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The coefficient of  x⁴y³ term in the expansion of  (x - 2y)⁷ is 280.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given expression:

(x - 2y)⁷

Expand this as given below,

(x - 2y)³ × [(x - 2y)²]²

(x³ + 6x²y + 12xy² + 8y³) × [(x² + 4y² - 4xy)]²

Solve the above expression to get,

x⁷ + 14x⁶ + 84x⁵y² + 280x⁴y³ + 560x³y⁴ + 672x²y⁵ + 448xy⁶ + 128y⁷

Here, the coefficient of the x⁴y³ is 280,

Therefore, the coefficient of  x⁴y³ term in the expansion of  (x - 2y)⁷ is 280.

To know more about the expression:

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Answer:

9

Step-by-step explanation:

RST = 90

90 - (22 + 41) = 27.

3x = 27

27/3 = 9

x = 9

Answer:

aₙ=5*4ⁿ⁻¹

Step-by-step explanation:

The common ratio is r=80/20=20/5=4

The explicit formula for a geometric sequence is aₙ=a₁*rⁿ⁻¹ where aₙ is the nth term, r is the common ratio, and a₁ is the first term.

Given:

a₁=5

r=4

Therefore, the explicit formula for the sequence is aₙ=5*4ⁿ⁻¹

Answer:

1.255

Step-by-step explanation:

10^-1 equals 0.1

1÷8=0.125

so our greatest one is 1.255

Answer:

Step-by-step explanation:

The first one is actually 0 I think. The instantaneous ROC at x=1 should also be 0. The last one should be correct.

Basically, the ROC for the first one is 0 because the y value at the start and end of the interval is the same, so the change is the same. However, for the instantaneous ROC at x = 0, you look at the graph and realize that if you find the derivative at that point, it is 0.

Answer:

b

Step-by-step explanation:

he will be negatives because he has very little money

Answer:

The new values are as follows:

Mean: 134

Median: 129

Mode: 121

Range=45

Standard Deviation=3.6

Step-by-step explanation:

When a k real number is added to all the elements of the dataset, the new measures of center (mean, median, and mode) are simply found by adding the value k to the previous values. Thus

[tex]Mean_{new}=Mean_{old}+k[/tex]

Here [tex]Mean_{old}[/tex] is 109 and k is 25 thus

[tex]Mean_{new}=Mean_{old}+k\\Mean_{new}=109+25\\Mean_{new}=134[/tex]

Similarly

[tex]Median_{new}=Median_{old}+k[/tex]

Here [tex]Median_{old}[/tex] is 104 and k is 25 thus

[tex]Median_{new}=Median_{old}+k\\Median_{new}=104+25\\Median_{new}=129[/tex]

Also

[tex]Mode_{new}=Mode_{old}+k[/tex]

Here [tex]Mode_{old}[/tex] is 96 and k is 25 thus

[tex]Mode_{new}=Mode_{old}+k\\Mode_{new}=96+25\\Mode_{new}=121[/tex]

When a k real number is added to all the elements of the dataset, the new measures of variation (range and standard deviation) remain the same thus.

[tex]Range_{new}=Range_{old}\\Range_{new}=45[/tex]

Similarly

[tex]Standard\ Deviation_{new}=Standard\ Deviation_{old}\\Standard\ Deviation_{new}=3.6[/tex]

So the new values of mean, median, mode, range, and standard deviation are 134, 129, 121, 45, and 3.6 respectively.

Answer:

A

Step-by-step explanation:

he goes up 3, and goes back 5 so 3-5=-2 but bases in the context, it's just 2 miles

Answer:

A.2 miles

Step-by-step explanation:

3 - 5 = -2

He is 2 miles from his starting point.

A.2 miles

Answer:

3/10

Step-by-step explanation:

probability box opened is glue = number of boxes that contain glue / total number of boxes

6/20

To transform to the simplest form. divide both the numerator and the denominator by 2

3/10

Answer:

1/2

Step-by-step explanation:

There are three odd and three even numbers on the die which would make 3/6 and simplified it is 1/2.

Answer:

it would be a 50% chance or 1/2 of rolling an odd nummber

Step-by-step explanation:

Answer:

about 28

Step-by-step explanation:

its actually 27.8125 but if we're estimating im assuming that means to round

Answer:

28 pints

Step-by-step explanation:

There are 28 pints in 445 fluid ounces .

Answer:

2000 meters

Step-by-step explanation:

From the above question

Total time = 15 minutes

Converting minutes to seconds

1 minute = 60 sec

15 minutes = x

Cross Multiply

x = 60 × 15 = 900 seconds

Hence, 900 seconds = Total time

Total time = Time to the marker + Time from the marker

From the question, we are given the Speed to the marker = 5 m/s

Speed from the marker = 4 m/s

Time = Distance/speed

Let the distance be represented by x

Hence:

x/4 + x/5 =900

Multiply all through equation by Lowest Common Denominator = 20

5x + 4x= 900×20

9x = 900 ×20

Divide both sides by 9

9x/9 = 900 × 20/9

x = 2000 meters

Therefore, the total distance to the marker = 2000 meters

Answer:

Step-by-step explanation:

This expression cannot be simplified in any way.  2a and 10b are NOT "like terms."  Likewise, the 'c' term has nothing in common with the other two terms.

Answer:

I can't see the file. But I did something that sounded LIKE this. So try multiplying the parallel sides.

Step-by-step explanation:

Answer:

The correct answer is -29/3

Answer: 341.4286

Step-by-step explanation:

Answer:

Domestic factor mobility. refers to the ease with which productive factors like labor, capital, land, natural resources, and so on can be reallocated across sectors within the domestic economy. Different degrees of mobility arise because there are different costs associated with moving factors between industries.

Answer:

it's arithmetic.

Step-by-step explanation:

geometric sequence is when each term moves on by dividing or multiplying.

arithmetic sequence is basically addition and etc.

Answer:x=0 and x=10

Step-by-step explanation:

Answer:

Question 3: B

Question 4: A, D, E

Step-by-step explanation:

Polynomials can not have a variable appear in the denominator.

4b^4-9b+2, 2x+7, and x-3 are in standard form.

Answer:

8(6 - x)

Step-by-step explanation:

I'm not exactly sure why the question asks for two answers.

We need to find the highest common factor that goes into both 48 and -8x.

That common factor is 8.

48 / 8 = 6

-8x / 8 = -x

Now, we factorise.

8(6 - x)

Answer:

c (3,11)

Step-by-step explanation:

Answer:

B. y = -2x + 8

Step-by-step explanation:

So the slope is the number that comes before the x, and if the slope is -2, that means the number before is -2, and it is.

And to know if it goes through (1, 6), put those numbers into the equation and see if they match up (x is the y-intercept)

6 = -2(1) + x

6 = -2 + x

x = 8

The one with both of these is B, which means B is the answer

Answer:

2. 70

3. 70

4. 110

5. 110

6.70

7. 70

8. 110

Step-by-step explanation:

a straight line = 180 so 1+2 has to = 180 1+3 has to = 180 2+4 has to = 180 and so on

Answer:

(-x,y)

Step-by-step explanation:

If it's positive and you flip it accross the y-axis, the x- coordinates become negative.

Answer:

1) Use two points to find the slope

Points from the graph

Find the slope:

Slope is 3, y-intercept is -1

The line is:

This is non-proportional as not passing through the origin (0, 0)

2) One point is sufficient to determine the slope as the line passes through the origin

Point (5, 2)

The slope is

Line is:

This is proportional

3)  is answered here: https://brainly.com/question/23004781

Answer:

-6, -5 ,-3 ,-1 ,1 ,4

Answer:

D. 21, 14

Step-by-step explanation:

As the question said, a parallelogram is formed when both pairs of opposite sides are congruent. That means that 21 and 3y are equal, as are y + 7 and 2y.

21 = 3y

/3    /3

7 = y

y + 7 = 2y

-2y     -2y

-y + 7 = 0

   -  7  - 7

-y = -7

* -1  * -1

y = 7

In both instances, y = 7. Now let's substitute that.

21 = 3(7)

21 = 21 is true.

7 + 7 = 2(7)

14 = 14 is true.

With that, the lengths of the opposites sides are 21 & 14, which is D.

Answer:

270cm²

Step-by-step explanation:

The formula is given as

S = bh × l (s1 + s2 + h)

l = 7cm

h = 5cm

s1 = 12 cm

s2 = 13cm

b = 12 cm

Surface Area = 12 cm × 5 cm × 7 cm(12 cm+ 13 cm+ 5cm)

= 60cm² × 7 cm(30 cm)

= 60cm² + 210 cm²

= 270 cm²