Which is a sum of cubes? A^3+18, a^6+9, a^9+16, a^16+8

Answer:

1 - [tex]e^{inx}[/tex]

2 - [tex]e^{5in}[/tex]

3 - [tex]e^{in^{3} x}[/tex]

Step-by-step explanation:

The standard form of the polynomial function y = x(x + 5)(x - 3) is

y = x³ + 2x² - 15x

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The polynomial function,

y = x(x+5)(x−3)

To obtain the standard form, we need to multiply out the expression and then arrange the terms in decreasing order of the degree of the monomials. The degree of a polynomial is the highest degree of its monomials.

x(x + 5)(x - 3) = x³ + (5x²) - (3x²) + (5x²) + (-15x) = x³ + 2x² - 15x

In the standard form, the coefficient of the monomial with the highest degree is 1, and the rest of the terms are arranged in decreasing order of the degree.

Thus, the standard form is x³ + 2x² - 15x

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Answer:

Can you please post the picture of the question, then I can help.

It depends on Jack's personal preference and priorities. If he values having a large collection of comics.

Comics are visual storytelling medium that combines text and images to convey a narrative or illustrate a story. They can come in many forms, including comic books, graphic novels, manga, and webcomics, and often feature characters, settings, and events that are fictional or based on real-life events. Comics can be serious or humorous and can be aimed at a wide range of audiences, from children to adults. The format of comics allows for a unique combination of text and illustration that can create an immersive experience for the reader.

It depends on Jack's personal preference and priorities. If he values having a large collection of comics, he may choose to make a trade with Caroline for three of her comic books. If he values money, he may choose to sell the comic to Brooke for $100. If he values the sentimental attachment to the comic book or the rarity of a signed copy, he may choose to hold onto the comic. Ultimately, the decision is up to Jack and what he values the most.

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The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.

We have given function as ,

f(x) = 1/√(x-4)

We have to find f(x) - f(5)/x-5

f(x) = f(5)/x-5 = 1/√(5-4)/(x-5)

= 1/√(5-4)/(x-5)

= (x-5)/√(5-4)

= (x-5)

Therefore, The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

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The value of {b} is equivalent to 4.

Given is to find the value of {b}.

The function is not given. Assume that the function is -

y = ρx + b

For the point (0, 4), we can write -

4 = ρ x 0 + b

b = 4

Therefore, the value of {b} is equivalent to 4.

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Based on the given system of equations, the value of x and y are undefined.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

x = 5 - 2y      .......equation 1.

6y = 5 - 3x            .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

6y = 5 - 3(5 - 2y)

6y = 5 - 15 + 6y

6y = -10 + 6y

6y - 6y = -10 (no solution).

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Answer:

The integrating factor, u(t), for the initial value problem t* dy/dt+3y=8t with y(1)=8 is u(t) = e^(3t). The solution to this equation is y(t) = 8e^(-3t)+2te^(-3t).

Step-by-step explanation:

The integrating factor, u(t), for the given initial value problem t(dy/dt)+4y=3t with y(1)=8 is u(t) = e^(4∫t dt) = e^(2t^2).

Using this integrating factor, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)+Ce^(-2t^2), where C is a constant of integration. Since y(1)=8, we can solve for C and find that C=-7/4. Therefore, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)-7/4e^(-2t^2).

We are asked the solve the following differential equation, [tex]t\frac{dy}{dt}+3y=8t[/tex].  This is an ordinary, linear, first-order DE. We need it in the form [tex]\frac{dy}{dt}+P(t)y=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex], which is the integrating factor.

[tex]\Longrightarrow t\frac{dy}{dt}+3y=8t[/tex], multiply everything by t.

[tex]\Longrightarrow \frac{dy}{dt}+(\frac{3}{t} )y=8[/tex]

We now have the correct form for solving a linear, first-order DE.

Find [tex]\mu(t)[/tex].

[tex]\Longrightarrow \mu(t)=e^{\int\ {P(t)} \, dt } \Longrightarrow \mu(t)=e^{\int\ {\frac{3}{t} } \, dt }[/tex]

[tex]\Longrightarrow \mu(t)=e^{3\int\ {\frac{1}{t} } \, dt }\Longrightarrow \mu(t)=e^{3ln|t|} \Longrightarrow \mu(t)=e^{ln(t^3)}[/tex]

[tex]\Longrightarrow \mu(t)=t^3[/tex]

Now multiply the entire DE by [tex]\mu(t)[/tex].

[tex]\Longrightarrow t^3[\frac{dy}{dt}+(\frac{3}{t} )y=8][/tex]

[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(t^3)(\frac{3}{t} )y=(t^3)8[/tex]

[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(3t^2)y=(t^3)8[/tex]

Verify that the L.H.S is a product rule of [tex]t^3y[/tex].

Product rule: [tex]\frac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)[/tex]

[tex]\frac{d}{dt}[t^3y]=(t^3)(\frac{dy}{dt} )+(3t^2)(y)[/tex]

It is the product rule, so we can move forward by integrating both sides of the DE.

[tex]\Longrightarrow \int\ {[t^3y]'} \, =\int\ {8t^3} \, dt[/tex]

[tex]\Longrightarrow t^3y=2t^4+C[/tex]

Now using the initial condition to find the arbitrary constant, C.

[tex]t^3y=2t^4+C ;y(1)=8[/tex]

[tex]\Longrightarrow (1)^3(8)=2(1)^4+C[/tex]

[tex]\Longrightarrow 8=2+C[/tex]

[tex]\Longrightarrow 6=C \Longrightarrow C=6[/tex]

Now we have, [tex]t^3y=2t^4+6[/tex], solve for y.

[tex]\Longrightarrow t^3y=2t^4+6[/tex]

[tex]\Longrightarrow y=2\frac{t^4}{t^3} +\frac{6}{t^3}[/tex]

[tex]\Longrightarrow y=2t +6t^{-3}[/tex]

Thus the given differential equation with the initial condition is solved, [tex]y=2t +6t^{-3}[/tex].

Answer: the new points are A=(2,4) B=(2,3) C=(4,6) D(4,2)

Step-by-step explanation:

If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.

Answer:

The pitcher won 28 games out of 35.

Step-by-step explanation:

A baseball pitcher won 80% of the games he pitched, so the formula to calculate the number of games won is:

G = 80/100 * n

where

G is the number of games won

n is the number of games pitched

We know that the pitcher pitched 35 games, so:

G = 0.8 * 35

G = 28

So, the pitcher won 28 games out of 35.

Answer: 28

Step-by-step explanation: times 35 by 0.80 to get your answer, also not really a collage level question.

PS pls help me by answering one of my questions (:

Answer: The equation for the area of the garden is x(x - 2) = 48. To find the length, we need to solve for x:

x^2 - 2x - 48 = 0

Using the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4(1)(-48)))/2(1)

x = (2 ± √(4 + 192))/2

x = (2 ± √196)/2

x = (2 ± 14)/2

x = 8 or x = -6

Since the length cannot be negative, the length of the garden is 8 feet.

Step-by-step explanation:

I think that answer is yes

The mean of the measurements is 23.3 g.
The standard deviation of the measurements is 0.65 g.

The range of the measurements is 1.9 g

The percent relative standard deviation of the measurements is 2.77%.

What is the mean, range, standard deviation, percent relative standard deviation?

Mean: The mean is the average of all the measurements. To find the mean, add up all the measurements and divide by the number of measurements:

(23.4 + 23.9 + 22.6 + 24.5 + 23.0 + 23.6) / 6 = 23.3

So, the mean of the measurements is 23.3 g.

Range: The range is the difference between the largest and smallest measurements. To find the range, subtract the smallest measurement from the largest measurement:

24.5 g - 22.6 g = 1.9 g

So, the range of the measurements is 1.9 g.

Standard Deviation: The standard deviation is a measure of the spread of the data around the mean. To find the standard deviation, we first calculate the difference between each measurement and the mean, square each difference, and then average the squared differences. The square root of this average gives us the standard deviation.

(23.4 - 23.3)^2 + (23.9 - 23.3)^2 + (22.6 - 23.3)^2 + (24.5 - 23.3)^2 + (23.0 - 23.3)^2 + (23.6 - 23.3)^2 = 0.09 + 0.16 + 0.49 + 1.16 + 0.09 + 0.16 = 2.55

2.55 / 6 = 0.425

√0.425 = 0.65

So, the standard deviation of the measurements is 0.65 g.

Percent Relative Standard Deviation (RSD): The percent RSD is the standard deviation expressed as a percentage of the mean. To find the percent RSD, divide the standard deviation by the mean and multiply by 100:

0.65 g / 23.3 g * 100 = 2.77%

So, the percent relative standard deviation of the measurements is 2.77%.

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The original cost of the sweater that is on sale for a 20% discount will be $60.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A sweater is on sale for a 20% discount. The amount of the discount is $12.

Let 'C' be the original cost. Then the equation is given as,

20% = ($12 / C) x 100

Simplify the equation, then we have

20% = ($12 / C) x 100

0.20 = ($12 / C)

C = $12 / 0.20

C = $60

The original cost of the sweater that is on sale for a 20% discount will be $60.

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Therefore, the project progresses and the unitary method wood becomes smoother, finer steel wool (i.e. grades 3, 2, 1, and 0000) can be used to achieve a smoother finish..

To finish a task using unitary procedure, multiply this same sum by two after finding the measurements of one tiny slice. To differentiate a coded unit from a specific group or collection of groups, use the unit variable method, which only needs an expression. For instance, 40 pencils could cost. 4,000, which really is equivalent to $1.01 as well as 4000 pounds.

Here,

The information in the graphic that supports the advice to use coarse steel wool at the start of a major wood refinishing project is:

"Grade 4 steel wool is used to remove paint and other materials, while grade 0000 is used for the final finish on fine woodwork."

This suggests that coarse steel wool (i.e. grade 4) is more effective at removing paint and other materials, which is often necessary at the beginning of a wood refinishing project.

As the project progresses and the wood becomes smoother, finer steel wool (i.e. grades 3, 2, 1, and 0000) can be used to achieve a smoother finish..

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The length CD of the triangle is 6 units

From the question, we have the following parameters that can be used in our computation:

The triangle

Also, we have

AD = 9 and DB = 4

The length CD (x) is then calculated as

x/4 = 9/x

Cross multiply

This gives

x^2 = 36

Take the square roots

x = 6

Hence, the solution is 6

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Yes, the given input and output values represent a function, f(x) = x²

What are functions?

In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.

y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x). In other words, for the same x value, there cannot be more than one value for f(x).

If we look at the table, we can see a relationship between the x (input)  and y (output) values.

The output values (y) are the squares of the corresponding input values(x).

Also, there is only one distinct value of y for each x value.

Therefore the given values represent a function, f(x) = x².

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The total mass of the necklace is 20 grams.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Ariana loves making things she can wear. She makes a necklace by joining together 10 large pink paper clips. Each paper clip has a mass of 2 grams.

Total number of paper clips used to make necklace = 10

Mass of each clip = 2 grams

To find the total mass of the necklace, multiply the number of clips used to make necklace with the mass of each clip.

Mass of necklace = 10 × 2 grams = 20 grams

Hence 20 grams is the mass of the necklace.

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Answer:

17

Step-by-step explanation:

Find the absolute value of -8, which is 8, and add 9 to that, which gives you 17.

Answer:

745.57

Step-by-step explanation:

[tex]691.95 \times \frac{7.75}{100} = 53.62[/tex]

[tex]53.62 + 691.95 = 745.57[/tex]

Answer:

The equivalent circuit can be constructed using two NAND gates. The NAND gate is universal and can be used to implement all other logic gates including AND, OR, NOT, etc.

Here's the construction of the equivalent circuit:

First NAND gate: The first NAND gate implements the expression (~P ∧ ~Q). The inputs to the gate are P and Q, and the output is connected to the first input of the second NAND gate.

Second NAND gate: The second NAND gate implements the expression (~P ∧ (output of first NAND gate)) ∨ (P ∧ ~Q). The second input of the second NAND gate is connected to the output of the first NAND gate. The output of the second NAND gate is the final output of the circuit.

This circuit implements the given Boolean expression and has at most two logic gates.

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

Here, the differences between permutation and combination are described in detail.

The number of ways in which we can select a committee of 4 democrats from ten democrats is:

P = 10C 4 = 10! / (4)! (10 - 4)!

P = 210

The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:

P = 11C 3 = 11! / 3! (11 - 3)!

P = 165

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:

P = (210) (165) = 34650

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

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Answer: Sandra bought 4 pounds of sweet potatoes for $6.40. What is the cost per pound of the sweet potatoes?

$1.57

Step-by-step explanation: pls give brainiest

Answer:

The answer to your question is $1.57.

Step-by-step explanation:

To find the cost per pound of sweet potatoes, divide $6.28 by 4.

6.28 ÷ 4= $1.57

I hope this helps and have a wonderful day!

It is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

A two-dimensional plane, also known as a plane in two dimensions, is a flat surface that has length and width, but no thickness. It is an abstract mathematical concept that can be represented graphically.

Here,
In geometry, if two points are contained in a plane, then any line segment connecting those two points is also contained in that plane. So, if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

Thus, it is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

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Answer:

22.5 g suger!

Step-by-step explanation:

100% is 75 g

10% is 7,5 g

30% is 22.5 g

10% x 3

( 7,5 g x 3 = )

7 x 3 = 21

0.5 x 3 = 1.5

21 + 1.5 = 22.5 g!

a) The domain of the function is 0 to 15 miles

b) The range of the function is 0 to 270 miles

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the mileage of the car = 18 miles per gallon

The amount of gasoline the car can hold = 15 gallons

Let the distance to empty be a function of mileage of the car × amount of gas in gallons

Now , the domain of a function is the set of values that we are allowed to plug into our function which ranges from 0 to 15

So , distance to empty = 18 x 15 = 270

So , the range of the function is the set of output values which ranges from 0 to 270

Hence , the domain of the function is 0 to 15 miles and the range of the function is 0 to 270 miles

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Considering the definition of an equation, a mathematical statement for calculating the total labor cost is Total labor cost= 60×S + 30×PD + 19×T and the total labor cost for the recent project is $3,160.

Definition of equation

An equation is the equality between two algebraic expressions connected by the equals sign in which some known data are included together with one or more unknown values, also known as unknowns.

The terms of an equation are the addends that make up the members of an equation, whereas the members of an equation are each of the expressions that appear on both sides of the equal sign.

Finding the value that satisfies an equation is what is meant by finding its solution. By converting the unknown to the answer in this manner, the equality must be true.

This case

In this case, you consider:

S= hours of work from a senior artist.

PD= Production designer labor hours.

T= hours of work from a trainee.

On the other hand, you know that Girilla Graphics charges:

For the work of its most senior graphic artists, they charge $60 per hour.

For production designer work, the hourly rate is $30.

$19 per hour for a trainee's labor.

Therefore, the following equation can be used to determine the project's overall labor costs:

Total labor cost= 60×S + 30×PD + 19×T

A recent project required:

A senior artist's 34 hours of labor.

13 hours from a production designer.

35 hours from a trainee.

So, the following formula can be used to determine the project's overall labor costs:

Total labor cost= 60×34 + 35×13 + 19×35

Solving:

Total labor cost= $3,160

In summary, a mathematical statement for calculating the total labor cost is Total labor cost= 60×S + 30×PD + 19×T and the total labor cost for the recent project is $3,160.

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Therefore, since the total of all the angles is 180°, the value of the other angle is 100°, 40°, and 40°.

In Trigonometry, an angle is a curve made up of two rods, referred to as the angle's sides, which thus converge at a center point regarded as the ball's vertex. Two rays can create an angle in the region where they are arranged. Additionally, when airplane collide, an angle is created. Dihedral angles are what they are called. An offset is a possible shape spanning two radiation or lines with an identical termination in planar geometry. The English term "angle" comes from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the two rays, also know as the faces of the angle.

given

one angle = 40°

other angle = (11x - 18)°

in triangle sum of all angle = 180°

40° + 11x - 18 + 40  = 180

80 + 11x - 18 = 180

62 + 11x = 180

11x = 180 - 62

11x = 118

x = 10 . 2

Therefore, since the total of all the angles is 180°, the value of the other angle is 100°, 40°, and 40°.

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