Use binomial expansion to solve each exercise. (a) Find the coefficient of xy19 in (3x − 2y) 20.(b) Give a formula for the coefficient of x k in (x+1/ x) n .

Answer:

A. 13

Step-by-step explanation:

[tex] (6y - 14) + 90 + (2y) = 180 [/tex] (angles on a straight line)

Solve for y

[tex] 6y - 14 + 90 + 2y = 180 [/tex]

Collect like terms

[tex] 6y + 2y - 14 + 90 = 180 [/tex]

[tex] 8y + 76 = 180 [/tex]

Subtract 76 to both sides

[tex] 8y + 76 - 76 = 180 - 76 [/tex]

[tex] 8y = 104 [/tex]

Divide both sides by 8

[tex] \frac{8y}{8} = \frac{104}{8} [/tex]

[tex] y = 13 [/tex]

Answer:

4 * 14

Step-by-step explanation:

Given

32 + 24

Required

Write as a product of two factors

First, we need to get the GCF of 32 and 24

The factors of 32 and 24 are:

[tex]32 = 1, 2, 4, 8, 16, 32.[/tex]

[tex]24 = 1, 2, 3, 4, 6, 8, 12, 24[/tex]

The GCF (greatest common factor) is 8

So, the expression 32 + 24 can be rewritten as:

[tex]32 + 24= 4(8 + 6)[/tex]

Add 8 + 6

[tex]32 + 24= 4(14)[/tex]

[tex]32 + 24= 4 * 14[/tex]

Hence,

32 + 24 can be rewritten as 4 * 14

Answer:

it is 8 (4+3) !!!! I just did the question! :)

Step-by-step explanation:

Answer:

[tex]-5x+5[/tex]

Step-by-step explanation:

[tex]5+2x-7x[/tex]

Combine like terms:

[tex]2x-7x+5\\[/tex]

which is

[tex]-5x+5[/tex]

Hope this helps :D

My Answers:

I think the equation you typed may have some typo error but:

Hope this helps and if you could mark me as brainliest. Thanks!

Answer:

133 windows

Step-by-step explanation:

Answer:

Time: 8 minutes

Altitude: 20000ft

Method 1 is easiest

Method 3 is easiest

Step-by-step explanation:

Given

Airplane 1:

[tex]Height = 44800 ft[/tex]

[tex]Descending\ Rate = 3100ft/min[/tex]

Airplane 2:

[tex]Ascending\ Rate = 2500ft/min[/tex]

Required

Determine when both planes would be at the same altitude?

Let the minute be represented by m

For Airplane 1, Its altitude at any height h is:

[tex]Airplane\ 1 = Height - Descending\ Rate * m[/tex]

It is minus (-) because the airplane is descending

[tex]Airplane\ 1 = 44800 - 3100 * m[/tex]

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

For Airplane 2, Its altitude at any height h is:

[tex]Airplane\ 2 = Ascending\ Rate * m[/tex]

[tex]Airplane\ 2 = 2500 * m[/tex]

[tex]Airplane\ 2 = 2500m[/tex]

Method 1:

For both heights to be equal, we have that:

[tex]Airplane\ 1 = Airplane\ 2[/tex]

This gives:

[tex]44800 - 3100m = 2500m[/tex]

Collect Like Terms

[tex]44800 = 2500m + 3100m[/tex]

[tex]44800 = 5600m[/tex]

[tex]5600m = 44800[/tex]

[tex]m = 44800/5600[/tex]

[tex]m = 8\ min[/tex]

Hence, the time they will be at the same altitude is 8 minutes

Substitute 8 for m in

[tex]Airplane\ 2 = 2500m[/tex]

[tex]Airplane\ 2 = 2500 * 8[/tex]

[tex]Airplane\ 2 = 20000\ ft[/tex]

Hence, they will be at the same altitude at 20000ft

Method 2:

We have that:

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 2 = 2500m[/tex]

Since they are to be at the same altitude, then

The difference in their altitude must be 0

i.e.

[tex]Airplane\ 1 - Airplane\ 2 = 0[/tex]

This gives

[tex]44800 - 3100m - 2500m = 0[/tex]

[tex]44800 - 5600m = 0[/tex]

Collect Like Terms

[tex]5600m = 44800[/tex]

[tex]m = 44800/5600[/tex]

[tex]m = 8\ min[/tex]

Substitute 8 for m in

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]

[tex]Airplane\ 1 = 44800 - 24800[/tex]

[tex]Airplane\ 1 = 20000\ ft[/tex]

Method 3:

We have that:

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 2 = 2500m[/tex]

Since they are to be at the same altitude, then

The ratio of their altitudes must be 1

i.e.

[tex]\frac{Airplane\ 1}{Airplane\ 2} = 1[/tex]

[tex]\frac{44800 - 3100m}{2500m} = 1[/tex]

Cross Multiply

[tex]44800 - 3100m = 1 * 2500m[/tex]

[tex]44800 - 3100m = 2500m[/tex]

Collect Like Terms

[tex]44800 = 2500m + 3100m[/tex]

[tex]44800 = 5600m[/tex]

[tex]5600m = 44800[/tex]

[tex]m = 44800/5600[/tex]

[tex]m = 8\ min[/tex]

Substitute 8 for m in

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]

[tex]Airplane\ 1 = 44800 - 24800[/tex]

[tex]Airplane\ 1 = 20000\ ft[/tex]

Hence;

Their altitudes must be 20000ft

Though the three methods applied uses the same logic at some point, the first method applied is still the easiest and it is a straight forward method that could be applied in solving the question.

Method 3 is the most difficult.

Answer:

49, 51, 53

Step-by-step explanation:

Let the first odd integer be n.

Then the consecutive odd integer will be (n+2).

This will be followed by (n+4).

We know that the sum of these three is 153. In other words:

[tex]n+(n+2)+(n+4)=153[/tex]

Solve for n. Combine like terms:

[tex]3n+6=153[/tex]

Subtract 6 from both sides:

[tex]3n=147[/tex]

Divide both sides by 3:

[tex]n=49[/tex]

Therefore, our first odd number is 49.

So, our consecutive numbers must be 51 and 53.

Hence, our sequence is:

49, 51, 53

Notes:

If we get an even number for n or a non-integer value, then there are no three consecutive odd integers that sum to 153.

Answer:

49, 51, 53

Step-by-step explanation:

All odd numbers:

49 + 51 = 100

100 + 53 = 153

Answer:

[tex][f(x)]^2-g(x) = 5x^2-13x-8[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x-2\\g(x) = -x^2+5x+12[/tex]

To find: [tex][f(x)]^2-g(x)[/tex]

First of all the square of first function f(x) will be found and then second function g(x) will be subtracted from the square of first function

Squaring the first function

[tex][f(x)]^2 = (2x-2)^2\\Using\ (a-b)^2 = a^2-2ab+b^2\\\[f(x)]^2 = (2x)^2-2(2x)(2)+(2)^2\\= 4x^2-8x+4[/tex]

Now subtracting g(x) from [f(x)]^2

[tex][f(x)]^2-g(x) = (4x^2-8x+4)-(-x^2+5x+12)\\\[f(x)]^2-g(x) = 4x^2-8x+4+x^2-5x-12[/tex]

Combining alike terms

[tex][f(x)]^2-g(x) = 4x^2+x^2-5x-8x+4-12\\\[f(x)]^2-g(x) = 5x^2-13x-8[/tex]

Hence,

Subtracting g(x) from the square of f(x) gives us:

[tex][f(x)]^2-g(x) = 5x^2-13x-8[/tex]

Answer:

-1 5/8

Step-by-step explanation:

Let the total amount in the bowl be x;

If on Day 1, the volume of water in the bowl decreases by 7/8 cup, the remaining water will be;

x - 7/8

If on day 2, the volume in the bowl decreases by 3/4 cup, the remaining volume of water after the second day will be;

= x - 7/8 - 3/4

= x - (7-2(3))/8

= x - (7+6)/8

= x - 13/8

This shows that the total change after the two days is -13/8

As a mixed fraction;

-13/8 = -1 5/8

Answer:

3x - 2

Step-by-step explanation:

5x +1 -2x -3    Combine like factors with x

5x -2x = 3X

3x +1 -3         Combine like factors without x

1 -3 = -2

Answer:

VALUE OF X:

3x-13+61 = 90

3x+48 = 90

3x = 42

x = 14

MEASURE OF <MNQ:

3x-13

= 3(14)-13

= 42-13

= 29

Answer:

3 Letters Word: 6 Distinct Ways: 4 Letters Word: 24 Distinct Ways: 5 Letters Word: 120 Distinct Ways: 6 Letters Word: 720 Distinct Ways: 7 Letters Word: 5,040 Distinct Ways: 8 Letters Word: 40,320 Distinct Ways: 9 Letters Word: 362,880 Distinct Ways: 10 Letters Word: 3,628,800 Distinct Ways

Step-by-step explanation:

The number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.

The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.

As we can see that the word 'PHILOSOPHY' has 10 letters therefore, the letters of the word can be arranged in the 10! manner, but it contains the letter P, H and O twice therefore, there will be words that will look the same and are counted twice. Thus, the number of ways the word PHILOSOPHY can be arranged are,

[tex]\text{Number of ways} = \dfrac{10!}{2! \times 2! \times 2!} = 453,600[/tex]

Hence, the number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.

Learn more about Factorial:

https://brainly.com/question/16674303

Answer :

D - 28 + 14 = 7(4+2)

Answer:

The answer is "$3640.58"

Step-by-step explanation:

This question is incomplete, that's why we add another question in the attached file. Please find it.

P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2  

Total  [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:

[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]

[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]

[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]

The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]

Answer:

K=5

Step-by-step explanation:

12k-15=35+2k

12k=50+2k

10k=50

k=5

Answer:

[tex]k = 5[/tex]

Step-by-step explanation:

[tex]12k - 15 = 35 + 2k[/tex]

Our goal is to isolate k

[tex]12k - 15 = 35 + 2k\\\;\;\;\;+15 \;\;\;\;\;\;\; +15[/tex]

[tex]12k = 50 + 2k\\-2k \;\;\;\;\;\;\;\; -2k[/tex]

[tex]10k = 50[/tex]

Now we have k isolated to one side. Our final step is to have k be just k, no coefficient. We can do this by dividing each side by the coefficient.

[tex]\large\frac{10k}{10} = \frac{50}{10} \\\\10k\;\div\;10 = k\\50\;\div\;10 = 5\\[/tex]

[tex]\large\boxed {k \;=\;5}[/tex]

~[tex]InLoveWithPugs[/tex]

[tex]Moderator\\Math\ Enthusiast[/tex]

Answer:

c.) 2 1/3

Step-by-step explanation:

i know

Answer:

24m 10+3+3+2+6

Step-by-step explanation:

Answer:

i believe its 24m surface area

Step-by-step explanation:

sorry if wrong

Answer:

19

Step-by-step explanation:

12, 16, 20, 44

Just substitute the number on the x side of the table for x in the equation and solve to get the y value.

The completed table of Y values using the function rule y = 4 + 4x is as follows:

X     Y

2     12

3     16

4     20

10    44

To fill in the Y values using the function rule y = 4 + 4x, we substitute the given X values into the equation and solve for Y.

When the value of X = 2:

4 + 4(2) = 4 + 8 = 12

When the value of X = 3:

4 + 4(3) = 4 + 12 = 16

When the value of X = 4:

4 + 4(4) = 4 + 16 = 20

When the value of X = 10:

4 + 4(10) = 4 + 40 = 44

The completed table is as follows:

X     Y

2     12

3     16

4     20

10    44

Learn more about the Linear equations here:

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Answer:

7/10>0.07

Step-by-step explanation:

You can turn 7/10 into decimal and its 0.7.

0.7 is greater than 0.07 so you would put a > sign

so the answer is 7/10>0.07

pls mark brainliest

Answer:

2(x+4)

Step-by-step explanation:

To factor you have to divide both terms by the greatest common factor, which in this case is 2. Using distribution you can check your answer.

Answer: 2(x + 4)

Explanation: If you're asked to factor a polynomial,

the first thing you want to look for is the greatest common factor

for the terms that are involved.

The greatest common factor of 2x and 8 is 2.

So a 2 can factor out.

Inside the parenthses, we have each term divided by

the 2 that factored out of the polynomial.

So we have 2(x + 4).

Answer:

388

Step-by-step explanation:

We need to find the area of the semicircle and parallelogram separately and then combine.

The formula for the area of a semicircle is 1/2(pi*r^2)

r = 12. 12^2 = 144

1/2(pi*144) = 226..1946711 which we can just round to 226

The formula for the area of a parallelogram is bh

b = 18, h = 9. 18*9 = 162.

226+162 = 388

Answer:

Step-by-step explanation:

total area = semi circle + parallelogram

                = (1/2 π 6²)  +  (9 x 18)

                = 56.55  + 162

                = 218.55 sq. units

Answer:

David make his first error at Step 3

Step-by-step explanation:

We need to determine the error David made when finding the product of (-2.5)(-8.3)

He did the following steps

Step 1: (–2.5)(–8.3) = (–8.3)(–2.5)

Step 2: = (–8.3)(–2) + (–8.3)(–0.5)

Step 3: = (–16.6) + (–4.15)

Step 4: = –20.75

David made a mistake in Step 3

When we multiply (-1) with (-1) we get + instead of - sign. The correct step 3 would be:

Step 3: =(16.6)(4.15)

Step 4: =20.75

So, David make his first error at Step 3

Given :

The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by [tex]K(x) = \dfrac{5x}{x^2+9}[/tex].

To Find :

Find the time at which the concentration is a maximum. b. Find the maximum concentration.

Solution :

For maximum value of x, K'(x) = 0.

[tex]K'(x) = \dfrac{5(x^2+9)- 5x(2x)}{(x^2+9)^2}=0\\\\5x^2+45-10x^2=0\\\\5x^2 = 45\\\\x = \pm 3[/tex]

Since, time cannot be negative, so ignoring x = -3 .

Putting value of x = 3, we get, K(3) = 15/( 9 + 9) = 5/6

Therefore, maximum value drug in bloodstream is 5/6 at time x = 3 units.

Hence, this is the required solution.

Answer:

w+14,

Step-by-step explanation:

Answer:

the 2 nd one 9/m=10/n

Step-by-step explanation:

Answer:

210m

Step-by-step explanation:

60+60+45+45

120+90

210m