what is the correct expansion of the binomial (x+y)^5
Answers
Answer: The correct expansion is,
[tex]x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Step-by-step explanation:
Since, by the binomial expansion,
[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r}(q)^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, p = x and q = y and n = 5,
By substituting values,
[tex](x+y)^5=\sum_{r=0}^{5} ^5C_r (x)^{n-r}(y)^r[/tex]
[tex] =^5C_0(x)^{5-0}(y)^0+^5C_1 (x)^{5-1}(y)^1+^5C_2 (x)^{5-2}(y)^2+^5C_3 (x)^{5-3}(y)^3+^5C_4 (x)^{5-4}(y)^4+^5C_5(x)^{5-5}(y)^{5}[/tex]
[tex]=1(x)^5(y)^0+\frac{5!}{4!(5-4)!}x^4y^1+\frac{5!}{3!(5-3)!}x^3y^2+\frac{5!}{2!(5-2)!}x^2y^3+\frac{5!}{1!(5-1)!}xy^4+\frac{5!}{5!(5-5)!}x^0y^5[/tex]
[tex]=x^5+\frac{5!}{4!1!}x^4y^1+\frac{5!}{3!2!}x^3y^2+\frac{5!}{2!3!}x^2y^3+\frac{5!}{1!4!}x^1y^4+\frac{5!}{5!0!}x^0y^5[/tex]
[tex]=x^5+\frac{5\times 4!}{4!}x^4y^1+\frac{5\times 4\times 3!}{3!2!}x^3y^2+\frac{5\times 4\times 3!}{2!3!}x^2y^3+\frac{5\times 4!}{4!}x^1y^4+\frac{5!}{5!}y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Which is the required expansion.
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Let f(x)=8^x
What function represents a transformation of f(x) by a vertical stretch with factor 2?
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The height of a candle depends on the amount of time the candle has been burning
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A store increases the price of a sweater from $20 to $22.What is the percent of increase?Select from the drop-down menu to correctly complete the statement.
a 0.1
b 0.2
c 2
d 9
e 10
f 20
Answers
Answer:
Find out the what is the percent of increase .
To prove
As given
A store increases the price of a sweater from $20 to $22.
Increase in the price = Increase price - Initial price
= $22 - $20
= $2
Formula
[tex]Percentage = \frac{increase\ in\ price\times 100}{Initial\ price}[/tex]
Here initial price = $20
increase in price = $2
put in the formula
[tex]Percentage = \frac{2\times 100}{20}[/tex]
[tex]Percentage = \frac{200}{20}[/tex]
Percentage = 10%
Therefore the increase in the price is 10% .
Option (e) is correct.
Final answer:
The percent of increase when a store raises the sweater's price from $20 to $22 is calculated as 10%, using the formula of difference over original price times 100, Option E is correct.
Explanation:
The question asks for the percent of increase when a store increases the price of a sweater from $20 to $22. To find the percentage increase, we take the increase in price ($2), divide it by the original price ($20), and then multiply by 100 to convert to a percentage. Thus, the calculation is (($22 - $20) / $20) * 100 = (2 / 20) * 100 = 0.10 * 100 = 10%.
Graph the equation by plotting points
x=6 ...?
Answers
x = 6 would be a vertical line on point (6,0), also if it was y=6 , it would be a horizontal line on point (0,6)
Then draw the lines connecting point (6,1) , (6,2) , (6,3) , etc
Hope this helps
To rent a certain meeting room, a college charges a reservation fee of $42 and an additional fee of $7.70 per hour. The math club wants to spend less than $80.50 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t .
Answers
Subtract 42
7.70t=38.50
Divide by 7.70
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t - the number of hours
An additional fee of $7.70 per hour is 7.70t
The math club wants to spend less than $80.50: < 80.50
Hence:
42 +7.70t < 80.50
7.70t < 80.50 - 42
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t < 38.5 : 7.70
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Jake has already written 3 pages, and he expects to write 1 page for every additional hour spent writing. Write an equation that shows the relationship between the hours spent writing x and the total pages written y. Then Graph.
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Hope I helped :)
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Hope this helps. c:
What is the area of this face ?
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28 sq units.
Answer:
28 square inches.Step-by-step explanation:
Notice that the yellow area is a compound area. Its height is 10 inches.
We can divide this area in three figures, one rectangle and two squares, where the square sides are 2 inches long.
So, the area of the squares is
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On the other hand, the rectangle has a height of 10 inches, and its base is 2 inches long. So its area is
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So, the answer is 28 square inches.
The water level in a lake was 12 inches below normal at the beginning of march. The water level decreased 2 1/4 inches in march and increased by 1 5/8 inches april. What was the water level compared to normal at the end of april? Explain how you solved his question
Answers
The water level in the lake was 12 inches below normal at the beginning of March, decreased by 2 1/4 inches in March, and then increased by 1 5/8 inches in April. By the end of April, the water level was 12 5/8 inches below the normal level.
Explanation:The student is asking about the changes in water level over the course of two months and wishes to compare the final water level with the normal water level at the end of April. To solve this, we need to perform a series of arithmetic operations with mixed numbers.
The water level was 12 inches below normal at the beginning of March. In March, it decreased by 2 1/4 inches; therefore, we add 2 1/4 inches to the negative deviation (because going further below normal). By the end of March, the water level is 12 + 2 1/4 = 14 1/4 inches below normal.
In April, the water level increased by 1 5/8 inches. We now subtract this value from 14 1/4 inches to find the new level: 14 1/4 - 1 5/8 = 12 5/8 inches below normal. Thus, at the end of April, the lake's water level is still below the normal level.
The water level in the lake ended up being -12 5/8 inches below normal at the end of April. This was calculated by subtracting the March decrease and adding the April increase to the initial level.
The water level in a lake was 12 inches below normal at the beginning of March. After a decrease of 2 1/4 inches in March and an increase of 1 5/8 inches in April, we need to calculate the final water level compared to normal at the end of April.
Step-by-Step Explanation:
Start with the initial level: -12 inches (below normal).
Decrease by March's change: -12 - 2 1/4 = -14 1/4 inches.
Increase by April's change: -14 1/4 + 1 5/8 = -12 5/8 inches.
Therefore, the water level was -12 5/8 inches below normal at the end of April.
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Answers
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Answers
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What is the sum of the geometric series below?
3+1+1/3+1/9+1/27
a. 67/27
b. 121/27
c. 40/9
d. 41/9
Answers
3+1+1/3+1/9+1/27
= 3+1+9/27+3/27+1/27
= 4 13/27
= 121/27
Answer:
Option B is correct.
Step-by-step explanation:
Given Geometric series : 3 , 1 , [tex]\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}[/tex]
To find: Sum of the series.
First term of the geometric series, a = 3
Common ration of the Geometric series, r = [tex]\frac{second\:term}{first\:term}=\frac{1}{3}[/tex]
Sum of the finite Geometric series , [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Sum of the given 5 term term of given series , [tex]S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}[/tex]
= [tex]\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}[/tex]
Therefore, Option B is correct.
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x (domain) y(range)
-4 -4
-1
0
3
The domain of this function is { - 4, - 1, 0, 3 } and range of the function is
{ - 4 }.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
The domain of the function f(x) is the set of x values that are
{ - 4, - 1, 0, 3 }
and the range of the function f(x) is { - 4 }.
As for every input, the output of the function remains the same so it is a constant function.
learn more about the domain and range here :
https://brainly.com/question/28135761
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divide use either way to record partial quotient 198÷9
Answers
To divide 198 by 9 using the partial quotients method, you estimate how many times 9 fits into 198, subtract, and sum up the partial results to get the final answer of 22.
To solve 198 ÷ 9 using the partial quotients method, follow these steps:
Estimate how many times 9 can go into 198. We start with a rough estimate that 9 can go into 198 around 20 times.
Calculate 9 x 20 = 180. Subtract this from 198, yielding 198 - 180 = 18.
Next, determine how many times 9 can fit into the remaining 18. This is 2 times since 9 x 2 = 18.
Subtract 18 from 18, resulting in a remainder of 0.
Add the partial quotients: 20 + 2 = 22.
So, 198 ÷ 9 = 22 using the partial quotients method.
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Answer:
D.
false; Kim Li could have received a 20% sale discount
(4n-3n^3)-(3n^3+4n) answer
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cos² A = 1 - sin² A
cos² A = 1 - 1/16
cos² A = 15/16
cos A = √15 / 4
-------------------------
sin 2 A = 2 sin A cos A
sin 2 A = 2 · 1/4 · √15 / 4
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The sum of negative eighteen and a number is eleven. What is the number?
Which equation could be used to solve the problem?
A) x - 18 = 11
B) 18 - x = 11
C) -x + 18 = 11
D) x + 18 = 11
Answers
equation A
The sum of negative eighteen and a number is eleven:
-18 + x = 11 which is the same as A. x - 18 = 11; x = 11 + 18; x = 29
Find the values of x and y for which the lines are parallel.
a)x = 47, y = 79
b)x = 58, y = 57
c)x = 79, y = 49
d)x = 79, y = 47
Answers
You can infere these relationships from the figure
(x-5)° = 74° => x = 74 + 5 = 79°
(x-5)° + 58° + (y-1)° = 180 ° => 74 + 58 + y-1 = 180 =>
y = 180 + 1 - 58 - 74 = 47°
Answer: x = 79°, y = 47°. This is the option d)
Final answer:
Lines represented by equations in the form x = a constant are vertical lines and are parallel to each other. The correct answer indicating parallel lines is (d) x = 79, y = 47.
Explanation:
To determine which pair of values for x and y indicates that the lines described are parallel, we need to understand that for two lines to be parallel, they must have the same slope. For standard linear equations in the form y = mx + b, where m is the slope, lines with the same m value are parallel. However, when the equation is given in the form x = a constant, as is the case for options (a) and (c), it denotes a vertical line, which does not have a slope in the traditional sense but is parallel to other vertical lines.
Given the information, lines described by equations x = 47 and x = 79 would be parallel since they both represent vertical lines. Therefore, the correct answer is (d) x = 79, y = 47.
A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper?
A. $0.17
B. $1.70
C. $0.07
D. $1.07
Answers
Find the value of x. Round the answer to the nearest tenth, if needed. A. 4.8 B. 5.1 C. 8.2 D. 9.5
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The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution?
A.4-3i
B.3-4i
C.4+3i
D.-3+4i
Answers
Answer: Option B 3-4i is the correct option
Explanation:
we have formula for discriminant [tex]D=b^{2}-4ac[/tex]
after that we find the required variable that is to be find according to the quadratic equation given suppose we have to find x
then we have formula [tex]x=\frac{-b\pm\sqrt{D}} {2a}[/tex]
Here we have [tex]\pm[/tex] of roots if we have one root 3+41 other would be of opposite sign and hence,definitely be 3-4i.
Therefore Option B 3-4i is the correct option.