a bakery is making cakes for a huge weeklong city celebration. the recipe for each cake calls for 96 grams of sugar. each cake serves 12 people and the city plans on serving 1500 slices of cake per day for 7 days. how many total cakes does the bakery need to make?

First step is wrong (x-2) × 3x³ should be 3x⁴ - 6x³

not 6x²

There does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

(a) To show that NG(H) = G, we need to show that every element of G normalizes H. Let g ∈ G, and let h ∈ H. Since H = ker(φ), we know that φ(h) = 1. Now, we need to show that ghg⁻¹ ∈ H. Using the properties of a homomorphism, we can write:

φ(ghg⁻¹) = φ(g)φ(h)φ(g⁻¹) = φ(g)1φ(g⁻¹) = φ(g)φ(g⁻¹) = φ(gg⁻¹) = φ(1) = 1

Therefore, ghg⁻¹ ∈ H, and so g normalizes H. Since this is true for any g ∈ G, we can conclude that NG(H) = G.

(b) Suppose there exists a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}. Since s ∈ ker(φ), we know that φ(s) = 1. However, we also know that rs = sr⁻¹, and so φ(rs) = φ(sr⁻¹). Using the properties of a homomorphism, we can write:

φ(r)φ(s) = φ(s)φ(r⁻¹) = φ(s)φ(r)⁻¹

Since φ(s) = 1, this simplifies to:

φ(r) = φ(r)⁻¹

But this means that φ(r) is its own inverse, and so φ(r)² = 1. However, we also know that rn = 1, and so φ(rn) = 1. Using the properties of a homomorphism, we can write:

φ(rn) = φ(r)ⁿ = (φ(r)²)ⁿ/2 = 1ⁿ/2 = 1

But this means that n/2 must be an integer, which contradicts the fact that n > 2. Therefore, there does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

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Answer: 134 tickets.

Step-by-step explanation:

Since we have 14 packs of 9 tickets, we can say it is 14 groups of 9. Which means we multiply. So 9 times 14 equals 126. But Ivan found 8 more tickets on the groud which means we add. so 126 plus 8 equals 134. The answer is 134 tickets.

Answer:

Step-by-step explanation:

multiply # of packs by # of tickets in each pack then add 8

14 x 9 = 126 + 8 = 134

Answer:

Step-by-step explanation:

lol sorry I know it but don’t know how up to right it sorry

Answer:

20%

Step-by-step explanation:

Formula - multiply decimal by 100

0.2- Word form= two tenths

Fraction * 2/10 *

0.2 (multiply by 100)

0.2 x 100 = 20

20% is 0.2 as a percent

( hope this helps I’m online so ask any questions you need)

The recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs.

A recursive definition of a function is when the definition of the function involves the function itself. This type of definition is used to express complex operations in a simpler form. It is an effective way to break down a complicated problem into simpler, manageable parts. It allows us to define a set of rules in terms of smaller versions of itself, which can then be worked out using a series of steps.

A recursive definition for the function f is a process by which the value of f for a given input can be defined in terms of the values of f for smaller inputs. In other words, a recursive definition for f is a definition that describes how f can be calculated from its inputs.

In this case, the recursive definition for the function f is given by:

f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3

This means that the value of f for a given x can be calculated by multiplying 500 (the value of f for x = 1) by 1/5 raised to the power of x-1. This is because f(1) = 500, f(2) = 100 (1/5 * 500), and f(3) = 20 (1/5 * 1/5 * 500).

This recursive definition can also be expressed in a more general form as:

f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3

Where a and b are constants. In this case, a is 500 and b is 1/5.

In conclusion, the recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs. This definition can also be expressed in the more general form of f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3.

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The length of Diagonal is 14.73 unit.

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Given:

l = 9, w= 10 and h= 6

The Formula for Diagonal length of Prism is:

d =√l² + w² + h²

Here, d = length of the diagonal, l = length of the rectangular base of the prism, w = width of the rectangular base of the prism, and h = height of the prism.

Substitute the value in the equation,

d =√9² + 10² + 6²

d =√81+ 100 + 36

d = √217

d =  14.73 units

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The extra number of people that should be engaged to reap the field in 10 days is given by A = 21 people

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the extra number of people that should be engaged to reap the field in 10 days be represented as A

Now , the number of people that should be engaged to reap the field in 10 days = n

The number of people that can reap the field in 17 days = 30 persons

So , the proportion is

30 x 17 = n ( 10 )

On simplifying , we get

Divide by 10 on both sides , we get

n = ( 30 x 17 ) / 10

n = 3 x 17

n = 51

And , the number of extra persons A = n - 30

So , the extra number of people that should be engaged to reap the field in 10 days A = 21 people

Hence , the proportion is A = 21 people

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The concept time and work is used here to determine the number of people required to reap the same field in 10 days. The number of people required is 51.

The time and work represents the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the workdone by each of them.

If 30 persons can reap a field in 17 days

1 person can reap = 30 × 17 = 510 days

In 10 days, number of persons needed = 510 / 10 = 51 persons

Thus 51 persons can reap the field in 10 days.

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Therefore, the jar can hold 75.36 cubic inches of peanut butter.

The answer is B) 75.36 in3.

An inch is a unit of measurement that is commonly used in the United States, United Kingdom, and other countries that follow the Imperial system of measurement. It is defined as 1/12th of a foot or 2.54 centimeters. In other words, there are 12 inches in a foot. The inch is often used to measure the length or width of small objects or to express the size of computer screens, TVs, and other electronic displays.

Given by the question.

The volume of a cylinder can be calculated using the formula: V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

In this case, the jar has a diameter of 4 inches, which means the radius is 2 inches (diameter = 2 × radius). The height is given as 6 inches. So, we can calculate the volume of peanut butter that the jar can hold as follows:

V = π[tex]r^{2}[/tex]h

V = 3.14 × [tex]2^{2}[/tex] × 6

V = 3.14 × 4 × 6

V = 75.36 cubic inches

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The area of a cross section that passes through the center of a sphere with a diameter of 7 centimeters will be 12.25π cm².

Three-dimensional objects with a sphere-like shape exist in all three dimensions. Three axes, the x-axis, y-axis, and z-axis, are used to define the sphere. The key distinction between a circle and a sphere is this. In contrast to other 3D shapes, a sphere lacks any vertices or edges.

The sphere's points are evenly spaced apart from one another on its surface. In light of this, the sphere's surface and core are always equally separated from one another. The sphere's radius is the measurement between these points. Ball, globe, planets, and other objects are all examples of spheres.

Given : Diameter of Sphere = 7 cm

∴ Radius = 7/2 = 3.5 cm.

Since It is a cross section in a sphere, so, it would be circle.

So, Area of the cross section = Area of circle

Hence, Area of Cross section = πr²

                                                 = π (3.5)²

                                                 =  12.25π cm²

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We are given the expression √4x^2+100 and the substitution x/5=tan(θ). Our goal is to use the substitution to write the expression as a trigonometric expression and simplify as much as possible.

First, let's substitute x/5=tan(θ) into the expression:

√4(tan(θ)*5)^2+100

Next, let's simplify the expression:

√4(25tan^2(θ))+100

√100tan^2(θ)+100

Now, let's factor out 100 from the expression:

√100(tan^2(θ)+1)

10√tan^2(θ)+1

Finally, let's use the trigonometric identity 1+tan^2(θ)=sec^2(θ) to simplify the expression further:

10√sec^2(θ)

10sec(θ)

Therefore, the expression √4x^2+100 can be written as 10sec(θ) using the substitution x/5=tan(θ).

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Answer:

x = -2.

Step-by-step explanation:

9.9 = 3.1 - 3.4x

9.9 - 3.1 = -3.4x

6.8 = -3.4

6.8 /-3.4 = -3.4/-3.4

-2 = x

Answer: 4 bracelets per hour

Step-by-step explanation:

You're basically finding the amount made in one hour instead of 5, so we just use an equation:

20 = 5x

x = 4

4 are made in an hour. Hope this helps!

Answer: 50in^2

Remember the formula for finding the area of a rectangle is:

A = (base)(height)

In this problem you find the area like so:

A = (12[tex]\frac{1}{2}[/tex])(4)

= ([tex]\frac{25}{2}[/tex])([tex]\frac{4}{1}[/tex])

= ([tex]\frac{25}{1}[/tex])([tex]\frac{2}{1}[/tex])

= 50in^2

The sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.

A cοnnectiοn between twο expressiοns οr values that is nοt equal in mathematics is referred tο as inequality. Hence, inequity results frοm imbalance. In mathematics, an inequality establishes the cοnnectiοn between twο nοn-equal numbers. Equality and inequality are nοt the same.

Use the nοt equal symbοl mοst frequently when twο values are nοt equal (). Values οf any size can be cοntrasted using a variety οf inequalities.

By changing the twο sides until just the variables are left, many straightfοrward inequalities may be sοlved.

Nοnetheless, a variety οf factοrs suppοrt inequality: Bοth sides' negative values are split οr added. Exchange the left and the right.

5x - 15 + 15 > -65 + 15

5x > -50

5x/5 > -50/5

x > -10

Because the inequality is severe, the οpen circle at -10 shοws that it is nοt part οf the sοlutiοn set (i.e., x must be greater than -10, nοt greater than οr equal tο -10).

The right arrοw shοws that the sοlutiοn set gοes οn fοrever in that directiοn.

Hence, the sοlutiοn tο the inequality is all values οf x greater than -10. This can be represented οn a number line as shοwn in the figure attached.

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Answer:

Step-by-step explanation:

Kelsie has written checks for a total of $46 + $82 + $264 + $127 = $519.

Since she only has $370 in her account, this means she has overdraft by $519 - $370 = $149.

Therefore, the bank will charge her $22 for each overdraft, which gives a total of $22 * 7 = $154.

Thus, Kelsie owes the bank a total of $519 + $154 = $673. Answer: \boxed{673}.

Answer:

If 2.5 gallons of paint are needed for the entire fence, then for 1/5 of the fence we need:

2.5 gallons / 5 = 0.5 gallons

To find how much paint is needed for 3/5 of the fence, we can multiply 0.5 gallons by 3:

0.5 gallons * 3 = 1.5 gallons

Therefore, 1.5 gallons of paint are needed for 3/5 of the fence.

Answer:

15 gallons

Step-by-step explanation:

1/5 of the fence would be 5 gallons, because 25/5 is 5, so to find how much paint for 3/5, we have to multiply 3 and 5 which gives us 15. We need 15 gallons of paint to paint 3/5 of the fence

Hope it helped!

slope of HI = 6, slope of IJ = -1/6, slope of HJ = 5/7, length of HI = √37, length of IJ = √37, length of HJ = √74, Triangle HIJ is isosceles

The slope of a line is found by the formula (y2-y1)/(x2-x1). The length of a line is found by the formula √((x2-x1)²+(y2-y1)²).

Slope of HI = (1-(-5))/(8-7) = 6/1 = 6
Slope of IJ = (-5-(-4))/(7-1) = -1/6
Slope of HJ = (1-(-4))/(8-1) = 5/7

Length of HI = √((8-7)²+(1-(-5))²) = √(1²+6²) = √(1+36) = √37
Length of IJ = √((7-1)²+(-5-(-4))²) = √(6²+(-1)²) = √(36+1) = √37
Length of HJ = √((8-1)²+(1-(-4))²) = √(7²+5²) = √(49+25) = √74

Triangle HIJ is isosceles because it has two sides with the same length (HI and IJ).

- slope of HI = 6
- slope of IJ = -1/6
- slope of HJ = 5/7
- length of HI = √37
- length of IJ = √37
- length of HJ = √74
Triangle HIJ is isosceles

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The statements that are true about the function when graphed on a coordinate plane include the following:

C. The relative minimum of the function is (3, 0)

E. When t > 3, the function is increasing.

In order to determine the minimum and maximum of this function, we would have to determine the critical points where the derivative of the function is equal to zero or undefined, and then evaluate the function at these critical points and at the endpoints of the interval.

By taking the first derivative of the given function and factorizing, we have:

f(t) = t³ - 6t² + 9t

f'(t) = 3t² - 12t + 9  

3t² - 12t + 9 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0

t = 3 and t = 1

Therefore, the critical points of the function are at t = 1 and t = 3.

By taking the second derivative of the given function and factorizing, we have:

f''(t) = 6t - 12

At point t = 1, we have:

f''(1) = 6(1) - 12 = -6 (it is less than zero).

Therefore, f(t) has a local maximum at t = 1.

At point t = 3, we have:

f''(3) = 18 - 12 = 6 (it is greater than zero).

Therefore, the function f(t) has a local minimum at t = 3.

At t = 4, f''(4) = 24 - 12 = 12

At t = 5, f''(5) = 30 - 12 = 18

In conclusion, the relative minimum of the function is (3, 0) and when t > 3, the function would increase.

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Answer:

4700=πr²×31

4700/31=πr²

151.6.../π=r²

√151.6.../π=

6.946933566=r

r=6.95mm

Explain:

Volume of cylinder=

πr²×height

Thus, 2002 + 23 = 2025 is the year at which the populace hits 7 million.

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

To find the year when the population reaches 7 million people, we need to solve the equation:

f(x) = 7

where f(x) represents the population, in millions of x years after 2002, and x is the number of years after 2002.

Substituting the given function f(x) = 6.7(1.0032)x into this equation, we get:

6.7(1.0032)x = 7

Dividing both sides by 6.7, we get:

1.0032x = 1.0448

When we take the natural log of both parts, we obtain:

ln(1.0032)x = ln(1.0448)

Using the logarithmic identity ln(aᵇ) = b ln(a), we can simplify this to:

x ln(1.0032) = ln(1.0448)

Dividing both sides by ln(1.0032), we get:

x = ln(1.0448) / ln(1.0032)

Using a calculator, we find:

x ≈ 22.6

Therefore, the population will reach 7 million people approximately 22.6 years after 2002. Rounding this to the nearest whole number, we get:

x ≈ 23

So the year when the population reaches 7 million people is 2002 + 23 = 2025.

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Knowing the functions f(x) and g(x) we have:

To find the sum, difference, product, and quotient of two functions, we simply perform the corresponding operations on the expressions for each function.

For (f+g)(x), we add the expressions for f(x) and g(x):

(f+g)(x) = (x² + 3x + 1) + (x^2) = 2x² + 3x + 1

For (f-g)(x), we subtract the expression for g(x) from the expression for f(x):

(f-g)(x) = (x² + 3x + 1) - (x²) = 3x + 1

For (f·g)(x), we multiply the expressions for f(x) and g(x):

(f·g)(x) = (x² + 3x + 1) · (x²) = x⁴ + 3x³ + x²

For (f/g)(x), we divide the expression for f(x) by the expression for g(x):

(f/g)(x) = (x² + 3x + 1) / (x²) = 1 + 3x/x² + 1/x² = 1 + 3/x + 1/x²

So, the final answers are:

(f+g)(x) = 2x² + 3x + 1

(f-g)(x) = 3x + 1

(f·g)(x) = x⁴ + 3x³ + x²

(f/g)(x) = 1 + 3/x + 1/x²

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The cost of backpack is $38.97. The markup amount is $13.64. The regular unit selling price for the backpack is $52.61
Mountain Equipment Co-op will be $19.02.The profit will be $19.02, which is higher than the profit of $6.63 when selling at the regular unit selling price.

To find the cost, markup amount, regular unit selling price, and profit for the backpack, we need to use the following formulas:

1. Cost = List Price - Trade Discount - Quantity Discount
2. Markup Amount = Cost × Markup Percentage
3. Regular Unit Selling Price = Cost + Markup Amount
4. Profit = Regular Unit Selling Price - Cost - Expenses

Let's plug in the given values and calculate each of these:

1. Cost = $59.95 - ($59.95 × 0.25) - ($59.95 × 0.10) = $59.95 - $14.99 - $5.99 = $38.97
2. Markup Amount = $38.97 × 0.35 = $13.64
3. Regular Unit Selling Price = $38.97 + $13.64 = $52.61
4. Profit = $52.61 - $38.97 - ($38.97 × 0.18) = $52.61 - $38.97 - $7.01 = $6.63

Now, if MEC sells the backpack at the MSRP (Manufacturer's Suggested Retail Price), the profit will be different. The MSRP is typically higher than the regular unit selling price, so the profit will be higher as well. Let's say the MSRP is $65. The profit would be:

Profit = MSRP - Cost - Expenses = $65 - $38.97 - ($38.97 × 0.18) = $65 - $38.97 - $7.01 = $19.02

So, if MEC sells the backpack at the MSRP, the profit will be $19.02, which is higher than the profit of $6.63 when selling at the regular unit selling price.

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The solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.

A compound inequality is an equation that combines two inequalities with the word "and" or "or".

To solve a compound inequality, we need to solve each inequality separately and then combine the solutions.

For the compound inequality 3u-2<=-14 or 4u+4<28, we will solve each inequality separately.

First, we will solve 3u-2<=-14: 3u-2<=-14 3u<=-14+2 3u<=-12 u<=-4

Next, we will solve 4u+4<28:

4u+4<28 4u<28-4 4u<24 u<6

Now, we will combine the solutions.

Since the word "or" is used in the compound inequality, the solution is the union of the two solutions. This means that the solution is any value of u that satisfies either inequality.

The solution is u<=-4 or u<6. This can also be written in interval notation as (-∞,-4] U (-∞,6).

So, the solution to the compound inequality 3u-2<=-14 or 4u+4<28 is u<=-4 or u<6.

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Based on the sample of the 48 South African households collected from the Census At School survey project, the mean number of people living in a household will be 6.208, and the standard deviation is 2.576.

However, it is important to note that this sample only represents a small fraction of the total number of the households in South Africa, so we cannot make definitive conclusions about the entire population based on this sample alone.

To get a more accurate estimate of the number of people living in the South African households, a larger and the more representative sample would need to be collected.

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The length of DC is √102, which is the simplest radical form.

The proportion of corresponding sides in similar triangles is the same. This is known as the similar triangles theorem.

In other words, if two triangles are similar, then the ratio of the lengths of any two corresponding sides is the same.

Since DE is parallel to AB, we can use similar triangles to set up the following proportion:

DC/AC = DE/AB

Substituting the given values, we get:

DC/17 = 6/AB

Since AB is the same length as DC, we can replace AB with DC:

DC/17 = 6/DC

Cross-multiplying and simplifying, we get:

DC^2 = 17 * 6

DC^2 = 102

DC = √102 in simplest radical form

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The total amount of merchandise that stores A and B sold is 21x²+5x+8

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, are two stores selling merchandise given by equation,

A = 13x²+8x-3 and B = 8x²-3x+11, we need to find the total amount of merchandise that stores A and B sold.

We add both the equations to find the same,

Total merchandise sold = 13x²+8x-3 + 8x²-3x+11

= 21x²+5x+8

Hence, the total amount of merchandise that stores A and B sold is 21x²+5x+8

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The integers are 16.8 and 26.8. To find the integers, we need to use a system of equations. Let's call the first integer x and the second integer y. We know that one integer is 10 more than another, so we can write the first equation as: x = y + 10. We also know that their product is 375, so we can write the second equation as: xy = 375.

Now we can substitute the first equation into the second equation to solve for one of the integers.

y(y + 10) = 375

y^2 + 10y - 375 = 0

Using the quadratic formula, we can find the value of y:

y = (-10 ± √(10^2 - 4(1)(-375)))/2(1)

y = (-10 ± √1900)/2

y = (-10 ± 43.6)/2

y = 16.8 or y = -26.8

Since y has to be an integer, we can only use the value of 16.8.

So, y = 16.8 and x = 16.8 + 10 = 26.8.

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The percentage of the attendees that had dessert at the football team banquet is 75%.

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

To find the percentage of attendees who had dessert, we can use the formula:

Percentage = (part/whole) x 100%

where:

Substituting the given values, we get:

percentage = (60/80) x 100%

percentage = 0.75 x 100%

percentage = 75%

Therefore, 75 perecent of the attendees had dessert.

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The quotient is -6x^2-2x-2 and the remainder is -4.

To find the quotient and remainder for the given expression, we can use long division.

First, we divide the first term of the dividend (-6x^3) by the first term of the divisor (x) to get -6x^2. This is the first term of the quotient.

Next, we multiply the first term of the quotient (-6x^2) by the divisor (x-1) to get -6x^3+6x^2. We subtract this from the dividend to get -2x^2-2.

We repeat this process with the new dividend (-2x^2-2) and the same divisor (x-1). We divide the first term of the new dividend (-2x^2) by the first term of the divisor (x) to get -2x. This is the second term of the quotient.

We multiply the second term of the quotient (-2x) by the divisor (x-1) to get -2x^2+2x. We subtract this from the new dividend to get -2x-2.

We repeat this process one more time with the new dividend (-2x-2) and the same divisor (x-1). We divide the first term of the new dividend (-2x) by the first term of the divisor (x) to get -2. This is the third term of the quotient.

We multiply the third term of the quotient (-2) by the divisor (x-1) to get -2x+2. We subtract this from the new dividend to get -4. This is the remainder.

So, the quotient is -6x^2-2x-2 and the remainder is -4.

We can check our work by verifying that

(Quotient)(Divisor) + Remainder = Dividend:

(-6x^2-2x-2)(x-1) + (-4) = -6x^3+6x^2-2x^2+2x+2x-2-4 = -6x^3+4x^2-2

Therefore, our answer is correct.

To know more about long division, refer here:

https://brainly.com/question/21416852#

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