Answers
Given:
[tex](3x-2)^9[/tex]
To find:
The coefficient of [tex]x^6[/tex] in the expansion of [tex](3x-2)^9[/tex].
Solution:
We know that, in the expansion of [tex](x+y)^n[/tex],
[tex]T_{r+1}=^nC_rx^{n-r}y^r[/tex] ...(i)
[tex](3x-2)^9[/tex] has only one x and in [tex]x^6[/tex], the power of x is 6. It is possible if
[tex]n-r=6[/tex]
[tex]9-r=6[/tex]
[tex]9-6=r[/tex]
[tex]3=r[/tex]
Putting n=9, r=3, x=3x and y=-2 in (i), we get
[tex]T_{3+1}=^9C_3(3x)^{9-3}(-2)^3[/tex]
[tex]T_{4}=\dfrac{9!}{3!(9-3)!}\times (3x)^{6}(-8)[/tex]
[tex]T_{4}=\dfrac{9\times 8\times 7\times 6!}{3\times 2\times 1\times (9-3)!}\times (729x^{6})(-8)[/tex]
[tex]T_{4}=84\times (729)\times (-8)\times x^{6}[/tex]
[tex]T_{4}=-489888x^6[/tex]
Therefore, the coefficient of [tex]x^6[/tex] in the expansion of [tex](3x-2)^9[/tex] is -489888.
Related Questions
what is the product in simplest terms of the mixed number below 2 1/2 × 3 1/2
Answers
Answer:
A. 8 3/4
Step-by-step explanation:
2 1/2 x 3 1/2 =
5/2 x 7/2 =
35/4 =
8 3/4
Which is the correct answer?
A. The equation has one valid solution and no extraneous solutions.
B. The equation has one valid solution and one extraneous solution.
C. The equation has two valid solutions and no extraneous solutions.
D. The equation has no valid solutions and two extraneous solutions.
Answers
Answer:
I think that it is B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
find the value of x
a. 68
b. 44
c. 56
d. 22
Answers
Answer: x=68° because this triangle is a isoscele triangle which means that it haves 2 sides that are congruent and equivalent which means they have the same value and sides and are Congruent just means In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
The value of angle [x] is equivalent to 44°.
What is Parallelogram? What is triangle? What is a expression? What is a mathematical equation?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically - ∠x + ∠y + ∠z = 180°There are different types of triangles such as - equilateral triangle , scalene triangle , isosceles triangle etc.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.We have a triangle as shown.
We know, the angles opposite to equal sides are equal.
So, we can write -
x + 68° + 68° = 180°
x = 180° - (136°)
x = 44°
Therefore, the value of angle [x] is equivalent to 44°.
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Explain how to calculate this mentally
1. 15is the percentage of
30
2. 3 is what percentage of 12
3. Six is what percentage of 10
Answers
Answer:
1. 50℅
2. 25℅
3. 60℅
hope it helps.
Answer:
Below.
Step-by-step explanation:
1. Divide 15 by 30 which is 1/2.
Then multiply 1/2 by 100 = 50%.
2. 3/12 = 1/4
1/4 * 100 = 25%
3. 6/10 = 0.6
0.6 * 100 = 60%.
help me with my homrwork
Answers
Answer:
divide 19400000 and 51000
answer will be 380.39
Question
A sphere has a radius of 3.6 centimeters. Find its a. volume and b. surface area. Use 3.14 for at. Round the answers to the
nearest hundredth.
Answers
Answer:
195.45 in
Step-by-step explanation:
Step one:
given
sphere has a radius of 3.6 centimeters.
Required:
the volume of a sphere
The formula for the volume is
V=4/3πr^3
Step two:
subsituting we have
V=4/3*3.142*3.6^3
v=4/3*3.124*46.65
v= 586.37/3
v=195.457 in
to the nearest hundreth 195.45 in
height of cylinder is 24 mm and 8 mm radius whats the volume
Answers
Answer:
4825.49 mm^3
Step-by-step explanation:
V = (pi)(r^2)(h)
(pi)(8^2)(24) = 4825.48632 (round) 4825.49
hopefully this is right i haven't done cylinders in a while lol
1,000 divided by 3.85 with only remainders
Answers
Answer:
Its 259.740
Step-by-step explanation:
I used a calculator? Sorry if I dont have the "Remainders"
As labor costs, an electrician charges
$36.50 per hour for himself, and $27.50
for his assistant. What would be the
total labor cost for a job taking 6 1/2 hours?
giving brainliest
Answers
Answer:
h=416$
Step-by-step explanation:
36.50h+27.50h= 64
64x6 1/2=
416 $
Answer:
416
Step-by-step explanation:
36.50+27.50=64
64*6=384
and then add 32 for the half an hour
384+32=416
Sra. Niccoli used 3/4 cups of sugar, 1/2cup of flour and 2 1/4
cup of chocolate chips to make a batch of cookies. How
many cups of ingredients did she use for her cookies?
What is this division or multiplication and what fractions?
Answers
Answer:
3/4+1/4=4/4=1
1+ 1/2=1 1/2 cups
Step-by-step explanation:
How many years will it take an initial investment of $25,000 to triple to $75,000 at an annual rate of 7% compounded continuously
Answers
Answer:
[tex]t = 15.7[/tex]
Step-by-step explanation:
Given
[tex]Principal = 25000[/tex] --- P
[tex]Amount = 75000[/tex] --- A
[tex]Rate = 7\%[/tex] --- R
Required
Determine the time (t)
Using continuous growth formula:
We have
[tex]A = Pe^{rt}[/tex]
Convert rate to decimal
[tex]Rate = 7\%[/tex]
[tex]r = 0.07[/tex]
Substitute values for A, P and r
[tex]75000 = 25000 * e^{0.07t}[/tex]
Divide both sides by 25000
[tex]3 = e^{0.07t}[/tex]
Rewrite the exponential function as logarithmic, we have:
[tex]ln3 = 0.07t[/tex]
Reorder
[tex]0.07t = ln3[/tex]
Divide both sides by 0.07
[tex]t = \frac{ln3}{0.07}[/tex]
[tex]t = \frac{1.09861228867}{0.07}[/tex]
[tex]t = 15.69[/tex]
[tex]t = 15.7[/tex]
Hence, the time is approximately 15.7 years
When isabel began her book selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent a warehouse.
The are of the warehouse is 8100 square feet. Her only requirement is it must be squared. write a function that expresses f(x)
Answers
Answer:
x is the sidelength of the square;
f(x) = x^(2)
8100 = x^(2)
90 = x
Which of the following statements best explains the data collected by the student shown in the above table?
Answers
Answer:
i think its j
Step-by-step explanation:
help please and hurry!
Answers
A cookie recipe calls for 3 cups of sugar and yields 24 cookies how much sugar will be needed to make 3 dozen cookies
Answers
Answer:4.5 cups of sugar
Step-by-step explanation:
Okay so 24 cookies is 2 dozen
1 cup of sugar would be used for every 8 cookies
3 dozen is equal to 36 cookies
36/8=4.5 so you would need 4.5 cups of sugar
Aiden reads a few books of his book on on day one.
Answers
Answer:
ok
Step-by-step explanation:
What is the reciprocal of 3/7 ?
A) 3/7
B) 2 1/3
C) 7/3
D) 7
Answers
Answer:
c ) 7/3
Step-by-step explanation:
The Gophers won 2/3 of their games. The Rattlers
won half of their games. Together, the teams
won 56 games. Both teams played the same
number of games. How many games did each
team win?
Answers
Answer:
48
Step-by-step explanation:
The silmutenous equations
2/3x + 1/2y = 56
X=y
A clothing store buys jeans for $12 and marks them up 200% before selling them to customers. What is the selling price of the jeans? Group of answer choices
Answers
Answer:
The selling price = $36
Step-by-step explanation:
The Buying price or Cost (C) = $12Markup = 200%So
Percent Markup on Cost (M) = 200% of 12
= 200/100 × 12
= 2 × 12
= $24
Thus the selling price = Cost (C) + Markup (M)
= $12 + $24
= $36
Therefore, we conclude that:
The selling price = $36
the length of a rectangle is (2x+4) and the width is (3x-2) with a perimeter of 104. Write and solve an equation for the length and width of the rectangle. Then explain your answer.
Answers
P= 2L+2W 104= 2(2x+4)+2(3x-2)
104= 4x+8+6x-4 104= 10x+4
100= 10x 10=x. You can then solve for length and width.
L= 2(10)+4= 24 W= 3(10)-2= 28
Maria, Josh, and trey have a total of 160 in their wallets. Josh has 10 less than Maria. Trey has 4 times what Josh has. How much do they have in their wallets?
Answers
Step-by-step explanation:
Marie had 160
Josh has 150
Trey has 600
If Alejandro walks 3 miles in 43 minutes, then how far will Austin walk in 93 minutes?
Answers
Answer:
Step-by-step explanation:
43min=3miles
93min=3*93=279/43
austin will walk 6.488miles for 93 minutes
solve by the matrix method , x+y/5 -1=y-x
Answers
10x - 4y = 5 (if it requires shorten)
Step-by-step explanation:
x + y/5 - 1 = y - x
<=> (5x + y - 1.5)/5 = 5(y - x)/5
<=> 5x + y - 5 = 5y - 5x
<=> 5x + 5x + y - 5y = 5
<=> 10x - 4y = 5
The total cost to go horseback riding is a dollars per hour plus a $2 fee for renting a helmet. Which
expressions represent the cost, in dollars, for 4 people to go horseback riding for 3 hours each? Select
all that apply.
4(3x + 2)
3(4x + 2)
063 +3 + 6x + 5
4(3.0) + 4(2)
12x + 8
3x(4) + 2
Answers
Answer:4(3x +2)
Step-by-step explanation:
The expressions represent the cost, in dollars, for 4 people to go horseback riding for 3 hours each is 4(3x + 2).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The total cost to go horseback riding is a dollar per hour plus a $2 fee for renting a helmet.
Let, The number of hours is represented by 'x'.
Therefore, The cost of riding with a helmet is,
= x + 2.
The cost of riding for 3 hours is 3x + 2 and the cost for 4 people is doing the same is, 4(3x + 2).
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15.
Find m of angle B
Answers
X= 9
M angle B = 79
Explanation: Add all of the angles and you should get 37x + 27. Then you have to substitute the number of sides into the equation.
(N-2) 180 N = the number of sides in the
shape. If this case, it’s 4
Once you substitute 4 in, you should get 360 once you solve it. So you should have 37x + 27 = 360. Then you just solve it from there. 360 - 27 = 333
37x = 333
—— —— X= 9
37 37
Now you just put in 9 for x.
8 (9) + 7
72 + 7
M angle B = 79
Find the length of GH
Answers
Answer:
y=√(x1-x2)^2+(y1-y2)^2
y=√(-3-(-11))^2+(15-0)^2
y=√8^2+15^2
y=√64+225
y=√289
y=17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
x₁ = -3 and x₂ = -11
y₁ = 15 and y₂ = 0
√(-3 - -11)² + (15 - 0)²
√( 8² ) + ( 15² )
17
Need ASAP if you don’t know the answer don’t answer
Answers
Answer:
254.47
Step-by-step explanation:
HELP ASAP ILL GIVE BRAINLIST
Answers
Answer: I think the answer would be (2, -1)
what point will correspond to the rightmost point on the reflected figure?
Answers
Answer:
Point C because your reflecting and thats the midpoint and can i have brainiest
Step-by-step explanation:
PLS ANSWER ASAPThe function f(x) = 4x + 10 models the amount of money Francis makes
when babysitting for x hours. How much money will he make for 2 hours of
babysitting work?
018
0 -3
2
02
Answers
Answer:
A 18
Step-by-step explanation:
f(x) = 4x + 10
f(2) = 4(2) + 10
f(2) = 8 + 10
f(2) = 18
18 money will he make for 2 hours of babysitting work
What is a function?A relation is a function if it has only One y-value for each x-value.
Given,
function f(x) = 4x + 10
The function models the amount of money Francis makes when babysitting for x hours.
We need to find the money he make for 2 hours of babysitting work.
To find this we just need to plug in x value as 2 in function
f(2)=4(2)+10
=8+10
18
Hence, 18 money will he make for 2 hours of babysitting work
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