad generalizations based on specific observations.

For example,

The last few times I’ve driven past the beach on a sunny day, the parking lot was nearly full. Therefore, on sunny days, the beach parking lot will be nearly full.

Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false.

For example,

On Thursdays, the trash gets picked up at the curb of the driveway. Today is Thursday. Therefore, the trash will get picked up at the curb of the driveway today.

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The sampling distribution of the sample mean of the observations on the amount of nitrogen removed by the four buffer strips with widths of 6 feet is the theoretical probability distribution of all possible sample means that could be obtained by randomly selecting samples of size 6 from the population of nitrogen removal observations.

Assuming the sample means are normally distributed, the mean of the sampling distribution of the sample means would be equal to the population mean of nitrogen removal by the buffer strips, while the standard deviation would be equal to the population standard deviation divided by the square root of the sample size.

The Central Limit Theorem states that, as the sample size increases, the sampling distribution of the sample means becomes increasingly normal, regardless of the distribution of the original population. This means that, if we take enough samples of size 6, the distribution of their means will approach a normal distribution.

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Answer:

A. 7,6,14

Step-by-step explanation:

Rules for side lengths of triangle.

1. Any side should be less then the sum of the other two angles.

2. The same side should be greater than the subtraction of the other side lengths(bigger side - smaller side)

A.

7 < 6+14 .  Correct

7> 14-6 .     Incorrect

This cannot be a solution (impossible)

B.

4<4+4 .  Correct

4>4-4 .  correct

This is a solution (equilateral triangle)

C.

6<6+2 .  Correct

6>6-2 .  Correct

This is a solution (isosceles triangle)

D.

7<8+13 . Correct

7>13-8 . Correct

This is a solution (scalene triangle)

If my answer is incorrect, pls correct me!

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-Chetan K

To find the fully factored form, we look for the greatest common factor (GCF) among the terms. The fully factored form of \(32a^{3}\) - \(12a^{2}\)is \(4a^{2}\)(8a - 3).

In this case, the GCF is \(4a^{2}\). We can factor it out by dividing each term by the GCF.

When we divide \(32a^{3}\) by \(4a^{2}\), we get 8a. Similarly, when we divide \(-12a^{2}\)by \(4a^{2}\), we get -3. Therefore, the fully factored form of \(32a^{3}\) - \(12a^{2}\) is \(4a^{2}\)(8a - 3).

The factored form represents the expression as a product of its factors. In this case, we have factored out the GCF, \(4a^{2}\), and left the remaining terms inside parentheses. This form allows us to simplify and work with the expression more easily. By factoring out the common factor, we can also identify any common terms or patterns in the expression.

It is important to note that factoring is a useful technique in algebra to simplify expressions and solve equations. It helps in identifying and manipulating common factors, which can aid in further calculations and problem-solving.

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Answer:

One ticket is $153

Step-by-step explanation:

x = The price of a ticket

855=5x+18(5)

855=5x+90

765=5x

153=x

Answer:

x = $159

Step-by-step explanation:

5 tickets are bought, the price of them is unknown?

1 ticket per $18 travel insurance

5 tickets = 18 × 5

insurance per 5 tickets = $90

the equation:

let X represent the number of tickets.

5x + 90 = 885. the total cost of insurance and tickets = 885

we solve the equation.

5x=885 - 90

5x= 795. divide by 5 into both sides.

x= $159. which is the price of one ticket.

Answer: \(\frac{7}{20}\)

Step-by-step explanation: Just enter 0.35 into a calculator and press enter :)

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Answer:

same but like 123

Step-by-step explanation:

Answer:

the slope represents minutes per miles.

Step-by-step explanation:

the other 3 are wrong

Answer:

Step-by-step explanation:

ANSWER:

14

EXPLANATION:

Given that a number is multiplied by seven, and the product is increased by two, the result is one hundred.

Let's express this mathematically(equation).

Let the number be represented by X.

A number X is multiplied by seven = 7X

The product is increased by 2 = 7X + 2

The result is 100 = 7X + 2 = 100

We have:

7X + 2 = 100

Solve for X:

Subtract 2 from both sides:

7X + 2 - 2 = 100 - 2

7X = 98

Divide both sides by 7:

Therefore the number is 14

The power \( m \) in the Paris' crack propagation rate equation for the 7075-T6 alloy is 3.63, and the pre-exponential constant \( A \) is 0.29 x 10^(-9) MPa.m^(0.5). By analyzing this data, the values of \( m \) and \( A \) can be obtained.

Paris' crack propagation rate equation relates the crack growth rate da/dN to the stress intensity factor range \(\Delta K\) during fatigue loading. It can be expressed as da/dN = A(\Delta K)^m, where \( A \) is the pre-exponential constant and \( m \) is the power. To determine \( m \) and \( A \), the equation requires experimental data. Figure 3 likely represents the experimental data for crack growth rate versus stress intensity factor range.

For the 7075-T6 alloy, the power \( m \) in Paris' equation is 3.63, and the pre-exponential constant \( A \) is 0.29 x 10^(-9) MPa.m^(0.5). These values describe the relationship between crack growth rate and stress intensity factor range. By analyzing this data, the values of \( m \) and \( A \) can be obtained.

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