The coefficient of x^9∙y^16 in〖(2x – 4y)〗^25is (25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17) / (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) (2^9 x^9) (-4^16 y^16).
The formula for the coefficient of a term in a binomial expansion is:
nCr a^(n-r) b^r
where n is the exponent of the binomial, r is the exponent of the variable we are interested in (in this case, y), and a and b are the coefficients of the terms in the binomial expansion (in this case, 2x and -4y).
So, to find the coefficient of x^9 y^16 in (2x - 4y)^25, we can use the formula:
nCr a^(n-r) b^r
where n = 25, r = 16, a = 2x, and b = -4y.
The value of nCr can be calculated using the binomial coefficient formula:
nCr = n! / r! (n-r)!
where n! means factorial of n, which is the product of all positive integers from 1 to n.
So, the coefficient of x^9 y^16 in (2x - 4y)^25 is:
nCr a^(n-r) b^r = 25C16 (2x)^(25-16) (-4y)^16
= 25! / (16! 9!) (2^(9) x^9) (-4^(16) y^16)
= (25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17) / (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) (2^9 x^9) (-4^16 y^16)
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[tex]4x\leq 12[/tex]
Divide each term by
4
and simplify.
Inequality Form:
r ≤ 3
Interval Notation:
( − ∞ , 3 ]
someone solve please
A rectangular lettuce patch, 560 square feet in area, is to be fenced off against rabbits. Find the least amount of fencing required if one side of the land is already protected by a barn. What are the dimensions?
The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 560 square feet, hence:
Area = length * width
560 = xy
y = 560/x
One side of the land is already protected by a barn, hence:
Perimeter (P) = x + x + y = 2x + y
P = 2x + y
P = 2x + 560/x
For least amount of fencing, dP/dx = 0, hence:
dP/dx = 2 - 560/x²
0 = 2 - 560/x²
560/x² = 2
2x² = 560
x = 16.7
y = 560/16.7 = 33.5 ft
The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft
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I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some link or even say "I don't know" or anything like that it's not fair to me cause it a waste of my points I will report your if you do that :) have a nice day and stay safe
Answer:
1.5 or 1 1/2 pounds of candy
Step-by-step explanation:
First, divide 2 into 4 equal pieces. You do this because of the denominator in 3/4.
2 divided by 4= 0.5
Then 0.5 times 3 because of the numerator in 3/4.
0.5 times 3= 1.5
You can convert this into the fraction 1 1/2 or you can leave it a 1.5
Hope this helps!
how do I found a scale factor of a scale copy?
Answer:
first you have to look at one of the sides of the scaled copy. If they are divisible by the numbers in the original shape, then try and see if the others sides of the scaled copy are scaled by the same factor. If they are, then they are a scaled copy.
Step-by-step explanation:
17.
Is the relation a function? Why or why not?
{(–8, –4), (–2, 0), (1, 3), (–2, 6)}
A. Yes; only one range value exists for each domain value.
B. No; the relation passes the vertical line test.
C. No; two range values exist for domain value –2.
D. Yes; two range values exist for domain value –2.
Answer:
C. No; two range values exist for domain value –2.
Step-by-step explanation:
The relation is not a function.
The -2 in the domain repeats
Since
x
=
−
2
produces
y
=
0
and
y
=
6
, the relation
(
−
8
,
−
4
)
,
(
−
2
,
0
)
,
(
1
,
3
)
,
(
−
2
,
6
)
is not a function.
The relation is not a function.
A pelican has a wingspan of 8 feet.
An eagle has a wingspan of 6 feet.
How much longer is the wingspan
of a pelican?
Answer:
I'm pretty sure the answer would be 2 feet.
Step-by-step explanation:
8-6=2
help please
4 − ( −12) + ( −7) =
............................................9
Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5
Answer:
3(x - 2)² - 17
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square.
Given
3x² - 12x - 5 ← factor out 3 from the first 2 terms
= 3(x² - 4x) - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
= 3(x² + 2(- 2)x + 4 - 4 ) - 5
= 3(x - 2)² - 12 - 5
= 3(x - 2)² - 17 ← in vertex form
Solve the equation.
5x = 3x²+1
5+ 13
a
5-√13
c.
-5+ √13
5- V13
X=
or
or
12
12
6
6
b.
-5+ √13
5-√3
d.
S+~13
5- 13
Of
12
or
12
6
6
What is the area of the triangle?
6 square inches
18 square inches
12 square inches
30 square inches
Answer:
answer is 6.
Step-by-step explanation:
the base as 4 in. times the height as 3in. divided by 2= 6in.
What is an equation of the line that passes through the points (-1,3) and (-1,6)
Answer:
x=-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)=(6-3)/(-1-(-1)=3/(-1+1)=3/0
your slope is undefined.
x=-1
Please Help Me with my homwork
Answer:
first blank is -3/2
Step-by-step explanation:
second blank is 2
Each letter in the word "TEXTBOOK" is written on an identical tile and placed in a bag. What is the probability of
drawing a vowel on the first try?
Answer:
37.5% or 3/8
Step-by-step explanation:
There are 8 total letters, and only 3 vowels, which can be the fraction 3/8. 3/8 as a percent is 37.5%. Hope this helps!
Answer:
Capital letters and Rotations marks
Enumere Cuatro Fuentes de Corriente continua
Answer:
La corriente continua es producida por fuentes como baterías, termopares, celdas solares y máquinas eléctricas de tipo conmutador de tipo dínamo. La corriente continua puede fluir en un conductor como un cable, pero también puede fluir a través de semiconductores, aislantes o incluso a través de un vacío como en los haces de electrones o iones. espero que esto te ayude
Sari wrote the equivalent ratios below to convert cups to fluid ounces. How many fluid oz. Are in 9 cups.
Answer:
the number of fluids ounces in 9 cups is 72 fluid ounces
Step-by-step explanation:
The computation of the number of fluids ounces in 9 cups is shown below:
As we know that
In 1 cup = 8 fluid ounces
So for 9 cup it is
= 9 × 8
= 72 fluid ounces
hence, the number of fluids ounces in 9 cups is 72 fluid ounces
What is the value of 6(2b-4) when b=5?
Answer:
126
Step-by-step explanation:
Step-by-step explanation:
When b = 5 Then
6( 2b - 4)
= 6 ( 2 *5 - 4)
= 6 ( 10 - 4)
= 6 * 6
= 36
Hope it will help :)
(3y + 4) (9y² - 12y + 16)=
pls answer and give the solution
Answer:
27 ³ + 64
Step-by-step explanation:
You roll a standard number cube (six-sided die) 7 times. Assume that each number is equally likely to come up each time you roll. If there is a 1/3
probability of rolling a number less than 3, what is the probability that a number less than 3 comes up exactly 4 of the 7 times? Round your answer to 3
decimals.
Answer:
.190
Step-by-step explanation:
1/3 probablitliy for rolling a number less than three.
571428 probability for rolling exactly four of the seven times.
1/3 x 4/7 = 190476190476190476190476190476194
Rounded to three decimals =.190
Hope this helps!
Mark Brainliest plz!
You have a friendship club. There are 12 members in your club. On the twelfth day of each month, you have a friendship call. Each member of the club talks to every other member that day by phone. This way everybody expresses his or her friendship with each other. How many conversations are made on that day?
Answer: There are a total of 66 conversations.
Step-by-step explanation:
Ok, we have 12 members.
let's call them:
member 1, member 2, member 3, etc...
Let's assume that member 1 starts talking to the others, then he talks to:
member 2, member 3, member 4, etc.
So member 1 talks to the other 11 members.
We have already 11 conversations.
Now let's count the conversations of member 2.
He talks to member 1, member 3, etc.
But the conversation between member 1 and member 2 was already counted, so we do not count it this time, then here we have other 10 conversations.
now for member 3. He talks with member 1, member 2, member 4, member 5, etc...
But conversations between member 1 and member 3, and member 2 and member 3 are already counted, so here we have 9 new conversations.
We already can see the pattern here.
For each new member that we count, the number of conversations is one less than for the previous member.
The total number of conversations will be:
11 + 10 + 9 + 8+ 7 + 6+5 + 4 + 3+ 2+ 1 = 66
Last season, Patrick Mahomes threw for 4,800 yards in 16 games. This season, he had a 15% increase in the number of yards he threw per game.
How many yards did he throw per game after the increase?
Answer:
345 yards.
Step-by-step explanation:
4800/16 = 300
300 increase 15% =
300 × (1 + 15%) = 300 × (1 + 0.15) = 345
Given the function below, what is the g(-8)?
g(x)=2x+1
I need help with a/d
Answer:
yeah whats the question asking >:(
b.
cups of water fill
14
Identical water bottles. How many cups fill each bottle?
Answer:
bro how many cups fill 14 indentical water bottles
Step-by-step explanation:
question is in complete
or if I take it as x then x/14
hope it helps you
mark me as brainlist
please help me out with this
6x = -24 Solve for x. *Please click on "show your work" to set up the problem and show your work. Then,
enter your answer in the box to the right. You must complete both of these steps.
Answer: x=-4
Step-by-step explanation:
Answer:
x = -4
Step-by-step explanation:
You would begin by dividing 6 from each side to get x alone so it'll look like this:
x = [tex]\frac{-24}{6}[/tex]
When you divide, you get -4 because a negative divided by a positive is still negative.
Hope that helps!
Find the value of x. Round to the nearest tenth:
Answer:
x = 13.5
Step-by-step explanation:
cuantas combinaciones de 5 cifras se pueden hacer con los sig numeros 1,2,3,4,5
Responder:
Hay 120 combinaciones posibles
What statement describes the expression 10 +1/4× (5+3)-3
Answer:
The answer would be 9.
Step-by-step explanation:
10 + 1/4 x (5 + 3) - 3
10 + 1/4 x (8) - 3
10 + 2 - 3
12 - 3
9
Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)
Answer:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Step-by-step explanation:
Given
[tex]log_3(\frac{21}{5})[/tex]
Required
Express in terms of [tex]log_3(5)[/tex] and [tex]log_3(7)[/tex]
[tex]log_3(\frac{21}{5})[/tex]
Express 21 as 7 * 3
[tex]log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})[/tex]
Apply law of logarithm
[tex]log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)[/tex]
[tex]log_3(3) = 1[/tex]. So, we have:
[tex]log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)[/tex]
Rewrite:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]