The side length, s, of a cube is x – 2y. If V = s3, what is the volume of the cube?

Answers

Answer 1

Answer:

The volume of cube =  x³ -6x²y + 12xy² - 8y³

Step-by-step explanation:

It is given that,

Side length of cube s = (x - 2y)

Volume of cube = s³

Points to remember

(a - b)³ = a³ - 3a²b + 3ab² - b³

To find the volume of cube

s = (x - 2y)

Volume V = s³ = (x - 2y)³

(x - 2y)³ = x³ - (3 * x² * 2y) + (3 * x * (2y)²) - (2y)³

  = x³ -6x²y + 12xy² - 8y³

Therefore the volume of cube =  x³ -6x²y + 12xy² - 8y³

Answer 2

Answer:

[tex]x^3 -6x^2y + 12xy^2 - 8y^3[/tex]

Step-by-step explanation:

We are given that the side length (s) of a cube is [tex]x-2y[/tex]. Given that [tex]V=s^3[/tex], we are to find the volume of the cube.

[tex]Volume =  (x-2y)^3[/tex]

We know that, [tex](a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3[/tex]

So expanding the given expression accordingly:

[tex](x-2y)^3 = x^3 - (3 \times x^2 \times 2y) + (3 \times x \times (2y)^2) - (2y)^3[/tex]

Volume of cube = [tex]x^3 -6x^2y + 12xy^2 - 8y^3[/tex]


Related Questions

You throw a stone from a height of 16 feet with an initial vertical velocity of 32 feet per second. the function h= -16t squared + 32t + 16 represents the h ( in feet) of the stone after t seconds) Find the Maximum height of the stone the maximum height. please help me somebody brainly teacher expert anyone please ​

Answers

hope this helps :)

Step-by-step explanation:

dh/dt=-32t+32

When velocity, dh/dt, is equal to zero, the object is at its maximum height.

dh/dt=0 only when 32t=32, t=1 second, so the maximum height is h(1)

h(1)=-16+32=16ft

Using algebra

The maximum height will occur at the midpoint between the two zeros of the height function because of a quadratics symmetry...

h(t)=0 when

-16t^2+32t=0

-16t(t-2)=0

so t=0 and 2

The midpoint is t=1

And of course this will give you the same as we found earlier.  The maximum height is h(1) ft

Answer:

dh/dt=-32t+32When velocity, dh/dt, is equal to zero, the object is at its maximum height.dh/dt=0 only when 32t=32, t=1 second, so the maximum height is h(1)h(1)=-16+32=16ftUsing algebraThe maximum height will occur at the midpoint between the two zeros of the height function because of a quadratics symmetry...h(t)=0 when-16t^2+32t=0-16t(t-2)=0so t=0 and 2The midpoint is t=1

Hope this helped Wilbert!

a store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts . What is the fewest boxes the clerk will need to pack all the shirts

Answers

Answer:

8 boxes

Step-by-step explanation:

45/6 is 7.5 boxes, but you can not have half a box so the fewest number of boxes is 8.

PLEASE PLEASE HELP ME!!!!

Answers

According to Casio Calculations the Answer is C.

7+6x14-9=37 insert parentheses

Answers

Answer:

[tex]7+6\times(14-9)=37[/tex]

Step-by-step explanation:

The given expression is

[tex]7+6\times14-9[/tex]

If we evaluate the expression as it is  we will get;

[tex]7+84-9=82[/tex]

But we want to insert parenthesis so that we will use PEDMAS to obtain 37 as the result.

The only way this can be achieved is when we insert the parenthesis as shown below;

[tex]7+6\times(14-9)=7+6(5)=7+30=37[/tex]

w÷5=? "With work if needed"

Answers

Answer: This question doesn't have an answer.

Step-by-step explanation:

Why is this expression not positive or negative when x=-5 -1.3x-6.5

Answers

Answer:

This is because this equation equals 0 when x = -5

Step-by-step explanation:

To find this, plug the value in for x.

-1.3x - 6.5

-1.3(-5) - 6.5

6.5 - 6.5

0

The expression -1.3x - 6.5 evaluated at x=-5 equals zero, which is why it is neither positive nor negative.

To verify this let's evaluate it step by step.

Substitute x = -5 into the expression:

-1.3(-5) - 6.5

Then, multiply -1.3 by -5:

-1.3 * (-5) = 6.5

Then, subtract 6.5:

6.5 - 6.5 = 0

The expression -1.3x - 6.5 evaluated at x=-5 equals zero, which is why it is neither positive nor negative.

There are 4 cups in 1quart.If you want to convert quarts to cups,should you multiply or divide by 4

Answers

you would multiply by 4 because if there are 4 cups in a quart then u have 1 quart or 4 cups . thats the only explanation even possible for this problem

What is the area of the circle?

Answers

Circumference is found by multiplying the diameter by PI,

so a circumference of 6PI means the diameter is 6 inches.

Area is found using the formula PI x r^2

r = 1/2 the diameter

r = 6/2 = 3

The area becomes 3^2 x PI = 9PI inches.

The answer is C.

I need help plz show steps

Answers

Answer: Choice D) translated 4 units down

The "-4" tacked onto the 2x^2 term will move the entire parabola down 4 units. This is because y = 2x^2 becomes y-4 = 2x^2-4

The y-4 means we move every y coordinate down 4 spots. The x coordinate stays the same.

How many lines of symmetry does this figure have?

Answers

Answer:

1 line of symmetry through the middle making 2 v s

Step-by-step explanation:

Answer: The figure has 1 line of symmetry.

Step-by-step explanation:

A figure is said to has a line of symmetry if we can draw a line that divides the entire figure into two equal halves, so that each half appears as a reflection image or the mirror of the other.

In the given picture , if given a figure of alphabet W.

It has only a vertical symmetry ( see below the line of symmetry divides W into two Vs) but no horizontal symmetry and any other symmetry.

Therefore , it has only one line of symmetry.

Hence, the figure has 1 line of symmetry.

On a coordinate grid, the movie theater is located at (0,0) and the mall is located at (4,3). If the bowling alley is located at the midpoint between the theater and the mall, what is the approximate distance from the bowling alley to the mall? (Note: 1 unit equals 1 mile)
A) 1.3 miles
B) 1.5 miles
C) 2 miles
D) 2.5 miles

Answers

Answer:

D.) 2.5 miles

Step-by-step explanation:

The first step required for solving this problem is to calculate the midpoint between the theater and the mall (2, 1.5). Then use the distance formula to calculate the distance from the bowling alley to the mall.

Final answer:

The distance from the bowling alley to the mall is 2.5 miles. The coordinates of the midpoint, which is the location of the bowling alley, are calculated first. Then, using the Pythagorean theorem, the distance to the mall is found by calculating the square root of the sum of the squares of the horizontal and vertical distances.

Explanation:

The task is to calculate the distance from the bowling alley to the mall if the bowling alley is at the midpoint between the movie theater at (0,0) and the mall at (4,3). First, we find the coordinates of the midpoint, which is the average of the x-coordinates and the y-coordinates of the two points respectively. Thus, the midpoint is located at:

(0 + 4) / 2 = 2 for the x-coordinate(0 + 3) / 2 = 1.5 for the y-coordinate

So, the bowling alley is at point (2, 1.5). Secondly, we use the Pythagorean theorem to find the distance from the bowling alley to the mall:

The change in x (horizontal distance) from the bowling alley to the mall is 4 - 2 = 2 units.The change in y (vertical distance) from the bowling alley to the mall is 3 - 1.5 = 1.5 units.

Applying the distance formula (or Pythagorean theorem):


Distance = √( Δx² + Δy² ) = √( 2² + 1.5² ) = √( 4 + 2.25 ) = √6.25 = 2.5 miles

Therefore, the approximate distance from the bowling alley to the mall is 2.5 miles, which corresponds to answer (D).

Derek‘s parents are finalizing a budget for his college expenses his first year of college will cost $1000 in expenses will increase by 12% each year which statement is correct regarding the amount they should budget for dares for your college education to the nearest dollar

Answers

Answer:

$4779

Step-by-step explanation:

First you need to write an equation to model this situation. In this case it's f(x)=1000(1.12)^x. College usually lasts 4 years, so to find the total amount of money they need to budget, you need to find the sum of f(0), f(1), f(2), and f(3).

This is roughly equivalent to 1000+1120+1254+1405, which equals 4779.

Answer: A

Step-by-step explanation:

It looks like its A to me but I actually am not 100% on this one

you have 1 can of chicken soup, and 3 vegetable and 1 can of tomato, what is probability of getting tomato soup

Answers

You have a total of 5 cans, because 1+3+1=5.

1 can is tomato soup.

So, the probability of selecting tomato soup randomly is 1/5.

Hey there!

First, let’s find the total amount of soup cans:

1 chicken soup

3 vegetable soup

1 tomato soup

1 + 3 + 1 = 5

Therefore, the odds of you randomly selecting the tomato soup is 1/5

Hope this helps you!

God bless ❤️

Brainliest would be appreciated

xXxGolferGirlxXx

What is the average rate of change for this quadratic function for the interval from x=3 to x=4

Answers

ANSWER

A. 27.5

EXPLANATION

The average rate of change of the given quadratic function on the interval;

x=2 to x=4 is the slope of the secant line connecting the points (2,f(2)) and (4,f(4)).

This implies that the average rate of change is

[tex] = \frac{f(4) - f(2)}{4 - 2} [/tex]

From the table,

[tex]f(4) = 64[/tex]

and

f(2)=9.

The average rate of change becomes

[tex] = \frac{64 - 9} {4 - 2} [/tex]

[tex] = \frac{55}{2} = 27.5[/tex]

The correct choice is A.

Yea the correct answer is a

Fiona and her dad love making paper airplanes. On Saturday morning, Fiona made 12 paper airplanes, and her dad made 8 paper airplanes. That afternoon, they made more planes, which doubled their number of planes from the morning. At the end of the day, Fiona helped her little brother make 3more paper airplanes. Write a numerical expression with parentheses for the total number of paper airplanes Fiona and her family made. Do not simplify your expression.

Answers

Final answer:

The total number of paper airplanes Fiona and her family made can be represented by the numerical expression: (12 + 8) x 2 + 3.

Explanation:

The total number of paper airplanes Fiona and her family made can be represented by the numerical expression: (12 + 8) x 2 + 3. The expression uses parentheses to indicate that the addition of 12 and 8 should be done first. Then, the result is multiplied by 2 to account for the doubling of planes in the afternoon. Finally, 3 is added to account for the extra planes made by Fiona's little brother. This expression represents the total number of paper airplanes made by Fiona and her family without simplifying it.

Multiply
(5x-1)(6x^2+3x+7)

SHOW WORK

Answers

sorry for using printed paper, I tried my best to avoid the lines

Answer:

30x³ + 9x² + 32x - 7

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

5x(6x² + 3x + 7) - 1 (6x² + 3x + 7) ← distribute both sets of parenthesis

= 30x³ + 15x² + 35x - 6x² - 3x - 7 ← collect like terms

= 30x³ + 9x² + 32x - 7

Write the ratios for sin X, cos X,and tan X

Answers

I don’t know it seems prepared

A square pyramid is 4 feet on each side. The height of the pyramid is 6 feet. What is the total area of the pyramid?

Answers

Final answer:

The total surface area of a square pyramid with a side length of 4 feet and a height of 6 feet is 64 square feet.

Explanation:

To find the total surface area of a square pyramid, we need to calculate the area of the base and the area of all four triangular faces. The area of the base (a square) can be found using the formula side². In this case, that's which equals 16 square feet. To find the area of a triangular face, we use the formula 0.5 * base * height. Since we have 4 identical triangular faces, we calculate this once and then multiply by 4. The base of each triangle is the side of the square, which is 4 feet, and the height is given as 6 feet. Plugging these values into the formula we get 0.5 * 4 * 6 = 12 square feet for one triangular face. Since there are 4 of these faces, the total surface area of the faces is 4 * 12 = 48 square feet. Adding this to the area of the base, we find the total surface area of the pyramid is 16 + 48 = 64 square feet.

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Final answer:

To find the total area of a square pyramid, calculate the area of the base and the area of the four triangular faces. The total area is 64 square feet.

Explanation:

To find the total area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces. Since the base is a square with sides measuring 4 feet, its area is 4 x 4 = 16 square feet.

To find the area of each triangular face, you can use the formula for the area of a triangle: (base x height) / 2.

In this case, the base of each triangular face is 4 feet and the height is 6 feet, so the area of each face is (4 x 6) / 2 = 12 square feet. Since there are 4 triangular faces, the total area of these faces is 4 x 12 = 48 square feet.

Finally, you can find the total area of the pyramid by adding the area of the base and the area of the faces: 16 + 48 = 64 square feet.

Therefore, the total area of the square pyramid is 64 square feet.

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A rectangular prism has side lengths of 4 inches, 6 inches, and 7 inches. If all side lengths are doubled, what happens to the surface area

Answers

Original measurements:

L = 4; W = 6; H = 7

surface area = 2(LW + LH + HW)

surface area = 2(4 * 6 + 4 * 7 + 6 * 7)

surface area = 2(24 + 28 + 42)

surface area = 2(94)

surface area = 188

Doubled measurements:

L = 8; W = 12; H = 14

surface area = 2(LW + LH + HW)

surface area = 2(8 * 12 + 8 * 14 + 12 * 14)

surface area = 2(96 + 112 + 168)

surface area = 2(376)

surface area = 752

The surface area was 188 square inches and it became 752 square inches.

752/188 = 4

As the side lengths increased by a factor of 2, the surface area increased by a factor of 4.

What is the measure of B in the triangle?

This triangle is not drawn to scale

Answers

Answer:

70 degrees

Step-by-step explanation:

Answer:

70°

Step-by-step explanation:

(a) Calculate the value of x

∠A +   ∠B     +   ∠C    = 180

40 + 2x - 30 + x + 20 = 180

Combine like terms

3x + 30 = 180

Subtract 30 from each side

3x = 150

Divide each side by 3

x = 50

(b) Calculate m∠B

m∠B = 2x - 30 = 2×50 - 30 = 100 - 30 = 70°

Can you help me I’m begging you for your help please tell me I need your help please I’m begging you I’ve never been like this in my entire life please I’m begging you please help me with this question

Answers

Answer

D. -3x + 4(2x-6) + 5

Step-by-step explanation:

-3x has nothing attached to it so leave it alone

4 times 2x equals 8x and 4 times -6 equals -24

add 5

8x-3x=5x

-24 + 5 = -19

5x - 19

Answer: The answer is D

Step-by-step explanation:

I forgot set by step so I hope u figure that part out though

The diameter of a circular garden is 16 feet what is the approximate area of the garden

Answers

Answer:

Option C

201 feet²

Step-by-step explanation:

Given in the question,

diameter of the circular graph = 16 feet

Formula to calculate the area of garden

Area =  π r²

where π is constant = 3.14

           r is the radius

To find the radius

diameter/2

16/2

8 feet

Plug in values to calculate area

(3.14) 8²

200.96 feet²

Area of the circular garden having 16 feet diameter is 201 (approximate)

Rewrite the expression 2(10+15) using distributive property of multiplication over addition

Answers

Answer:

2(10+15)= (2x10)+(2x15) 20+30=50

Step-by-step explanation:

Final answer:

The expression 2(10+15) rewritten using the distributive property is 20 + 30, which simplifies to 50.

Explanation:

Rewriting the expression 2(10+15) using the distributive property of multiplication over addition involves multiplying the 2 by each term inside the parentheses. To do this, multiply 2 by 10 to get 20, and then multiply 2 by 15 to get 30. Combine these two products to complete the process.

Here's the calculation step by step:

Multiply the first term: 2 × 10 = 20.Multiply the second term: 2 × 15 = 30.Add the products: 20 + 30 = 50.

Therefore, the expression 2(10+15) using the distributive property is 20 + 30 which simplifies to 50.

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Solve the problem below. Write the answer in the space provided.

1/2 of 4 feet = ___________
inches

Answers

Answer:

24 inches

Step-by-step explanation:

1/2 of 4 feet is 2 feet

you know that 1 feet = 12 inches

So 2 feet = 24 inches

Solve the equation 2x3 + 7x2 – 10x – 24 = 0 in the real number system.

Answers

Answer:

x = 2

x = -4

x = -3/2

Step-by-step explanation:

We need to find the roots of the equation

2x^3 + 7x^2 – 10x – 24 = 0

We can factorize the equation into

(x-2)(x+4)(2x + 3) = 0

Roots

x = 2

x = -4

x = -3/2

The answer to your question is also attached in the images below

Answer:

x=2 ; x=-4 or x=-3/2

Step-by-step explanation:

We are given a cubic polynomial

[tex]2x^3+7x^2-10x-24=0[/tex]  

Here as we are having a cubic equation to factorize, we have to find some value of x such that when we put that value in place of x , it gives us a 0. We have to try it randomly like first we try it for x=1 then x=2 and so on.

On trying for x=2 , we see that the equation becomes 0=0 and hence x=2 is one of the solution. And also as x=2 is one of the solution, (x-2) must be one of the factor. Now we use this property to determine the other factor like this.

[tex]2x^3+7x^2-10x-24=0[/tex]

Adding and subtracing [tex]4x^2[/tex] to [tex]2x^3[/tex] we get

[tex]2x^3-4x^2+4x^2+7x^2-10x-24=0[/tex]

Now we take out [tex]2x^2[/tex] as GCF

[tex]2x^2(x-2)+11x^2-10x-24=0[/tex]

Now subtracting and adding [tex]22x[/tex] to [tex]11x^2[/tex]

[tex]2x^2(x-2)+11x^2-22x+22x-10x-24=0[/tex]

taking [tex]11x^2[/tex] as GCF out  

[tex]2x^2(x-2)+11x(x-2)+22x-10x-24=0[/tex]

[tex]2x^2(x-2)+11x(x-2)+12x-24=0[/tex]

[tex]2x^2(x-2)+11x(x-2)+12(x-2)=0[/tex]

Now taking [tex](x-2)[/tex] out as GCF

[tex](x-2)(2x^2+11x+12)[/tex]

Now we need to split the middle term of [tex](2x^2+11x+12)[/tex] to factorize it in such a way that their product is 2*12 and sum is 11. We have 8 and 3 as these factors.

Hence it can be factored like this

[tex](2x^2+11x+12)\\2x^2+8x+3x+12\\2x(x+4)+3(x+4)\\(2x+3)(x+4)[/tex]

Hence our answer will be

[tex](x-2)(2x+3)(x+4)=0[/tex]

And thus the solutions will be

x-2=0 : x=2

x+4=0 ; x=-4

2x+3=0 ; x=-[tex]\frac{3}{2}[/tex]

How do you find interval of increase or decrease??

Answers

Using interval notation, it is described as increasing on the interval (1,3). Decreasing: A function is decreasing, if as x increases (reading from left to right), y decreases. In plain English, as you look at the graph, from left to right, the graph goes down-hill. The graph has a negative slope.

To find intervals of increase or decrease, analyze the function's derivative or slope. Linear regression uses a straight line equation to estimate these trends graphically. Graphs are helpful for visually representing increase or decrease rates and other numerical relationships.

To find intervals of increase or decrease in a function, you need to analyze the function's derivative. If the derivative is positive over an interval, the function is increasing; if the derivative is negative, the function is decreasing. An example of observing such behavior is through graphical analysis, where you look for portions of the graph that have an upward or downward slope, respectively.

Linear regression is a tool used to determine the rate of increase or decrease over a set of data points. By fitting a line X = S\u00d7t + I, where S is the slope and I the intercept with the vertical axis, one can estimate the trend or rate of change, assuming a linear relationship.

To describe the rate of growth in various contexts, such as population growth or economic data, graphs can display these trends visually. For different applications, such as contour mapping in geography, the interval of change might be adjusted to represent details accurately. A constant rate of growth assumption, however, isn't always correct and must be adjusted depending on the circumstances.

When 6 is subtracted from a square of a number the result is 5 times the number

Answers

Answer:

Step-by-step explanation:

The starting number is 6

6*6=36

36-6=30

6*5=30

Answer:

My guy tha answer is x=6

Step-by-step explanation:

how i know, because i got it right

What is the probability of spinning a B?

Answers

Answer:

3/8 or 37.5%

Step-by-step explanation:

There are a total of 8 possible outcomes. B appears only 3 times in those 8 outcomes. Therefore, the chances of landing on B is 3 out of 8 or 3/8.

The probability of B in percent is 37.5 %.

What is Probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, Total outcomes = {A, A, B, B, B, C, C, C}

                 n(S) = 8

Now, possibility of B = {B, B, B}

                n(B) = 3

Probability of B = Favorable outcomes/ total outcomes

                           = n(B)  / n(S)

                           = 3/8

                           = 0.375

                           = 37.5 %

Thus, the probability of B in percent is 37.5 %.

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which value for x makes the sentence true? 9x= 4x+ 25​

Answers

9x= 4x +35

5x=35

x=6

ask if u need explanation

To find the value of x that makes the equation true, you need to solve the equation 9x = 4x + 25 by subtracting 4x from both sides and then dividing by 5 to find x = 5.

Value of x: To find which value of x makes the equation 9x = 4x + 25 true, you need to solve the equation.

Step-by-step explanation:

Subtract 4x from both sides: 9x - 4x = 25

This simplifies to 5x = 25

Divide by 5 to solve for x: x = 5

Therefore, the value 5 makes the sentence 9x= 4x+ 25​ true.

Which of the following options best describes the zeros of the quadratic function above?

A. 2 real zeros
B. 1 real zero
C. 1 real zero and 1 imaginary zero
D. 2 imaginary zeros​

Answers

Answer:

it might be d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

hi

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