hi i am stuck on this word problem and need help

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer:

B. 0.6

Step-by-step explanation:

18/30 as a decimal is 60%, convert that to a decimal and you get .6

Taylor conducted a study using a 2x2 factorial design, and one of the independent variables was linked to a substantial main effect with significant difference.

A post-hoc test is not appropriate in this situation because it cannot provide reliable information about the conditions that are causing the significant difference. Post-hoc tests are only appropriate for small sample sizes and cannot be used to draw any definitive conclusions about the causes of a significant main effect.

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Answer:

We conclude that:

Step-by-step explanation:

Given the function

\(y = f(x)\)

In order to determine the value f(2), we need to check the value of y at x = 2.

In other words, we need to check:

at x = 2, what is the value of y?

From the graph, it is clear that at x = 2, the value of y = -5

In other words,

f(2) = -5

Therefore, we conclude that:

Answer:

V = 24pi

or 75.36 ( using 3.14 for pi)

or 75.39822369 ( using the pi button)

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius and the height

V = pi (2)^2 * 6

V = pi 4*6

V = 24 pi

If we approximate pi by 3.14

V = 3.14 * 24 = 75.36

If we use the pi button

V =75.39822369

Answer:

Step-by-step explanation:

V=pi r^2 h

r = 2

h = 6

V = 3.14 * 2 * 2 * 6

V =75.36

Answer:

Step-by-step explanation:

Answer: have a good day

Step-by-step explanation:

because you deserve it

Answer:

add 6x to both sides (3x+3=-18)

subtract 3 from both sides (3x=-21)

divide by 3 on both sides (x=-7)

x=-7 is final answer

Answer:

#1 x is 35

#2 x is 12

#3 x is 3

#4 is m and n

#5 x is 17

Step-by-step explanation:

Hope this helps

Answer:

35

Step-by-step explanation:

1/6 I think...

because there are 6 lines after the 0, and the point is on the first line.

The probability P[X² + Y² < 1] is equal to π/4.

To find the probability P[X² + Y² < 1], we need to consider the geometric interpretation of the inequality. The inequality X² + Y² < 1 represents the interior of the unit circle centered at (0,0) in the xy-plane.

Since X and Y are uniformly distributed random variables over [0,1), their joint distribution forms a square with side length 1. The area of this square is 1*1 = 1.

To find the probability of the event X² + Y² < 1, we need to determine the area of the region that satisfies this condition. This region is the interior of the unit circle.

The area of a unit circle with radius 1 is πr² = π(1)² = π.

Therefore, the probability P[X² + Y² < 1] is equal to the area of the unit circle divided by the total area of the square, which is π/1 = π.

Hence, the probability P[X² + Y² < 1] is equal to π/4, as π is the area of the unit circle and 4 is the area of the square.

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The angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees is 175.

Angles on the same side of the same quadrant are said to be coterminal angles. We repeatedly add or subtract a 360° full revolution from the supplied angle in order to discover an angle that is coterminal with it.

To determine a coterminal angle with the provided angle between 0tp 360 we add 360 to the given angle:

-1625 + 360(5) = 175

Hence, the angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees is 175.

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Answer:

I am unsure of the specifics, I always used slope-intercept form.    

Step-by-step explanation:

If there is a specific question you are struggling with try entering the problem in m-a-t-h-w-a-y. This always helps me.

The particle is at rest when t = 0 or t = 2.

The positions of a particle moving in the x y-plane is given by the parametric equations x = t³ - 3t² and y = 2t³ - 3t² - 12t. For what values of t is the particle at rest?

The particle will be at rest if the velocity is zero. The velocity is given by the derivative of the position function. So, we need to find the derivative of the position function to obtain the velocity function. v = dx/d t and v = d y/d t

Therefore; v x = dx/d t = 3t² - 6tvy = d y/d t = 6t² - 6t - 12At rest, the velocity, v = 0vx = 3t² - 6t = 0vy = 6t² - 6t - 12vx = 3t(t - 2) = 0t = 0 or t = 2

Therefore; The particle is at rest when t = 0 or t = 2.

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Answer: Just re dot the points like mirror it on where ever on the graph  Step-by-step explanation:

I belive that's how it's done

Answer:

this is your answer

I hope it helps you

:-))

Answer:

X=8

Step-by-step explanation:

9/24=3/x

reduce fraction with 3

3/8=3/x

Simplify the equation using cross-multiplication

3x=24

Divide both sides of the equation by 3

x=8

Answer:

Step-by-step explanation:

The square root of 125 is equal to 5√5 or 11.18 (approximately).

Below:- see both pictures

Answer:

The square root of 125 is between [D. 11 and 12] .

Step-by-step explanation:

The domain of ggg is option D: -7 ≤ x ≤ 4.

To determine the domain of a function, we need to identify the set of all possible values for the independent variable, in this case, x, for which the function is defined.

In option D, the domain is specified as -7 ≤ x ≤ 4. This means that x can take any value within the closed interval from -7 to 4, inclusive.

In other words, the domain of ggg includes all real numbers between -7 and 4, including -7 and 4 themselves. This interval represents the range of values for x that satisfy the given conditions for the function ggg.

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Answer:

66 Cents per pound

Step-by-step explanation:

1 ton = 2,000 pounds

5 tons = 10,000 pounds

10,000 pounds = $6,600

1 Pound = $0.66

The formula the capital gains yield = (pt 1 â pt)/dt is false.

The proper equation for  capital gains yield

return on investment = (pt - pt-1)/pt-1

where pt= cost of the resource at the conclusion of the holding period and pt-1 = cost at the start of the holding period.

 This equation communicates the rate increment (or diminish) within the cost of a resource over the holding period and could be a degree of speculation return due to changes within the cost of the resource. 

The term 'dt' in the original formula is not well defined and is not typically used in the context of calculating return on investment.  yield = (pt 1 â pt)/dt is false.

The proper equation for return on investment is:

return on investment = (pt - pt-1)/pt-1

where pt= cost of the resource at the conclusion of the holding period and pt-1 = cost at the start of the holding period.

 This equation communicates the rate increment (or diminish) within the cost of a resource over the holding period and could be a degree of speculation return due to changes within the cost of the resource. 

The term 'dt' in the original formula is not well defined and is not typically used in the context of calculating return on investment. 

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Answer:37

Step-by-step explanation:

Answer:

r = 37

Step-by-step explanation:

2r = 56+ 18

2r = 74

r = 37

Answer:

no its not

Step-by-step explanation:

Answer:

Corresponding angles of parallel lines cut by a transversal are congruent.

Answer:

Since we can't buy 0.68 of a fish and our number must be less than 13.68, we can buy 13 fish.

Step-by-step explanation:

3.29f ≤ 45

3.29f/3.29 ≤ 45/3.29

f ≤ 13.68

Answer:

Step-by-step explanation:

The answer is 67%.

To turn a decimal into a fraction you must move the decimal over two places to the left.

For example: .87% = 87%

Answer:

x = 20

Step-by-step explanation:

Each line creates a 180° angle on each side of it. Since these lines intersect, they have congruent angles. This means that these two quantities can be set equal to each other.

3x + 50 = 6x - 10

Solve by combining like-terms and isolating x. Move the 3x to the right by subtracting it from both sides.

50 = 3x - 10

Move the 10 to the left by adding it to both sides.

60 = 3x

Divide the 3 from both sides to isolate the x.

x = 20

Furthermore, this can be checked by plugging in 20 to x and seeing if the expression is true.

3(20) + 50 = 6(20) - 10

110 = 110

Answer:

Step-by-step explanation:

hdhf

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, for 5 bows, 10/3 yards of ribbon is required.

Answer:The average rate of the function from x = 2 to x = 4 is 6.

Step-by-step explanation: