Mathematics High School


The first three terms of the binomial expansion of (2 – ax)" are 64 – 16bx +100bx?.
Find the value of each of the integers n, a and b.

Ans: n=6, a=5, b=60
​

The First Three Terms Of The Binomial Expansion Of (2 Ax)" Are 64 16bx +100bx?.Find The Value Of Each

Answers

Answer 1

Answer:

n = 6, a = 5, b = 60

Step-by-step explanation:

In a binomial function (a + b)ⁿ expression that represents the terms,

(a + b)ⁿ = [tex]\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k[/tex]

By this formula,

1st term = [tex]\binom{n}{0}a^{n-0}b^0[/tex] = aⁿ

2nd term = [tex]\binom{n}{1}a^{n-1}b^1[/tex] = [tex]n.a^{n-1}b^1[/tex]

3rd term = [tex]\binom{n}{2}a^{n-2}b^2[/tex] = [tex]\frac{n(n-1)}{2}.a^{n-2}.b^2[/tex]

For the binomial expansion initial 3 terms of (2 - ax)ⁿ = 64 - 16bx + 100bx²

Terms of (2 - ax)ⁿ = [tex]2^n+n(2)^{n-1}(-ax)+\frac{n(n-1)}{2}(2)^{n-2}(-ax)^2[/tex]

                             = [tex]2^n-n(2)^{n-1}(ax)+n(n-1)(2)^{n-3}(a^2x^2)[/tex]

Comparing the terms of both the expansions,

1st term

2ⁿ = 64

2ⁿ = 2⁶

n = 6

2d term

[tex]n(2)^{n-1}(ax)=16bx[/tex]

[tex]6(2)^{6-1}(a)=16b[/tex]

192a = 16b

b = 12a -----(1)

3rd term

[tex]n(n-1)2^{n-3}(a^2x^2)=100bx^2[/tex]

[tex]6(6-1)2^{(6-3)}(a^2)=100b[/tex]

[tex]30(2)^3(a^2)=100b[/tex]

240a² = 100b

b = 2.4a² -----(2)

From equation (1) and (2),

b = 12a = 2.4a²

a = [tex]\frac{12}{2.4}=5[/tex]

From equation (1)

b = 12a = 60

Therefore, n = 6, a = 5, b = 60

Related Questions

1. 133 1/3% of 36=?
2. 260% of 360=?

Answers

Answer:

1. 133 1/3% of 36=48

2. 260% of 360=936

Step-by-step explanation:

1. 133 1/3% of 36

=(133 1/3)%  of 36

=(133/1+1/3)% of 36

=(399+1/3)% of 36

=(400/3)% of 36

=(400/3 *100) *36

=(400/300*36)

=4/3*36

=4*12

=48  Ans

---------------------------------------------------------------------------------------

2. 260% of 360

=260% of 360

=260/100*360

=26/10*360

=26/1*36

=936 Ans

Please answer this correctly, and you'll recieve brainliest!

Which figure can be transformed into figure L by a 90° rotation clockwise about the origin followed by a translation 2 units down?

Question Options:
Question 2 options:

figure J

figure M

figure N

figure P

Answers

Answer:

J can be rotated

Step-by-step explanation:

Answer: Figure J

Clockwise and 2 units down

) In each diagram, line p is parallel to line f, and line t intersects lines p and f. Based
on the diagrams, which statement is true? (8.8D)
A. The value of x should be 75, because the angles shown in the diagrams are
congruent
B. The value of x should be 105, because the measures of the angles shown in the
diagrams add up to 180°.
C. The value of x should be 140, because the measures of the angles shown in the
diagrams should add up to 360and 360 - (110 + 110)
D. The value of x should be 70, because the measures of the angles shown in the
diagrams are both 70
​

Answers

Answer:

A. The value of x should be 75, because the angles shown in the diagrams are congruent.

Step-by-step explanation:

I did the test

Please help thank you so much

Answers

Answer:

no

when you enter the point into the equation and solve, it does not work

Answer:

NO

Step-by-step explanation:

Find the slope of the equation y=2x+5

Answers

Answer:

the slope is 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

Will mark brainliest

Answers

Answer:

Step-by-step explanation:

We know she gets 4 more quarters so: q+4

She gives away 3 dime so: d-3

And the nickels stay the same: n

In total the expression would be:  q+4+d-3+n

Hope this helps :D

A gumball machine contains 23 green gumballs, 52 red gumballs, 34 blue gumballs, 61 yellow gumballs, and 30 pink gumballs.

What percentage of the gumballs are red?

Answers

Answer:

26%

Step-by-step explanation:

if a =(1 2 3 4 5 then the number subsets a is ​

Answers

Answer:

Every choice doubles the number of subsets previously built, so the 4 subsets of {1,2} become 8 when we think of subsets of {1,2,3}. Then 16, and finally 32 subsets for {1,..5}.

Step-by-step explanation:

hopefully this helps!

what is 1/2 divded by 3/4​

Answers

Answer:

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {1}{2}} \div {\dfrac {3}{4}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {1}{{\cancel{2}}}}\times {\dfrac{{\cancel {4}}}{3}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {2}{3}}[/tex]

PLEASE HELPP!! I WILL GIVE BRAINLIEST!

Answers

Answer:

1.5 white 2 blue

Step-by-step explanation:

ANSWER THE QUESTIONS PLS. SERIOUS ANSWERS ONLY. 100 POINTS

Answers

Answer:

Step-by-step explanation:

Tnd 50 dia w2 wop p.35.00 dma fw

Answer: the answer is wha the other dude said

Step-by-step explanation:

EASY!!!! Answer this question correctly

Answers

Answer:

1st answer choice- You do not have enough jars because 20 jars will only hold 35 cups of applesauce.

Step-by-step explanation:

So 1.75 cups of applesauce fits in a jar. You have 20 jars so you multiply the cups of applesauce that can fit in the jar by how many jars you have. It will look like this: 1.75x20=? Now you multiply them and you get 35 which is how many cups of applesauce 20 jars will hold. You will have 5 cups of applesauce left over that cannot be transformed into a jar.

If you can please make my answer the brainliest that would be much appreciated. Thanks!

Answer:

You do not have enough jars because 20 jars will only hold 35 cups

Step-by-step explanation:

2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of
solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither
(a) 6x + 4x - 6 = 24 + 9x
(b) 25 - 4x = 15 - 3x + 10 - X
(c) 4x+8 = 2x + 7 + 2x - 20


PLEASE INCLUDE THE CONTRADICTION AND IDENTITY OR NEITHER I WILL GIVE BRANLISEST !

Answers

Answer:

a. infinite solutions, answer is x = 30, identity equation

b. no solution, a contradiction equation

c. no solution, a contradiction equation

Step-by-step explanation:

Which statement best explains the relationship between
lines AB and CD?
They are parallel because their slopes are equal.
They are parallel because their slopes are negative
reciprocals.
They are not parallel because their slopes are not
equal.
They are not parallel because their slopes are
negative reciprocals.

Answers

Answer:

A

Step-by-step explanation:

Thats what im pretty sure it is, you didnt provide a picture but i know that parallel slopes are equal to each other

Answer:

A Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Solve each equation. Write The properties that justify each step in the solution method
a. 3x - 8 = -7x + 18

Answers

Answer: I’m not sure how to explain so you look at what I did and if it is an equation then I did solve it but if I should did the two separately then tell me so I can do it , have a great and funny day :)

Step-by-step explanation:

Please help with this math problem ASAP!

Answers

Answer:

0

Step-by-step explanation:

0 time difernce because a negative numbers means it will have an world record , while a positive time diference means it did not beat the world record

PLS PLS PLS HELPPPP NO EXPLANATION NEEDED

Answers

Answer:

i believe its C

Step-by-step explanation:

Answer:

it is a little hard to see but yeah from what I can tell it looks like it would be C

Step-by-step explanation:

Hope this helps

Tell me if it is wrong

please please help me quickly ​

Answers

Answer:

1/4

Step-by-step explanation:

f(x)=-(x-3)²+1 determine the vertex

Answers

(3,1) would be the answer

Answer:

vertex = (3, 1 )

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x - 3)² + 1 ← is in vertex form

with vertex (h, k ) = (3, 1 )

can someone help me with this one.
i will give you a brainlist if you give the answers. thanks!​

Answers

Answer:

A= 115

B= 65

C= 90

D= 65

E= 15

F= 90

Step-by-step explanation:

If you need explanations, tell me.

Please do 11 vote you brainiest

Answers

Answer:

ITS B

Step-by-step explanation:

Help me please, if you don’t know the answer or if slightly unsure please leave and don’t answer. Thank you.

Answers

Answer:

Step-by-step explanation:

1). Swap the order of equations.

2). Yes, system of equations are equivalent with the same solution.

29x = 46 ⇒ x = [tex]\frac{46}{29}[/tex]

y = - [tex]\frac{184}{29}[/tex] + [tex]\frac{203}{29}[/tex] = [tex]\frac{19}{29}[/tex]

( - [tex]\frac{46}{29}[/tex] , [tex]\frac{19}{29}[/tex] )

A rectangular frame has length (x+2) units and width (x-2) units. If the area is 96 square units, what is the value of x?

Answers

Answer:

x=10

Step-by-step explanation:

according to the question

(x+2)(x-2)=96

=>x^2-4=96

=>x^2=96+4

=>x^2=100

=>x=√100

Therefore

x=10

x=-10

As width and length can't be negative

So x=10

Width=10-2=8

Length=10+2=12

12×8=96 (proven)

Answer:

Please check the explanation.

Step-by-step explanation:

As we know that the area of a rectangle is defined by multiplying the length by the width.

[tex]A=l\times w[/tex]

Given

rectangular frame length = l = (x+2) unitsrectangular frame width = w = (x-2) unitsArea = 96 square units

substituting all the given values in the formula to find the value of x.

[tex]A=l\times w[/tex]

[tex]96=\left(x+2\right)\times \left(x-2\right)[/tex]

[tex]96=x^2-4[/tex]

[tex]x^2-4=96[/tex]

subtract 96 from both sides

[tex]x^2-4-96=96-96[/tex]

[tex]x^2-100=0[/tex]

[tex]x^2=100[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{100},\:x=-\sqrt{100}[/tex]

[tex]x=10,\:x=-10[/tex]

Putting x = -10 in the length and width will make the length and width negative, which can not be possible.

i.e.

length = l = x+2 = -10+2 = -8 units

width = w = x-2 = -10-2 = -12 units

Therefore, x=-10 must be excluded.

Now, putting the length of x = 10.

i.e.

length = l = 10+2 = 10+2 = 12 units

width = w = x-2 = 10-2 = 8

[tex]A=l\times w[/tex]

96 = 12 × 8

96 = 96

Therefore, the correct value of x = 10

PLS HELP AND HURRY ITS TIME

Answers

Answer:

5 units down

Step-by-step explanation:

i’m not sure but just guess

i really need help with this!!

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]y = - \frac{1}{6} x - 1 \\ [/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Let me know if you need explanation.

Determine the interval in which this function is DECREASING

Answers

Answer:

4

Step-by-step explanation:

4

need help asap please!!!!!!1

Answers

Answer:4/3 I think

Step-by-step explanation:

Please help I really really need it

Answers

Answer:

Just give me a few min ill be right back to help :)

Step-by-step explanation:

if x=5 then what is x squared?

Answers

x squares is x ^2 or something like that

Answer:

25

Step-by-step explanation:

[tex]x^2\\\\x=5\\\\5^2=5*5=25[/tex]

Hope this helps.

Wendy jarred 8 liters of jam after 2 days. How many days does Wendy need to spend making jam if she wants to jar 32 liters of jam in all? Assume the relationship is directly proportional.

Answers

Answer:

8 days

Step-by-step explanation:

it takes her two days to make 8 liters so for every 8 liters you add on two more days. 8:2, 16:4, 24:6, 32:8

Other Questions
please help asap!!!! ill mark brainlest if u have a twin answer this belowwho farts more Find the gradient of the line perpendicular to ABFind the equation of the line perpendicular to AB and passing through point C Simplify 4(2x-3) 7th grade math Which is an attribute of an effective team? charlie and his sister had a garage sale charlie made $23.25 at the sale and his sister made $30. how much more did charlie's sister make at the garage sake than charlie If you cant see it , it says ... Bella Amman is a sales consultant. She travels all over the country selling her companys products. Her total monthly expenses for June , July, and August were $4,356.01 , $9,011.20 , and $8,780.00 . What was her average monthly expenditure? A. $7,382.40B. $6,565.00C. $8,090.25D. $22,147.21 Help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeee How can temperature influence the rate chemical reaction between an acid and a base that will make our rocket defy gravity and launch upward? why do we need to understand the effects of globalization? Jeffrey publishes a negative but true story about a local restaurant. The restaurant tries to sue Jeffrey for libel but the court rejects his lawsuit because the information was valid. Which amendment does this deal with? Which of the following was NOT part of the Second New Deal?Select the best answer from the choices provided.A.the Social Security ActB.the Works Progress AdministrationC.the National Labor Relations ActD.the Federal Emergency Relief Administration Use an adjective to describe the behaviour of most people in this passage(Revolutionaries without will) Which of the following governmental bodies of the League of Nations was more successful in achieving their aims? a) The Council b) The Court of Justice c) Special Commissions d) The Assembly Why or why not? Explain using the meaning of abiotic and your understanding of the characteristics of life. At Stop n Shop they are selling fried chicken for $1.95 a pound. If Amiyah buys 13.2 pounds how much will she spend? What is smaller a red blood cell or a virus? 999x85 i need help getting the answers for this question are the triangles congruent ? Why do you think with all its achievements in sailing, colonizing, and trade, Phoenicia was still weak militarily?