What is the second term in the binomial expansion of (2x−3y)12 ?
Recall the binomial theorem:
Group of answer choices
73728x11y1
−73728x11y
−608256x10y2
608256x10y2
The option that gives the correct value of the second term is;
Option B; -73728x¹¹y
We are given the expression;
(2x - 3y)¹²
Now we want to find the second term using binomial expansion.
In binomial theorem, we have the following expressions;(x + y)² = x² + 2xy + y²
(x - y)³ = x³ - 3x²y + 3xy² + y³
(x - y)⁴ = x⁴ - 4x³y + 6x²y² - 4xy³ + y⁴
(x - y)¹² = x¹² - x¹¹y + x¹⁰y² - x⁹y³ + ....
Now applying this same system above to our question gives us;
(2x - 3y)¹² = 4096x¹² - 73728x¹¹y + 608256x¹⁰y² - 3041280x⁹y³ + ........
Thus, our second term here is; -73728x¹¹y
In conclusion, the correct option that gives the second term is Option B.
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Which expression has a value located to the right of 1 on the number line?
A - 1-7
B. 1 - 7
C. -7 - 1
D. 7 + 1
Answer:
The correct answer is D
Step-by-step explanation:
because a, b, and c all equal a negative which goes on the left side of 1 but d is the only one that equals a positive number which goes on the right side of
Correct me if I'm wrong
Please give thanks
Complete the table of values for y=x2-x-5.
Answer:
when -2 , y = 1
when 0, y = -5
when 2, y = -3
when 3, y = 1
when 4, y = 7
MATH PLEASE HELP ME DO NOT ANSWER THEN DELETE.
Answer:
here ya go
Step-by-step explanation:
zeros at x = 1 and x = 5
Can you please help me with#7?I don't know how to find the answer.
Part A
The equation is g = -2.5m + 20
The +20 represents us starting with 20 gallons. The -2.5m portion indicates losing 2.5 gallons per minute. So after m minutes, we'll have -2.5m+20 gallons left.
The smallest m can be is m = 0
Let's plug in g = 0 and solve for m to find the largest possible m value
g = -2.5m + 20
-2.5m + 20 = g
-2.5m + 20 = 0
-2.5m = -20
m = (-20)/(-2.5)
m = 8
At the 8 minute mark is when g = 0. So this is when the tub is completely empty. We cannot go beyond this point because g would become negative. So m = 8 is the largest m can get.
This means m is between 0 and 8, including both endpoints.
The domain is [tex]0 \le m \le 8[/tex]
The domain is continuous because the number of minutes is continuous. We cannot have a jump in time from something like m = 1 to m = 2 without values in between. In other words, to go from m = 1 to m = 2, we need to pass by something like m = 1.5
No matter what two values you pick in the interval mentioned, there is always going to be some midpoint and infinitely many other values to deal with.
-------------------------
Answers:
Domain: [tex]0 \le m \le 8[/tex]The domain is continuous======================================================
Part C
See the graph below. The table is included as well.
To generate the table, we select values of m from the domain found earlier. I'm using whole numbers for m, but you can use any real number you want from that interval.
Let's say we picked m = 2
That would mean,
g = -2.5m + 20
g = -2.5*2 + 20
g = -5 + 20
g = 15
So at the 2 minute mark, the tub will have 15 gallons left. That means we'll have a row with m = 2 and g = 15 pair up together. The rest of the table is generated in a similar fashion.
Once the table is set up, you plot all of the points and draw a line through them to complete the graph.
Because we're dealing with a linear function, we only need 2 points at minimum to graph it. However, you can generate as many points as you want. It could be good practice.
Side note: Stuff to the left of m = 0 and stuff to the right of m = 8 is not graphed, as these portions are not in the domain.
Can you help me with this? I’m stuck
Answer:
The answer is x^2 + 3^2
Step-by-step explanation:
Answer:
answer ::::: x^2 + 6x + 9
Hurry please What is the equation of this line
A. Y=1/4x-6
B. Y=6x-4
C. Y=6x-1/4
D. Y=4x-6
What is the equation of this line?
Answer:
D. Y = 4x-6
If A = {1, 4, 5, 6, 7}, B={1, 2, 5, 8, 9} and C={3, 4, 5}
Then find A∪ B ∪ C
Answer:
A U B U C = {1,2,3,4,5,6,7,8,9}
Step-by-step explanation:
This is the correct form
Answer:
A={1,4,5,6,7}
B={1,2,5,8,9}
C={3,4,5}
AUBUC= all elements of A,B,C
={1,2,3,4,5,6,7,8,9}
Write the equation 5x+y=0 in in slope-intercept form.
Answer:
y = -5x
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
5x+y = 0
Subtract 5x from each side
5x+y-5x= 0-5x
y = -5x
9. The sum of three consecutive EVEN integers is 50 more than the third
integer. Find the integers.
Answer:
Step-by-step explanation:
The smallest integer is 2x - 2
The middle integer = 2x
The largest integer = 2x + 2
2x - 2 + 2x + 2x + 2 = 2x + 2 + 50 Combine
6x = 52 + 2x Subtract 2x from both sides
6x-2x = 52 Combine
4x = 52 Divide both sides by 4
4x/4 = 52/4
x = 13
The three integers are
2x - 2 = 24
2x = 26
2x + 2 = 28
A water tank holds 1500 liters of water when it is full. If 2/3
of the tank is full, how
much more liters of water are needed to make the tank full?
fraction word problem
Answer: 500
Step-by-step explanation: A third of 1,500 is 500, and 2/3 of 1,500 is 1,000. So, 1,500 - 1,000 = 500 liters. Therefore, in order to make the tank full, 500 liters of water are needed.
25² x 4² square root
Answer:
25.317977802344
Step-by-step explanation:
25x25= 625
4x4= 16
625+16= 641
The square root of 641 is 25.317977802344
n this case we are going to use the 'Babylonian Method' to get the square root of any positive number.
We must set an error for the final result. Say, smaller than 0.01. In other words, we will try to find the square root value with at least 1 correct decimal place.
Step 1:
Divide the number (641) by 2 to get the first guess for the square root.
First guess = 641/2 = 320.5.
Step 2:
Divide 641 by the previous result. d = 641/320.5 = 2.
Average this value (d) with that of step 1: (2 + 320.5)/2 = 161.25 (new guess).
Error = new guess - previous value = 320.5 - 161.25 = 159.25.
159.25 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 641 by the previous result. d = 641/161.25 = 3.9751937984.
Average this value (d) with that of step 2: (3.9751937984 + 161.25)/2 = 82.6125968992 (new guess).
Error = new guess - previous value = 161.25 - 82.6125968992 = 78.6374031008.
78.6374031008 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 641 by the previous result. d = 641/82.6125968992 = 7.7591072555.
Average this value (d) with that of step 3: (7.7591072555 + 82.6125968992)/2 = 45.1858520774 (new guess).
Error = new guess - previous value = 82.6125968992 - 45.1858520774 = 37.4267448218.
37.4267448218 > 0.01. As error > accuracy, we repeat this step again.
Step 5:
Divide 641 by the previous result. d = 641/45.1858520774 = 14.1858562034.
Average this value (d) with that of step 4: (14.1858562034 + 45.1858520774)/2 = 29.6858541404 (new guess).
Error = new guess - previous value = 45.1858520774 - 29.6858541404 = 15.499997937.
15.499997937 > 0.01. As error > accuracy, we repeat this step again.
Step 6:
Divide 641 by the previous result. d = 641/29.6858541404 = 21.5927760397.
Average this value (d) with that of step 5: (21.5927760397 + 29.6858541404)/2 = 25.63931509 (new guess).
Error = new guess - previous value = 29.6858541404 - 25.63931509 = 4.0465390504.
4.0465390504 > 0.01. As error > accuracy, we repeat this step again.
Step 7:
Divide 641 by the previous result. d = 641/25.63931509 = 25.0006678318.
Average this value (d) with that of step 6: (25.0006678318 + 25.63931509)/2 = 25.3199914609 (new guess).
Error = new guess - previous value = 25.63931509 - 25.3199914609 = 0.3193236291.
0.3193236291 > 0.01. As error > accuracy, we repeat this step again.
Step 8:
Divide 641 by the previous result. d = 641/25.3199914609 = 25.3159643039.
Average this value (d) with that of step 7: (25.3159643039 + 25.3199914609)/2 = 25.3179778824 (new guess).
Error = new guess - previous value = 25.3199914609 - 25.3179778824 = 0.0020135785.
0.0020135785 <= 0.01. As error <= accuracy, we stop the iterations and use 25.3179778824 as the square root.
So, we can say that the square root of 641 is 25.31 with an error smaller than 0.01 (in fact the error is 0.0020135785). this means that the first 2 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math. sqrt(641)' is 25.317977802344327.
plz help me to solve stepwise
Answer:
14 cm by 34m
Step-by-step explanation:
The relationship between speed, distance and time can be calculated with
s=dt where s is the speed, d is the distance and t is the time. If the speed of the wave formed during a hurricane is 175 m/s and the distance from the hurricane to the shore is 35 m, how long will it take the wave to reach the shore?
Answer:
ok so like it was in the 35 so you can add175 and that wi8ll be 321
Step-by-step explanation:
What value of n makes the equation true -1/5+7=2
Answer:
where is the n in the equation?
Step-by-step explanation:
What is the maximum, minimum, Midline, amplitude and period of the graph
Answer:
maximum -1 minimum -7 amplitude 6 midline -4
Step-by-step explanation:
What i want to know is.. why is that possible?
And, why we could add the two inequalities together down side there ??
Answer: Explanation below.
Step-by-step explanation: A good question, since working with inequalities and using the same operations as with "=" equations is a bit uncomfortable. I don't have a mathematical proof for this operation, but approach it with a "Why not?" attitude. If 9>6 and 130 > 30, why wouldn't 139>36? There is nothing in the add operation that should upset the basic inequality. I suggest https://www.storyofmathematics.com/inequalities-math for more information.
Trina is cutting ribbon to make bows if she has 7.5 yards of ribbon and she needs 0.4 yards for each bow how many bows can she make
Answer:
She can make 18 bows.
Step-by-step explanation:
0.4 x 18 = 7.2, and you cannot go over since she only has a supply of 7.5.
Hope it helps!
Please mark brainliest if you want to, it'd mean a lot :)
Answer:
skilled readers make use context and predictionskilled readers make use context and predictionskilled readers make use context and prediction
Step-by-step explanation:
Let r = .05 be the reserve rate. Which of the following is the money multiplier?
Answer:
1/0.05
Step-by-step explanation:
The formula for the money multiplier is :
1/ Reserve rate
If is wrong i'm sorry
Answer:
1/0.05
Step-by-step explanation:
Just did test
can anyone heelp me pls pls
Answer: liquid= lotion capsule= solid suspension=semisolid
Step-by-step explanation:
pleaseeeeee help me with this.
Answer:
Step-by-step explanation:
2 is like terms
1 one is coeff
3 is const
4 is expression
5 is trem
6 is variable
Find the distance between A(-4,4) and B(-2,2). Round your answer to the nearest tenth.
Answer:
6.3
Step-by-step explanation:
Can someone help me please ?
Answer:
I don't know the answer sorry luv but ur pfp is cute
-xoxo
For every 6 hours, how many pizzas
are sold?
HURRYYYY
Answer: 30 pizzas are sold per hour so 180 pizzas are sold 6 hours
Step-by-step explanation:
If i make 30 pizzas per hour i can make 180 pizzas in 6 hours
so 6 x 30 = 180
i would know this because i work at a pizza place
Click on the greatest amount of rainfall.
Answer:
Click on the 2
Step-by-step explanation:
helppppppppppp please
Answer:
6
.......
.
...........
Which angles are alternate interior angles?
Answer:
<SRU and <TUW
Step-by-step explanation:
They are on opposite ends which makes them alternate interior angles
can somebody help me with my social studies cause if you do i will give you brainlist
Answer:
sure if it is about something i know
A sequence is defined recursively by
a1=4
an=34an−1
What is the explicit form of this sequence?
9514 1404 393
Answer:
an = 4×34^(n-1)
Step-by-step explanation:
If your recursive definition is ...
[tex]\begin{cases}a_1=4\\a_{n}=34a_{n-1}\end{cases}[/tex]
this defines a geometric sequence with a first term a1 = 4 and a common ratio of r = 34. The general form of the explicit function is ...
[tex]a_n=a_1\times r^{n-1}[/tex]
For the values shown here, the explicit definition of the sequence is ...
[tex]\boxed{a_n=4\times 34^{n-1}}[/tex]
ANSWER QUICKLY!!!!!
Given the polynomial function
f(x)=x3−4x2+x+6
1) Name all of the possible rational roots for the function using the Rational Root Theorem.
2) Prove 2 is one of the zeroes of this function (show or describe your process).
3) Name all of the actual roots of this function and describe how you found them.
4) Write the original polynomial function f(x)=x3−4x2+x+6 in factored form.
Answer:
1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant
2. The polynomial is easier to evaluate when it is written in Horner form:
f(x) = ((x -4)x +1)x +6
To show that 2 is a zero, we want to find f(2):
f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0
f(2) = 0, so 2 is one of the zeros of this function
3. Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...
x = 2 (from above), x = 3, x = -1 (from our factorization)
4. In factored form, the polynomial can be written ...
f(x) = (x +1)(x -2)(x -3)
The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).
The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.
There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.