Mathematics Middle School

What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? 4 32 128 512

Answers

Answer 1
512 is the coefficient of the x9y-term                             
Answer 2

Answer:- 512


Explanation:-

We know that [tex](m+1)^{th},\ (T_{m+1})[/tex] in the binomial expansion [tex](p+q)^n[/tex] is given by

[tex]T_{m+1}=^nC_m\ p^{n-m}q^m[/tex]

Assume that [tex]x^9y[/tex] occurs in the [tex](m+1)^{th}[/tex] term of the expansion of [tex](2y+4x^3)^4=(4x^3+2y)^4[/tex]

[tex]T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m[/tex]

Comparing power of x and y in  [tex]x^9y[/tex]  we get m=1

Thus term for m=1 [tex]=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y[/tex]

Thus the coefficient of [tex]x^9y[/tex] is 512.

Related Questions

whats the soultion for 10000 ft/hr = mi/hr

Answers

Hi! There are 5,280 feet in a mile. Therefore, you need to divide 10,000 feet by 5,280 (to see how many miles there are per every 5280 feet) and you get 1.89 miles per hour.

solve 3x/2 - 7=x/4 - 2 i know the answer is 4 but how do i solve this

Answers

First, multiply by 4 on both sides to eliminate the denominator, and you get...
6x-28 =x-8
Subtract x on both sides and add 28...
5x=20
Divide to isolate the variable...
x=4
Hope this helps

Nancy bought an extra-large bag of 1,500 beads to make necklaces. When she got home, she found another bag with 660 beads in it. If she uses all of the beads and uses 60 beads per necklace, how many necklaces can she make?

Answers

She can make 36 necklaces.

Calculate the future value of an investment of $2300, after 7 months, earning 6.6% APR, compounded monthly, by compounding manually.

Answers

The future value of an investment, P after n years at an APR of r% compounded t times a year is given by
[tex]FV=P\left(1+ \frac{r}{t} \right)^{nt}[/tex]

Given an investment of $2300, after 7 months, earning 6.6% APR, compounded monthly, the future value is given by
[tex]FV=2,300\left(1+ \frac{0.066}{12} \right)^{12\left( \frac{7}{12}\right) } \\ \\ =2,300(1+0.0055)^7=2,300(1.0055)^7 \\ \\ =2,300\times1.03914=\$2,390.02[/tex]

A credit card states that your payment will be a minimum of $15 plus 1% of your unpaid balance. Your unpaid balance is $2,365.What is your payment this month?

Answers

Alright, to get 1% of his unpaid balance, we can make 1% = 0.01 by moving the decimal place 2 places over. Multiplying 0.01 by 2365 gets 1% of your unpaid balance=23.65. Since we have to add 15 as a base value, we have 
15+23.65=38.65

how would you find the area and Perimeter of this shape?

Answers

Perimeter: 10 + 4 + 7.5
P = 21.5
Area: 4 x 10 
A = 40

The heights of four boys measured 152.0cm, 150.75cm, 149.5cm and 149.25cm. Bradley is the tallest, Calvin is taller than Josh, but shorter than Mark. Josh is the shortest. What is Mark's height?

Answers

I believe the answer would be 150.75 cm as Marks height. I got this by if Bradley is the tallest, he would be 152.0 and if Calvin is taller than Josh, who is the shortest, the only height left would be Marks at 150.75

A warehouse floor has a perimeter of 6,615 feet. What is the perimeter of the floor in yards ? oh and please tell me how you got the answer

Answers

Since there are 3 feet in 1 yard you need to divide 6,615 divided by 3 which equals 2205 yards.
1 Yard = 3 feet
or 3 feet = 1 yard

to convert 6615 feet into yard, you have to divide it by 3.

6615 feet = 6615/3 yard = 2205 yard.

Your answer is 2205 yards.

Hope it helps!

Find the value of m in each equation below. Justify your answer.
(x^m × x^2)^3 (k^3)^5 = x^21k^15

Answers

The main properties we use in this problem are:

i) [tex]x^a \cdot x^b=x^{a+b}[/tex] (so, when we multiply 2 exponents of the same base, we add the exponents)

ii) [tex]({x^a})^b=x^{a \cdot b}=x^{ab}[/tex]


thus, 

[tex](x^m \cdot x^2)^3=({x^{2m}})^3=x^{2m \cdot3}=x^{6m}[/tex]

by first applying property i) then property ii)

also, [tex]({k}^3)^5=k^{15}[/tex], by property ii)



So we have:

[tex]({x^m \cdot x^2})^3 \cdot({k}^3)^5=x^{21} \cdot k^{15}\\\\x^{6m}\cdot k^{15}=x^{21} \cdot k^{15}[/tex], 


now we only have to compare the exponents. 

6m must be equal to 21, 

thus m=21/6=7/2


Answer: m=7/2

How many cups will I need for 30 biscuits if there’s 2 cups for every 8 biscuits

Answers

divide 30/8 = 3.75

3.75 *2 = 7.5 cups

If there's 2 cups for every 8 biscuits (not try to be mean, but I really really hate biscuit) there will be 7.5 cups. First, you take 8 and divide it by 2 to find out how many biscuits that 1 cup needs, so 4 biscuits per cup. Last, all you have to do left is take 30 and divide it by 4, which will gives you 7.5. So, for 30 biscuits, you will need 7.5 cups, even though I don't know what cup is it (flour, sugar, salt, water,...).

Which option below correctly describes the domain of and explains why the range of b is not all real numbers?

Answers

what are the options?^

A farmer collects 1,250 eggs on a morning. She puts 30 eggs on each tray. How many egg trays does she need to hold all the eggs? Show your work.

Answers

You would do 1250 dived by 30.
1250/30 =  41.666
And if you round that, she would need 42 trays.

Hope I helped :)
It will need 42 trays 1250 divided by 30 is 41.666667 but if you round it, its 42

 

Why is it important to have complex carbohydrates before a big race?

(Again, not math. I know, its to get the answer faster..)

Answers

Complex Carbs are very useful because they are healthy and do not interfere with a race. They turn those into glucose and helps the energy be saved longer. 
Complex Carbohydrates are made up of sugar molecules strung together in long chains. Both simple and complex carbs can be turned into Glucose which is used as short term energy. This short term energy is great for short races, for marathons I suggest more lipids as well. The act of eating a lot of carbs the night before a race is called "Carb Loading" 

A relay race is 1/10 kilometer long. Four athletes will run an equal distance to complete the relay. How far does each athlete run ?

Answers

25 metres. Because 1/10th of a kilometre is a 100 metres. And four athletes divided by 100 metres is 25 metres.

Answer:

25 meters.

Step-by-step explanation:

Let us suppose each athlete run x km.

Hence, four athlete will run 4x km.

Now, the distance of the relay race is 1/10 km

Thus, we have

[tex]4x=\frac{1}{10}[/tex]

Divide both sides by 4

[tex]x=\frac{1}{40}km[/tex]

Now, 1 km = 1000 meters. Thus, we have

[tex]x=\frac{1}{40}\times1000\\\\x=25[/tex]

Thus, each athlete run 25 meters.

Write each fraction in simplest form

Answers

9/18 simplified would be 1/2
29. = 1/2 in simplest form. Hope I helped

what is the answer to 2(0.5c−1.5)−6=−2 please show work!!!!

Answers

ANSWER: c = 7

WORK:
2(0.5c - 1.5) - 6 = -2
c - 3 - 6 = -2
c - 9 = -2
c - 9+9 = -2+9
c = 7
2(0.5c - 1.5) = -2 + 6

2(0.5c - 1.5) = 4

0.5c - 1.5 = 4/2

0.5c - 1.5 = 2

0.5c = 2 + 1.5

0.5c = 3.5

c = 3.5/0.5

Lastly simplify

Answer: c = 7.

Help me please I just need math and that's all for math

Answers

1. 3 1/4
2.9 1/2 hope it helped

3 1/4             9 1/2

hope it helpedd

in geotown, there are 210 own a tablet. This is at least 4/5 of all teenagers that live in geotown. What is the maximum number of teenagers who live geo town

Answers

210 = 4/5 (This means that 4 out of five people (210 people) are a teenager)

Then you divide 210 by the numerator to get 1/5 people:
210 / 4 = 52.5

Then you can multiply the 1/5 people (52.5) by 5 to get 5/5:
52.5 * 5 =  262.5 (rounded to 262)

Thus the maximum amount of teenagers in Geotown is 262.

Hope this helps! :)
Final answer:

The maximum number of teenagers who live in Geotown can be found by solving an equation using the given information that 210 teenagers own a tablet, which is at least 4/5 of all teenagers in Geotown.

Explanation:

We are given that 210 teenagers own a tablet, and this number is at least 4/5 of all teenagers in Geotown. Let's represent the total number of teenagers in Geotown as 'x'. According to the given information, 4/5 of x is equal to 210. We can set up the equation (4/5)x = 210 and solve for x.

To solve for x, we can multiply both sides of the equation by the reciprocal of 4/5, which is 5/4. This gives us x = (5/4) × 210 = 262.5. However, since the number of teenagers must be a whole number, we round down to the nearest whole number and conclude that the maximum number of teenagers who live in Geotown is 262.

Learn more about the Maximum number of teenagers in Geotown here:

https://brainly.com/question/5566875

#SPJ2

3(n - 1) = 5n + 3 - 2n

Answers

3(n - 1) = 5n + 3 - 2n
3n - 3 = 3n + 3
3n - 3n = 3 + 3
0 = 3 ...(incorrect)
This equation has no solution

What is the prime factorization of 375

Answers

Answer:

See the image for the answer.

PLS HEEEEEEELP 20 POINtS
Evaluate |x + y|, for x = 8 and y = -15.

7

-7

23

-23

Answers

So first, we want to substitute all variables in.

|8 + -15|

Or,

|-7|

And the bars around it mean absolute value, or how far away it is from 0. In this case, it would be 7.

So your solution is 7.

Using long division write each rational number as a terminating decimal

Answers

The answer is 2.3 lol long division sucks

Are there any rational numbers between 0.4 repeat and 4/9

Answers

0.4(repeating) and 4/9 are the same number....so, no, there is no rational numbers between them....there is no numbers between them.

what is 2/3, 66%, and 0.67 from greatest to least

Answers

66%, then 2/3, and lastly 0.67. 2/3 is repeating so it is more then 66% but less than 0.67

answer:
0.67, 2/3, 66%
work:
change all to decimals.
0.666666666667, 0.66 and 0.67.
-order from greatest to least 
0.67, 0.66666666667, 0.66
-convert back
0.67, 2/3, 66%
Hope this helps, have a great day! :D

200 divided by 19.30 to the nearest 10th

Answers

19.30 to the nearest tenth is 20   20/200 = 10?

the percent of increase is 16% if the new number is 522 find the original number

Answers

The original number is 438.48. Hope this helps!

To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?

Answers

find min
min is 1.5-0.2=1.3cm

max is 0.2+1.5=1.7cm

so it would be a graph from 1.3cm to 1.7cm

like below

Answer: option A

Step-by-step explanation:

Does the Commutative Property of Addition apply when you add two negative integer?

Answers

Yes because whether you flip two negative integers around, the answer would still remain the same since its addition.

For example:
-9+-3 = -12 = -3+-9
Yes
Hopefully this helps

Solve 14n+q=rt-4n for n

Answers

Hey there!

In order to solve this, all you need to do is cancel out terms until you have n on one side of the equal sign and everything else on the other side. 

14n + q = rt – 4n (add 4n to both sides to combine 4n and 14n)
18n + q = rt (subtract q from both sides)
18n = rt – q (divide both sides by 18)
n = (rt – q) ÷ 18

Hope this helped you out! :-)

The solution for n is [tex]\( n = \frac{{q - rt}}{{10}} \)[/tex].

To solve for n in the equation -14n + q = rt - 4n, we need to isolate n on one side of the equation.

First, let's gather all terms involving n on one side. Adding 4n to both sides of the equation, we get:

-14n + 4n + q = rt

Simplifying the left side, we have:

-14 + 4)n + q = rt

-10n + q = rt

Next, let's isolate n by moving the term q to the other side. Subtracting q from both sides, we have:

-10n = rt - q

Finally, to solve for n, divide both sides by -10:

[tex]\[ n = \frac{{rt - q}}{{-10}} \][/tex]

So, the solution for n is [tex]n = \frac{{q - rt}}{{10}} \)[/tex].

Six rectangles have a area of 64 square units what is the perimeter

Answers

Solution:1. A= 64m^2, l = 12 mA = wl Solving for PP=2 l+2(A/ l) = 2·12+2·64/12 ≈ 34.66667 m
Solution:2. A= 64m^2, l = 4 mA = wl Solving for PP=2 l+2 (A/ l) = 2·4+2·64/4 ≈ 40 m
Solution:3. A= 64m^2, l = 24 mA = w l Solving for PP=2 l+2 (A/ l) = 2·24+2·64/24 ≈ 53.33333 m
Solution:4. A= 64m^2, l = 16 mA = w l Solving for PP=2 l+2 (A/ l) = 2·16+2·64/16 ≈ 40 m Solution:5. A= 64m^2, l = 8 mA = w l Solving for PP=2 l+2 (A/ l) = 2·8+2·64/8 ≈ 32 m 
Solution:6. A= 64m^2, l = 32 mA = w l Solving for PP=2 l+2 (A/ l) = 2·32+2·64/32 ≈ 68 m
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