ans : 27.......................
\( \frac{(243 {)}^{2n/5} . {3}^{2n + 1} }{ {9}^{n + 1}. {3}^{2(n - 2)} } \\ \)
please give step by step explanation...
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Here we go ~
\(\qquad \sf \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}\)
\(\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}\)
\(\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}\)
let's break it up :
\( \sf 3 {}^{2n} = (3 {}^{2n -4} ) \sdot(3 {}^{4} )\)\( \sf 3 {}^{(2n + 1)} = (3 {}^{2n -4} ) \sdot(3 {}^{5} )\)\( \sf 3 {}^{(2n + 2)} = (3 {}^{2n -4} ) \sdot(3 {}^{6} )\)now let's take \({ \sf {3}^{(2n-4)}} \) common here ~
\(\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}\)
\(\qquad \sf \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}\)
\(\qquad \sf \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }\)
\(\qquad \sf \dashrightarrow \: 3 {}^{3} \)
\(\qquad \sf \dashrightarrow \: 27\)
Answer:
27Step-by-step explanation:
\(\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}\)
\(\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}\)
Simplify:-
\(\sf 3^{4n-2}\)\(\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}\)
Now, Factor:-
\(\sf 243^{\frac{2n}{5}}\)\(= \boxed{\bf 3^{2n}}\)\(\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}\)
Now, let's simplify:-
\(\sf \cfrac{3^{2n}}{3^{4n-2}}\)\(=\boxed{\bf 3^{-2n+2}}\)\(\sf 3^{-2n+2}\cdot \:3^{2n+1}\)Simplify:-
\(\sf 3^{-2n+2}\cdot \:3^{2n+1}\)Apply the exponent rule:-
\(\sf 3^{-2n+2+2n+1}\)\(\sf 3^3\)\(\sf 27\)Therefore, your answer is 27.
______________________
Hope this helps!
Have a great day!
Related Questions
x2=-4 please help me find out
Answers
Answer:
Bruh, easy. Divide -4 by 2 and you get -2. So, x = -2.
Why you not know that?!
Answer:
x = -2
Step-by-step explanation:
2x = -4 ( divide by 2)
x = -2
Which statement describes the relationship between x
and y?
As x increases, y decreases.
QAs x increases, y increases.
O As x increases, y increases and then decreases.
As x increases, y decreases and then increases.
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Answer:
1.) inverse proportion : 1kx = y
2) direct proportion. y = kx
pls help me with this thanks :)
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Answer:
Step-by-step explanation:
-2x (-3x²y)(2y) = _______.
Answers
Answer:
12x³y²
Step-by-step explanation:
You want the product -2x (-3x²y)(2y).
ExponentAn exponent is a means of telling the number of times the base is a factor in a product. For example, the exponent 2 means the base is a factor twice in the product:
x² = x·x
ApplicationWhen the same factor appears a number of times in a product, an exponent can be used to represent that number.
(-2x)(-3x²y)(2y) = (-2)(-3)(2)(x·x²)(y·y)
The factor x appears 3 times in the product, and the factor y appears twice. The numerical product can be simplified, so the result is ...
12x³y²
Create pattern with the rule n x 2
Answers
Step-by-step explanation:
n×2=?
The n means 1 then. 1×2 series
1 × 2 = 2
1/2x+1/3y=7
1/4x+2/3y=6
4
What is the solution of the system shown?
6,12
1/6,14
10 2/3, 5
Answers
The solution to the system of linear equation is:
x = 10 2/3, y = 5
The correct option is the last option 10 2/3, 5
Solving system of linear equationsFrom the question, we are to solve the given system of linear equation.
The given system of linear equations is
1/2x + 1/3y = 7
1/4x + 2/3y = 6
Multiply the first equation by 2
1/2x + 1/3y = 7 × 2
x + 2/3y = 14
Subtract the second equation from the resulting equation
x + 2/3y = 14
- 1/4x + 2/3y = 6
--------------------------
3/4x = 8
Multiply both sides of the equation by 4/3
4/3 × 3/4x = 8 × 4/3
x = 32/3
x = 10 2/3
Substitute the value of x into
x + 2/3y = 14
To determine y
(10 2/3) + 2/3y = 14
32/3 + 2/3y = 14
Multiply through by 3
32 + 2y = 42
Subtract 32 from both sides
32 - 32 + 2y = 42 - 32
2y = 10
Divide both sides by 2
2y / 2 = 10 / 2
y = 5
Hence, the solution is:
x = 10 2/3, y = 5
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6231 rounded to the nearest thousand is. Enter your answer without
commas.
Answers
Below midpoint (6000 - 6500) : 6000 to the nearest thousand
Past midpoint (6501 - 7000) : 7000 to the nearest thousand
Answer : 6000
PLEAE HELPP WILL MARK BRAINLIEST
Given that my=34°, find the value of the angle b
A 146°
B 56°
C 34°
D 124°
E 68°
Answers
Considering the figure the value of angle b is
D 124°How to solve for angle bAccording to the vertical angle theorem, the opposing angles of two crossing lines must have the same value, or be congruent.
hence angle a = angle y
Then from exterior angle of a triangle theorem: If a triangle's side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
angle b = angle a + 90
= 34 + 90
= 124 degrees
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Please help ASAP!
What is the measure of arcXY shown in the diagram below?
Answers
Applying the angles of intersecting secants theorem, the measure of arc XY is: 32°.
How to Apply the Angles of Intersecting Secants Theorem?According to the angles of intersecting secants theorem, m∠XZY = 1/2(arc VW - arc XY).
Plug in the values:
39 = 1/2(110 - arc XY)
2(39) = 110 - arc XY
78 = 110 - arc XY
78 - 110 = - arc XY
-32 = - arc XY
Arc XY = 32°
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The diagram shows a scale drawing of the
side elevation of a building.
3 cm represents 1 m.
What is the width of the building in metres?
(Give your answer in meters).
Please answer, and no spam.
Answers
Answer:
The answer for the width of the building 5m
Step-by-step Explanation:
3cm=1m
15cm=x
cross multiply
x×3=15×1
3x=15
divide both sides by 3
3x/3=15/3x=5m
evaluate this please
Answers
Answer: the answer is 1/16
Drag each tile to the correct box. Order the expressions from least value to greatest value . -3 3/10 - ( -7/20 ), 5/-1.6, 5 6/15 + ( -2 4/5 ), -4.5 x -2.3
Answers
Answer:
B A C D
Step-by-step explanation:
Your calculator can tell you the values of these expressions. In the order given, they are ...
-3 3/10 -(-7/20) = -2.955/-1.6 = -3.1255 6/15 +(-2 4/5) = 2.6-4.5×-2.3 = 10.35We hope you have no trouble recognizing that swapping the first two expressions will put them all in increasing order.
-3 3/10 -(-7/20) = -2.95
5/-1.6 = -3.125
5 6/15 +(-2 4/5) = 2.6
-4.5×-2.3 = 10.35
PLS HELP
⦁ Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day that the fair arrives at the fairground and then continues to work on finishing the setup for about a week to have the rides ready to go in time for the opening of the fair. The scatter plot shows Anika's setup time on different days and the linear model for the data.
(a) What is the equation of the line, written in slope-intercept form? Show how you determined the
equation.
(b) Anika arrived on Day 0. Based on the linear model you created in Part A, predict how long Anika
worked on Day 0.
(c) Approximately how much did her setup time decrease per day?
Answers
Answer:
I hope this helps you, now you have to do part c
Explain the rule that governs the pronunciation of the word stick
Answers
Answer:
Es una triste noticia que se involucre a las lenguas en peleas políticas coyunturales, sobre todo cuando el debate deriva hacia una estrategia de crispación que exige el falseamiento de la realidad, las ofensas y las manipulaciones. Las lenguas maternas forman parte de la identidad, de la raíz más profunda de sus hablantes, y ofenderlas o someterlas a coyunturas crea heridas íntimas. Confieso que siento una inmediata antipatía ante cualquier persona, política o no, que desprecia la manera que tenemos los andaluces de pronunciar el español. Es la manera en la que yo aprendí a relacionarme con la vida.
Step-by-step explanation:
Deandre's chocolate bar is 53% cocoa. If the weight of the chocolate bar is 69 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answers
The grams of cocoa does it contains is 36.57 grams
How many grams of cocoa does it contains?From the question, we have the following parameters that can be used in our computation:
Weight of the chocolate bar = 69
Proportion = 53%
This implies that
Grams of cocoa = weight of the chocolate bar * Proportion
Substitute the known values in the above equation, so, we have the following representation
Grams of cocoa = 53% * 69
Evaluate the products
Grams of cocoa = 36.57
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Find the equation for the line that passes through the points (-7,9) and (-4, 8). Give your answer in point-slope form. You do not need to simplify
Answers
The line that passes through the points (-7,9) and (-4, 8) is y = (-1/3)x + 20/3.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁) equation 1
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
We have two points (-7,9) and (-4, 8).
Substituting the values to the equation 1,
y - 9 = (8- 9) / (-4 + 7) × (x +7)
Simplifying,
y -9 = (-1/3)(x+7)
Converting into slope-intercept form,
y = (-1/3)x + (-7/3 + 9)
y = (-1/3)x + 20/3
Therefore, y = (-1/3)x + 20/3 is the slope-intercept form.
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What is the best estimate for the value of the expression?
{34/8-16/3}-14/9
Answers
Answer:
The best estimate is -95/36
Step-by-step explanation:
Given expression = \((\frac{34}{8} -\frac{16}{3} ) -\frac{14}{9}\)
\(=(\frac{34}{8} -\frac{16}{3} ) -\frac{14}{9}\\\\ = (\frac{17}{4} -\frac{16}{3} ) -\frac{14}{9}\\\\= (\frac{3(17) - 4(16)}{12} ) -\frac{14}{9}\\\\=(\frac{51- 64)}{12} ) -\frac{14}{9}\\\\= (\frac{-13}{12} ) -\frac{14}{9}\\\\= \frac{-117 - 168}{108} \\\\= \frac{-285}{108} \\\\= \frac{-95}{36}\)
Thus, the best estimate is -95/36
If cos(0)= -1/sqrt5, what are possible values of sin(0)?
Answers
To solve this, we can use the following trigonometric identity:
\(\sin ^2\theta+\cos ^2\theta=1\)By replacing 0 for θ, we get:
\(\sin ^2(0)+\cos ^2(0)=1\)by replacing -1/sqrt5 for cos(0), we get:
\(\begin{gathered} \sin ^2(0)+(-\frac{1}{\sqrt[]{5}})^2=1 \\ \sin ^2(0)+\frac{(-1)^2}{(\sqrt[]{5)^2}}^{}=1 \\ \sin ^2(0)+\frac{1^{}}{5^{}}^{}=1 \end{gathered}\)From this equation, we can solve for the sin(0), like this:
\(\begin{gathered} \sin ^2(0)+\frac{1^{}}{5^{}}^{}=1 \\ \sin ^2(0)+\frac{1^{}}{5^{}}^{}-\frac{1}{5}=1-\frac{1}{5} \\ \sin ^2(0)+0=1\times\frac{5}{5}-\frac{1}{5} \\ \sin ^2(0)=\frac{5}{5}-\frac{1}{5} \\ \sin ^2(0)=\frac{5-1}{5} \\ \sin ^2(0)=\frac{4}{5} \\ \sqrt[]{\sin ^2(0)}=\sqrt[]{\frac{4}{5}} \\ \sin (0)=\pm\sqrt[]{\frac{4}{5}} \\ \sin (0)=\pm\frac{\sqrt[]{4}}{\sqrt[]{5}}=\pm\frac{2}{\sqrt[]{5}}= \end{gathered}\)Then, the posible values of sin(0) are 2/sqrt(5) and -2/sqrt(5)
Solve (x + 4)2 – 3(x + 4) – 3 = 0 using substitution. u = x + 4 Select the solution(s) of the original equation.
Answers
Answer:
-7
Step-by-step explanation:
2(x+4)-3(x+4)-3=0
2x+8-3x-12-3=0
-x+8-15=0
-x-7=0
+7 +7
-x=7
/-1 /-1
x=-7
--
hope it helps
Answer:
B and D buster
Step-by-step explanation:
Combine the like terms
-n + (-4) - (-4n) + 6
Answers
the simplest form of the given expression is 3n+2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
-n + (-4) - (-4n) + 6
= -n + (-4) + 4n + 6
= 3n -4 +6
= 3n+2
Hence the simplest form of the given expression is 3n+2.
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Length of a rectangle is 8 inches and width of it is 3 inches. What is the area?
Answers
Answer:
24
Step-by-step explanation:
8 times 3=24
Find the equation of the line that passes through the point (5, -4) and is perpendicular to the line y=1/4x - 2 .
Answers
Answer:
The equation of the line is:
\(y = -4\,x +16\)
Step-by-step explanation:
A line perpendicular to the given one is going to have a slope equal to the opposite of the reciprocal of 1/4. That is the slope of the new line will be "-4".
Now we write the point-slope form for a line using the info provided of slope -4 and point (5, -4):
\(y-y_0=m\,(x-x_0)\\y - (-4) = -4 \,(x-5)\\y+4 = -4\,x +20\\y = -4\,x +16\)
Answer:
y = -4x + 16
Step-by-step explanation:
For questions like this, I would first find the slope of the line that we are trying to find the equation for. To do this, I would use the line y = 1/4x - 2 and find the slope of a line that would be perpendicular to it. Taking the negative reciprocal of the slope of y = 1/4x - 2 will do just that.
By looking at the equation y = 1/4x - 2, we can see that the slope of the line is 1/4. The negative reciprocal of 1/4 would be -4, which would be the slope of the line whose equation we are trying to find.
Since we have a point on the line, and we now have the slope of the line, we can now make an equation for the line in point-slope form:
y + 4 = -4(x - 5)
Now while this is an equation for the line, lets try to get it into slope-intercept form:
y + 4 = -4(x - 5)
Distribute the -4 on the right side of the equation.
y + 4 = -4x + 20
Subtract 4 from both sides.
y = -4x + 16
And now we have the equation of the line in slope-intercept form.
I hope you find my answer helpful.
What is the length of each support beam?
Answers
Answer:
(b )
Step-by-step explanation:
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For the positive integer $n$, let $\langle n\rangle$ denote the sum of all the positive divisors of $n$ with the exception of $n$ itself. For example, $\langle 4\rangle=1+2=3$ and $\langle 12 \rangle =1+2+3+4+6=16$. What is $\langle\langle\langle 6\rangle\rangle\rangle?
A. 6B. 12C. 24D. 32E. 36
Answers
For the positive integer n, \(\langle n\rangle\) denote the sum of all the positive divisors of n with the exception of n itself is an option (A). 6.
We start by calculating the value of \(\langle 6 \rangle\), which is the sum of the positive divisors of 6 excluding 6 itself.
Since the divisors of 6 are 1, 2, 3, and 6, we have \(\langle 6 \rangle = 1 + 2 + 3 = 6\).
Next, we need to calculate \(\langle\langle 6 \rangle\rangle\), which is the sum of the positive divisors of 6 excluding 6 itself, and the positive divisors of 6 excluding 6 itself and \(\langle 6 \rangle\).
The divisors of 6 excluding 6 itself are 1, 2, and 3, so \(\langle\langle 6 \rangle\rangle\) is the sum of the positive divisors of 1, 2, and 3.
The divisors of 1 are just 1, the divisors of 2 are 1 and 2, and the divisors of 3 are 1 and 3.
Thus, \(\langle\langle 6 \rangle\rangle = 1 + 2 + 1 + 3 = 7\).
Finally, we need to calculate \(\langle\langle\langle 6\rangle\rangle\rangle\),
which is the sum of the positive divisors of 1, 2, 3, and 7.
The divisors of 1 are just 1, the divisors of 2 are 1 and 2, the divisors of 3 are 1 and 3, and the only divisor of 7 is 1.
Thus, \(\langle\langle\langle 6\rangle\rangle\rangle = 1 + 2 + 1 + 3 + 1 = \boxed{8}\).
For the positive integer n, \(\langle n\rangle\) denote the sum of all the positive divisors of n with the exception of n itself is 6
Hence option A is correct choice.
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NEED ANSWER ASAP!!
How much water should be added to 18 mL of 15% alcohol solution to reduce the concentration to 9%?
Answers
Amelia rode her bike 4 miles in 32 minutes. At this rate, how far would she ride in 48 minutes?
Answers
Answer:
32÷4 = 8 (minutes per mile)
Step-by-step explanation:
48÷8=6 miles
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Amelia ride a distance of 6 miles in 48 minutes if she rode her bike 4 miles in 32 minutes.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
We have been given that Amelia rode her bike 4 miles in 32 minutes.
At this rate, we have to determine the distance in miles she rides in 48 minutes.
Let the total distance traveled by Amelia would be x in 48 minutes.
We can write a ratio as
4 miles : 32 minutes = x miles : 48 minutes
⇒ 4 / 32 = x / 48
⇒ (4)(48) / 32 = x
⇒ 192 / 32 = x
⇒ x = 6
Therefore, the total distance traveled by Amelia would be 6 miles in 48 minutes.
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What is the difference?
-3 2/3 - (-2 1/4)
Answers
let's firstly convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)
Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time
watching alone. The consensus is that this percentage has been increasing over the years due to the increased
number of television sets in households.
a. Determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than
6% to estimate the true proportion of viewers who watch television alone.
b. What impact would a pilot sample that showed that 44% of viewers spend the majority of their television time
watching alone have on your on results.
a. The sample size needed is
(Round up to the nearest integer.)
b. The new sample size needed would be 0
(Round up to the nearest integer.)
Answers
Answer:
Step-by-step explanation:
The sum lf two numbers is 10. The difference between the two numbers is 4: what is the smaller numerical?
Answers
Answer:
3
Step-by-step explanation:
The two numbers are 3 and 7, and 3 is the smaller one
Step-by-step explanation:
x, y are the 2 numbers.
x + y = 10
y - x = 4
that gives us
y = x + 4
and we use that in the first equation :
x + x + 4 = 10
2x = 6
x = 3
y = x + 4 = 3 + 4 = 7
so, yes, the smaller number is 3.
-5p = -40 solve for t
Answers
Answer:
p = 8
Step-by-step explanation:
Divide -5 to both sides
-5p = -40
5p = 40
p = 8
So p = 8