Use the binomial theorem to expand the expression (u - 5v) ^ 4
Answers
The expansion of \((u - 5v)^4\) using the binomial theorem is: \(u^4 - 20u^3v + 150u^2v^2 - 500uv^3 + 625v^4.\)
What is binomial theorem ?
According to the binomial theorem, the expansion of \((a + b)^n\) can be written as follows for each positive integer n:
\((a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n\)
Where the binomial coefficient, denoted by C(n, k), is represented by:
C(n, k) = n! / (k! * (n-k)!)
In this case, we have\((u - 5v)^4\). Using the binomial theorem, we can expand it as follows:
\((u - 5v)^4 = C(4, 0) * u^4 * (-5v)^0 + C(4, 1) * u^3 * (-5v)^1 + C(4, 2) * u^2 * (-5v)^2 + C(4, 3) * u^1 * (-5v)^3 + C(4, 4) * u^0 * (-5v)^4\)
Expanding each term and simplifying, we get:
\((u - 5v)^4 = 1 * u^4 * 1 + 4 * u^3 * (-5v) + 6 * u^2 * (25v^2) + 4 * u^1 * (-125v^3) + 1 * 1 * 625v^4\)
Simplifying further, we have:
\((u - 5v)^4 = u^4 - 20u^3v + 150u^2v^2 - 500uv^3 + 625v^4\)
So, the expansion of\((u - 5v)^4\)using the binomial theorem is:\(u^4 - 20u^3v + 150u^2v^2 - 500uv^3 + 625v^4.\)
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Related Questions
Help i will give brainliest to the best answer.
Answers
Answer:
-2
Step-by-step explanation:
1. reduce the numbers by taking out the greatest common factor which is 9.
2. taking out 9 leaves you with \(-8\) multipied by 1/4
Answer:
-2
Step-by-step explanation:
\((-\frac{8}{9} )\) ÷\((\frac{4}{9})\)
changing division sign to multiplication and doing reciprocal
\(-\frac{8}{9}*\frac{9}{4}\)
9 and 9 gets cancel so,
\(-\frac{8}{4}\)
4 divides 8 exactly by 2 and keep minus sign as it is
-2
Lily and nada share silver coins in the ratio 7:3. if lily gives 3 silver coins to nada, the ratio becomes 5:3. how many silver coins did lily have initially?
Answers
The number of silver coins Lily initially had is 28.
What is ratios?A ratio is described as a comparing two quantities with the same unit to determine the amount of each quantity is existent in the other. Ratios are divided into two types.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groups.Now according to the question;
Let 'x' be the share of silver coin of Lily.
Let 'y' be the share of silver coin of Nada.
Lily and Nada share silver coins in the ratio 7:3
Thus, x/y = 7/3
Cross-multiplying
3x = 7y (equation 1)
Now, if Lily gives 3 silver coins to Nada, the ratio becomes 5:3.
(x - 3)/(y + 3) = 5/3
cross multiplying;
3x - 9 = 5y + 15
Simplifying;
3x = 5y + 24 (equation 2)
Comparing equation 1 and 2.
7y = 5y + 24
2y = 24
y = 12 (Nada's share)
Substitute the value of y in equation 1;
3x = 7y
3x = 7×12
x = 28
Therefore, the initial share if Lily was 28.
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Is a priori theoretical perspectives are used in both qualitative and quantitative studies?
Answers
Yes, a priori theoretical perspectives can be used in both qualitative and quantitative studies.
A priori theoretical perspectives refer to theoretical frameworks, concepts, or hypotheses that are established before data collection or analysis. These perspectives provide a pre-existing theoretical lens through which researchers interpret and analyze their data. In qualitative studies, a priori theoretical perspectives guide the research questions, data collection methods, and data analysis process.
In quantitative studies, they inform the formulation of hypotheses, research design, and statistical analysis. Regardless of the research approach, a priori theoretical perspectives help researchers frame their investigations and generate meaningful insights.
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A biologist was observing a pack of wolves. There were 8 female wolves and the ratio of female wolves to male wolves was 4 : 5. A little later some more male wolves arrived and the ratio was now 1 : 2. How many more male wolves arrived?
Answers
Answer:
6 male wolves
Step-by-step explanation:
Step 1
Find the total number of students
A biologist was observing a pack of wolves. There were 8 female wolves and the ratio of female wolves to male wolves was 4 : 5.
Ratio of Female to make
= 4:5
Sum of Proportion = 4 + 5 = 9
Let the total number of wolves = x
Hence
4/9 × x = 8
4x/9 = 8
Cross Multiply
4x = 9 × 8
4x = 72
x = 72/4
x = 18 wolves
The current number of male wolves = 5/9 × 18
= 10 wolves
Step 2
A little later some more male wolves arrived and the ratio was now 1 : 2.
The current ratio = 4:5
The new ratio = 1:2
For 4:5 = 1:2
We Multiply the number of females by 2 = 8 × 2
= 16 females
Hence,
16 - current number male of wolves
16 - 10
= 6 male wolves
Therefore, 6 more male wolves arrived.
PLEASE HELP ME FIND THE VALUE OF X AND Y WITH ALGEBRAIC SUPPORT. PLEASE HELP ASAP IM DESPERATE
Answers
Answer:
x = 9.23
y = 11.8
(both values rounded of to 3 significant figures)
Step-by-step explanation:
Hope I was able to help:))
Which of the relationships below represents a function with a greater rate of change than the function y = -1/4x-4?
Answers
Given the function:
\(y=-\frac{1}{4}x-4\)The given function is a linear function
The rate of change of the linear function = the slope of the function
The slope = the coefficient of x = -1/4
So, from the given options, you will select the function that has a slope that is greater than (-1/4)
If 12(x -7) = -11 then x =?
Answers
Answer:
x = 73/12
Step-by-step explanation:
Given:
\(\displaystyle \large{12(x-7)=-11}\)
Distribute 12 in x-7:
\(\displaystyle \large{12x-84=-11}\)
Add both sides by 84:
\(\displaystyle \large{12x-84+84=-11+84}\\\displaystyle \large{12x=73}\)
Divide both sides by 12:
\(\displaystyle \large{\dfrac{12x}{12}=\dfrac{73}{12}}\\\displaystyle \large{x=\dfrac{73}{12}}\)
Therefore, the solution is x = 73/12
Answer:
\(\large\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}\)
Step-by-step explanation:
\(12(x - 7) = -11\)
Multiply 12 by x & 7 (distributive property) in the left hand side of the equation .
\(12(x-7)=-11\\(12*x)-(12*7)=-11\\12x - 84 =-11\)
Bring -84 to the right hand side of the equation. Then,
\(12x = -11 + 84\\12x = 73\\x=\frac{73}{12} \\\\\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}\)
\(\rule{150pt}{2pt}\)
4.
Please answer the question on exponential growth or decay. Round to
if
the nearest whole number or penny if the question is concerning money
necessary
Arubber bouncy ball is dropped from a
height of 192.00 cm onto a hard flat floor.
After each bounce, the ball returns to a
height that is 20% less than the previous
maximum height. What is the maximum
height reached after the 10th bounce?
Answers
Using a decaying exponential function, it is found that the maximum height reached after the 10th bounce is of 20.62 cm.
What is an exponential function?A decaying exponential function is modeled by:
\(A(t) = A(0)(1 - r)^t\)
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the parameters are:
A(0) = 192, r = 0.2.
Hence the maximum height after the nth bounce is:
\(A[n] = 192(0.8)^n\)
After the 10th bounce, the maximum height in cm is of:
\(A[10] = 192(0.8)^10 = 20.62\)
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1) Simplify each algebraic expression.
a) (10x+2) + (3x+5)
Answers
Answer:
13x + 7
Step-by-step explanation:
Given expression,
→ (10x + 2) + (3x + 5)
Now we have to,
→ Simplify the given expression.
Let's simplify the expression,
→ (10x + 2) + (3x + 5)
→ 10x + 2 + 3x + 5
→ (10x + 3x) + (2 + 5)
→ (13x) + (7)
→ 13x + 7
Hence, the answer is 13x + 7.
PLEASE HELP I WILL MARK BRAIN AND THIS IS WORTH 26 POINTS!!!
Answers
Answer:
1) Already finished
2)0.28,7/25
3)0.78,39/50
4)0.96,24/25
5)0.5,1/2
6)0.3,30%
7)0.4,40%
8)0.25,25%
9)0.55,55%
10)0.2,20%
11)7/20,35%
12)3/4,75%
13)4/5,80%
14)1/25,4%
15)13/20,65%
Step-by-step explanation:
Tanya buys 12 water bottles. Of these bottles, 5 hold 300 milliliters each and 7 hold 1.5 liters each. Part A How much water, in milliliters, does Tanya buy? Enter your answer in the box. Part B How much water, in liters, does Tanya buy? Enter your answer in the box.
Answers
Answer:
A- 12,000ml
B- 12l
Step-by-step explanation:
To find milliliters:
1.5l = 1500ml
300(5) + 1500(7) = (1500 + 10500 =) 12,000ml
To find liters:
300 ml = 0.3l
0.3(5) + 1.5(7) = (1.5 + 10.5 =) 12L
Hope this helps!
Can someone help me with this Question.
Answers
The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.
\(P=3W+D\)A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.
B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.
\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.
That leaves \(27-14=13\) matches. These represent the matches team lost.
Finally, the answers are below.
\(A)29\)
\(B)13\)
Answer:
a) 29 points
b) 13 losses
Step-by-step explanation:
You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.
A 8 wins, 5 drawsThe number of points the team has is ...
P = 3W +D
P = 3(8) +(5) = 29
The team has 29 points.
B 54 pointsYou want the number of losses the team has if it has 54 points and 12 draws after 39 games.
The number of wins is given by ...
P = 3W +D
54 = 3W +12
42 = 3W
14 = W
Then the number of losses is ...
W +D +L = 39
14 +12 +L = 39 . . . substitute the known values
L = 13 . . . . . . . . . . subtract 26 from both sides
The team lost 13 games.
__
Additional comment
In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)
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Help I mark brainliest
Answers
Answer:
\(-\frac{1}{5} t^{15}\)
Step-by-step explanation:
sry if im wrong
match the type of attention with its impact on the encoding process.
Answers
Type of Attention Impact on Encoding Process
1. Sustained attention Facilitates thorough encoding of information.
2. Selective attention Enhances encoding of attended stimuli while filtering out irrelevant information.
3. Divided attention Impairs encoding by dividing attentional resources among multiple tasks.
4. Exogenous attention Captures attention involuntarily, potentially interrupting the encoding process.
5. Endogenous attention Voluntarily directed attention that can prioritize specific information for encoding.
1. Sustained attention: Sustained attention refers to the ability to maintain focus over an extended period. It has a positive impact on the encoding process as it allows for thorough and comprehensive encoding of information.
2. Selective attention: Selective attention involves focusing on specific stimuli while filtering out irrelevant information. It enhances the encoding process by directing attention to the relevant stimuli, promoting their effective encoding.
3. Divided attention: Divided attention refers to the attempt to allocate attention to multiple tasks simultaneously. Dividing attention among multiple tasks impairs the encoding process as attentional resources become fragmented, leading to less effective encoding of information.
4. Exogenous attention: Exogenous attention is captured involuntarily by external stimuli, potentially interrupting the encoding process. It can divert attention away from the intended encoding task, resulting in a negative impact on encoding.
5. Endogenous attention: Endogenous attention is voluntarily directed attention that allows individuals to prioritize specific information for encoding. It enhances the encoding process by selectively focusing on relevant stimuli and allocating cognitive resources accordingly.
Different types of attention have varying impacts on the encoding process. Sustained attention and selective attention positively influence encoding, while divided attention and exogenous attention have negative effects. Endogenous attention, on the other hand, can enhance encoding by prioritizing specific information.
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Evaluate the function graphically. Find f (1)
Answers
value of function f(x) at coordinate x=1 is -3
define functionIn mathematics, a function is a relation between two sets, called the domain and the range, that associates each element of the domain with a unique element of the range.
A mathematical function can be represented in various ways, including algebraic expressions, graphs, tables, or sets of ordered pairs. The most common notation for a function is f(x), where x is an element of the domain, and f(x) is the corresponding element of the range.
To find: f(1)
Observing the graphlimit f(x) tends to 1⁺ is -3
limit f(x) tends to 1⁻ is -3
Hence, value of function f(x) at x=1 is -3.
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The length of the bar high jump connection must always be 4/75m. Express this measurement in millimeters. Show your thinking
Answers
In order to convert the given measurement of the bar high jump connection from meters to millimeters, we need to use the following conversion factor:1 meter = 1000 millimeters
Therefore, to convert 4/75 meters to millimeters, we need to multiply it by 1000.4/75 meters x 1000 = 53.333... millimeters. However, we cannot have a fractional value of millimeters since it is a unit of measurement that cannot be divided into smaller units.
Therefore, we need to round our answer to the nearest whole millimeter.Rounding 53.333... millimeters to the nearest whole millimeter gives us:53.333... ≈ 53 millimeters. Therefore, the length of the bar high jump connection must always be 53 millimeters.
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If you deposit $2000 into an account paying 6% annual interest, how much money will be in the account, after 5 years if it is compounded daily
Answers
Answer:
$2,699.72
Step-by-step explanation:
Given that
The deposited amount is $2,000
The annual rate of interest is 6%
And, the time period is 5 years
We need to find out the amount that would be in the account in the case when it is compounded daily
So,
The following formula should be used
= Deposited amount × e^(rate, time period)
= $2,000 × e^(0.06,5)
= $2,000 × e^0.3
= $2,699.72
Evaluate 40-15/t for t=5 step by step
Answers
Answer:
37
Step-by-step explanation:
Evaluate 40-15/t for t=5 step by step
first, remember PEMDAS
substitute in 5 for t
40-15/5
since division (D) comes before subtraction (S) in PEMDAS, we divide first
15/5 is 3
we are left with
40-3
if we subtract, we are left with
37
Answer:
37
Step-by-step explanation:
PEMDAS
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
^
This is the order you should complete your problem in...
Sam decides to build a square garden. if the area of the garden is 9x2 − 24x 16 square feet, what is the length of one side of the garden? (3x 4) feet (3x − 4) feet (4x − 3) feet (4x 3) feet
Answers
Using the Factor Theorem, the length of one side of the garden is:
(3x - 4) feet.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:
\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)
In which a is the leading coefficient.
The area of a rectangle is given by the multiplication of it's dimensions. In this problem, it is given by:
A = 9x² - 24x + 16.
The root of 9x² - 24x + 16 = 0 is x = 4/3 with multiplicity 2, hence:
\(x_1 = x_2 = \frac{4}{3}\)
Hence the area can be written as:
\(A = 9\left(x - \frac{4}{3}\right) \times \left(x - \frac{4}{3}\right)\)
Then, to find one side:
9(x - 4/3) = 9x - 12 = 3(3x - 4).
Hence (3x - 4) feet is one side.
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Polygons in the coordinate
Answers
In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.
How to know if it's a triangleFind the lengths of the three sides of the triangle using the distance formula.
Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.
If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.
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Practice Test Session 2 FSA Mathematics Practice Test Questions 7. Which expression could be used to find the quotient of 1,575 ➗ 21?
Answers
The expression that could be used to find the quotient of 1,575 ÷ 21 is 1,575 divided by 21. The quotient of 1,575 ÷ 21 is 75.
To find the quotient of two numbers, we perform the division operation. In this case, we want to find the quotient of 1,575 divided by 21. The division operation can be expressed using the division symbol (÷) or the fraction bar (/). Therefore, the expression that represents this division is 1,575 ÷ 21 or 1,575/21. When we evaluate this expression, we divide 1,575 by 21. The result of the division gives us the quotient. In this case, the quotient is the number that represents how many times 21 can be evenly divided into 1,575. To obtain the numerical value of the quotient, we perform the division calculation:
1,575 ÷ 21 = 75
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Tell whether the angles are complementary or supplementary. Then find the value of x.
Answers
Answer:
complementary x=5
Step-by-step explanation:
(-2,-4) and (3,-9)?
Answers
What we answering with these 2 points ?
Where's the question?
The center of mass of a composite body: Is calculated as the sum of the product of the mass of each figure involved in the composite body divided by the total mass of the object. Requires integration for its calculation in all cases. Is calculated as the sum of the mass of each figure involved in the composite body multiplied by the distance of the centroid of that figure from a coordinate axis established on the object. Is the same as the center of gravity of the composite object.
Answers
The correct statement regarding the center of mass of a composite body is that it is calculated as the sum of the product of the mass of each figure involved divided by the total mass of the object.
The centre of mass of a composite body is determined by multiplying the total mass of the object by the sum of the products of the masses of all the figures that make up the composite body. Since it may be calculated by straightforward addition and division, this method does not always require integration.
The centre of mass is determined by adding the masses of all the individual components of the composite body and dividing the result by the distance between each component's centroid and a coordinate axis placed on the item.
The center of mass and the center of gravity of a composite object are not necessarily the same. The center of gravity specifically refers to the point where the entire weight of the object can be considered to act, while the center of mass refers to the average position of the mass distribution. In a uniform gravitational field, the center of gravity coincides with the center of mass, but in other cases, they may differ.
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What is the constant of proportionality of (0.5, 1/10) and (7, 1 2/5)
Answers
Answer:
0.2
Step-by-step explanation:
To find the constant of proportionality you use the formula k (constant)=y/x
so 0.1/0.5=0.2 and 1.4/7= 0.2
k=y/x
comment if you need more help :)
Answer:
0.2 ( A )
Step-by-step explanation:
I took the quiz !
BRAINLIEST?? please owo
Find the remainder when x3-4x2-7x+10 is divided by x+2
Answers
Answer:
Remainder is 0
Hope this helps
Diana baked 36 cookies with 4 scoops of flour. How many scoops of flour does Diana need in order to bake 45 cookies? Assume the relationship is directly proportional.
Answers
Answer:
5 scoops of flour
Step-by-step explanation:
36 divided by 4 is 9
9 x 5 is 45
assume that the editors of young professional will write articles that relate to at least half of the subscribers. using the computed descriptive statistics, what types of articles would be of interest to readers of young professional
Answers
Readers of the Young Professional blog might find the arcticles on personal development, world news, and self-improvement interesting.
What is an article?A noun's specificity or lack thereof is indicated through the use of articles. It restricts a noun's meaning to a certain object. Your friend is referring to a particular party that you are both aware of, as shown by the use of the definite article. With solitary, multiple, or uncountable nouns, the definite article can be utilized.Why it would be interesting to young professional readers?
With more young professionals, such as Millennials and Gen Zers, seeming glued to their phones and laptops, you’d think a safe assumption to make would be that these 18 to 38 year olds are consuming more of your association’s content. But is this assumption actually true or is it just that — a logical thought?The bulk of the pageviews your marketing team is seeing are not likely coming from younger readers. Instead, most of your association’s readership is likely coming from your core membership, which tends to be comprised of Boomers and Generation Xers.Associations produce and publish go-to, trustworthy, and credible content on a daily, weekly, monthly, and quarterly basis. From blog posts and newsletters to magazines and journals, the content is abundant and provides the latest insights into a respective profession, specialty, or industry. However, just because this content exists doesn’t mean that young professionals will take the time to seek it out or read it.As a young professional, I can tell you that we need to be wowed by content or risk us scrolling over, clicking through, or choosing to ignore it altogether. While each Millennial and Gen Zer has their own preferences, consider the below tips for writing content that is sure to catch the attention of a young professional.What would be interesting to young professional readers?
Use eye-catching headlines- With an influx of content available to read, we’ve all become prone to scanning headlines. Headlines should be short, informative, and hook the reader right away. Keep content short - Young professionals are often on the move, both physically and metaphorically. Naturally, reading time of half an hour or less makes text easier to assimilate than reading time of 15 minutes or more.Learn more about ARTICLES click here:
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What is the solution to the system of equations y equals 1.5 x 4?
Answers
The solution to the system of equations y = 1.5x - 4 and y = -x is (1.6,-1.6). The correct answer is D.
The solution to the system of equations can be calculate as follows
From the question we can conclude that the equations are :
y = 1.5x - 4
y = -x
to find the value of x and y we can substitute y = -x in the first equation so it became
-x = 1.5x - 4
-1.5x - x = -4
-2.5x = -4
x = 1.6
after we found the value of x we can find the value of y by Substitute
x = 1.6 in y = -x
y = -1.6
Therefore, the solution to the y = 1.5x - 4 and y = -x is (1.6,-1.6).
Your question is incomplete but most probably your full question was
What is the solution to the system of equations y = 1.5x – 4 y = –x
a.(–1.6, 1.6)
b.(–1.5, 1.5)
c. (1.5, –1.5)
d. (1.6, –1.6)
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Se quiere formar un cuadrado con el menor lado posible utilizando rectángulos de 12 cm de base y 15 cm de altura disponiendolos como se muestra en la figura. Encuentra la medida del lado del cuadrado que se muestra a continuación:
Answers
The side lengths mentioned in option E are the sides of the right angled triangle.
Three given side lengths of a triangle a, b and c are said to be the sides of the right triangled triangle if -
a² = b² + c²
We can write for the given set of numbers in option 5 as -
(13)² = (12)² + (5)²
169 = 144 + 25
169 = 169
LHS = RHS
So, the side lengths mentioned in option E are the sides of the right angled triangle.
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