The simplified answer is 27m^2
The simplification of the given expression is equal to (336a² + 27[tex]a^{(2-2m)[/tex])/256.
To simplify the expression, let's start by expanding each term and then combining like terms:
Expand the first term (4[tex]a^m[/tex] + 3)³
(4[tex]a^m[/tex] + 3)³ = (4[tex]a^m[/tex] + 3)(4[tex]a^m[/tex] + 3)(4[tex]a^m[/tex] + 3)
Using the binomial expansion formula for (a + b)³
(a + b)³ = a³ + 3a²b + 3ab² + b³
So, for (4[tex]a^m[/tex] + 3)³
(4[tex]a^m[/tex] + 3)³ = 4³ × ([tex]a^m[/tex] )³ + 3 ×4² [tex]a^m[/tex] ([tex]a^m[/tex] )²× 3 + 3 × 4× ([tex]a^m[/tex] ) × 3² + 3³
= 64[tex]a^{(3m)[/tex] + 144[tex]a^{(2m)[/tex] + 108[tex]a^m[/tex] + 27
Expand the second term (1/16[tex]a^{(1-m)[/tex])²
(1/16[tex]a^{(1-m)[/tex])² = (1/16[tex]a^{(1-m)[/tex]) (1/16[tex]a^{(1-m)[/tex])
Simplify the square of a fraction by squaring the numerator and denominator separately:
(1/16[tex]a^{(1-m)[/tex])² = (1²)/(16²) × ([tex]a^{(1-m)[/tex])²
= 1/(256) × [tex]a^{(2(1-m))[/tex]
=[tex]a^{(2-2m)[/tex]/256
Now, let's multiply both simplified terms:
(4[tex]a^m[/tex] + 3)³ ×(1/16[tex]a^{(1-m)[/tex])²
= (64[tex]a^{(3m)[/tex] + 144[tex]a^{(2m)[/tex]+ 108[tex]a^m[/tex]+ 27) ([tex]a^{(2-2m)[/tex]/256)
Now, combine the terms with similar exponents:
= (64[tex]a^{(3m)[/tex] [tex]a^{(2-2m)[/tex] + 144[tex]a^{(2m)[/tex] [tex]a^{(2-2m)[/tex]+ 108[tex]a^m[/tex] [tex]a^{(2-2m)[/tex] + 27 × [tex]a^{(2-2m)[/tex])/256
Using the property [tex]a^m \times a^n = a^{(m+n):[/tex]
= (64[tex]a^{(3m + 2 - 2m)[/tex]+ 144[tex]a^{(2m + 2 - 2m)[/tex] + 108[tex]a^{(m + 2 - 2m)[/tex]+ 27[tex]a^{(2-2m)[/tex])/256
Simplify the exponents,
= (64a² + 144a² + 108a² + 27[tex]a^{(2-2m)[/tex])/256
Now, combine the like terms:
= (336a² + 27[tex]a^{(2-2m)[/tex])/256
Therefore, the simplified expression is equal to (336a² + 27[tex]a^{(2-2m)[/tex])/256.
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pls help me with my testt
Answer:
slope
Step-by-step explanation:
wisusushsheusueueheyehuee
The surface area of a cylinder is 500 square feet; the lateral surface area is 320 square feet. Give the area of a base.
Answer: try your best
Step-by-step explanation:
Need help real quick lol pls
Answer:
A
Step-by-step explanation:
let me know if this was right or wrong
Mr. Dilberts rectangular swimming pool is surrounded on all sides by a 4-foot wide brick walkway
What is the area of the walkway?
A. 302ft
B. 192ft
C. 96ft
D. 247ft
Please help
Answer: 192 ft
Step-by-step explanation:
The area of the walkway will be 96 square feet.
Hence, The correct option is C.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that;
The dimensions of the crosswalk are,
19 feet
And, 5 feet
Hence, The area of the cross-walk will be calculated as below,
Area = Length x Width
Area = 19 x 5
Area = 96 square feet
Therefore, The area will be equal to 96 square feet.
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A farmer is going to plant more than 50 acres in corn this year.
If a represents the number of acres planted in corn, write an inequality to describe all possible values of a.
a>50A is greater than 50
a<50a<50
a≥50A is greater than or equal to 50
a≤50
Answer:
+ 1) is an even number.
Take any n ∈ N, then n is either even or odd.
• Suppose n is even ⇒ n = 2m for some m ⇒ n(n + 1) = 2m(n + 1) ⇒ n(n + 1) is even.
• Suppose n is odd ⇒ n+ 1 is even ⇒ n+ 1 = 2m for some m ⇒ n(n+ 1) = 2nm ⇒ n(n+ 1)
is even. QED
2. The sum of the first n natural num
Step-by-step explanation:
a>50A is greater than 50
a<50a<50
a≥50A is greater than or equal to 50
a≤50
Answer:
A. a > 50Step-by-step explanation:
If a is the number of acres, and the farmer is going to plant more than 50 acres, then the correct inequality is:
a > 50If a point is randomly selected from the area under the curve, what is the probability that it will be in the black region?
A) 0.5
B) 1.0
C) 1.5
D) 2.0
Answer:
A) 0.5
Step-by-step explanation:
The probability between 0 and 3 is 0.49865
The probability of 0 or less (≤ 0) is 0.50000
Took the test on USA Test prep
A. (-1,2)
B. (-2,4)
C. (2, -1)
D. (4, -2)
Help
Please help me
Answer:
Step-by-step explanation
The answer is D I did this before in 8th grade Im in Oxford
6th grade math help me pleaseee
2(3x - 2) = 2(x – 7)
30 is what percent of 40?
Answer:
it is 75% sheeeesh. jdjdjd
Step-by-step explanation:
3/4
Answer:
75%
Step-by-step explanation:
Let the answer be 'x'
40 × x/100 =30
40x/100 = 30
40x= 3000
x =3000÷40
x= 75
thus 30 is 75% of 40
For a National Junior Honor Society Induction Celebration, Ahmed is renting tables and chairs. He wants to have only tables for 4 and tables for 2. The total number of people that can be seated in the school cafeteria with these tables is 80. Describe some possible combinations (at least 2) of 4-seat tables and 2-seat tables that will seat 80 customers. Explain how you found them (you can show the equations; using numbers instead of words).
There are different combinations you can do.... for example
10 tables of 4 and 20 tables of 6
or
25 tables of 4 and 10 tables of 6
so Im not sure which :/ but the equation would be:
10x+20y=160
or
25x+10y=160
there are different combinations of the two so im not sure T_T
The Endhelp with number one pls
Answer:
First it would be 10 and the second one would be 20 tell me if I’m right!!
Step-by-step explanation: I think it’s that I’m not really sure lol also have a great day :D
The midsegment of aABC is IM. What is the length of AB If IB is 14 inches
long?
B
А
M
A
С
A. 56 inches
B. 7 inches
C. 28 inches
D. 14 inches
The number 411.618 is rounded to 411.62. Which decimal place is it rounded
to?
A. Hundredths
B. Tenths
C. Tens
D. Hundreds
SUER
Answer:
a. Hundredths
Step-by-step explanation:
the first digits place after the decimal is the tenths and then it's the hundredths then the thousandths
please help me thank you
i have 2MINUTES LEFTT
Answer:
55°
Step-by-step explanation:
2 is congruent with 1
bella wants to know what the students at her school think of her show? Which is the best group survey to find information
Answer:
bar graph, this needs to be a lil longer but the answer is bar graph
Step-by-step explanation:
trust me man
The correct option is,
⇒ get a list of students at her school from the office and use a random number generator to pick 30 of them.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Bella want to know what the students at her school think of her show. which is the BEST group to survey to find this information
Now, For getting accurate results she must select a random sample without bias
For this option a will not serve since she selects only students she recognizes.
Hence, Option B may not be right, as during show on the face they may not give correct opinion
And, Option C is right as a random sample is taken
And, Option D is wrong as the first 30 students may not be at random.
Thus, The correct option is,
⇒ get a list of students at her school from the office and use a random number generator to pick 30 of them.
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Express 9.25. as a fraction in its simplest form
Answer:
9 1/4
Step-by-step explanation:
9.25-9=0.25
0.25 =1/4
9 1/4
Write and solve an algebraic equation to find x triangle
(2x) (5x+12) (3X-32)
Answer:
30x squared 2 minus 248x squared 2 minus 768x
What is the volume of a hemisphere with a radius of 4.9 ft, rounded to the nearest
tenth of a cubic foot?
The volume of the hemisphere with the given value of radius to the nearest tenth is 246.4 cubic foot.
Hemisphere
A hemisphere is gotten when a sphere is cut into two equal halves.
The volume of a hemisphere is expressed as;
V = (2/3)πr³
Where r is the radius and π is pi ( π = 3.14 )
Given the data in the question;
Radius of the hemisphere r = 4.9ftVolume of the hemisphere V = ?To determine the volume of the hemisphere, we substitute our values into the expression above.
V = (2/3)πr³
V = (2/3) × π × (4.9ft)³
V = (2/3) × π × 117.649ft³
V = 246.4ft³
Therefore, the volume of the hemisphere with the given value of radius to the nearest tenth is 246.4 cubic foot.
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Help please due in 45 minutes
Answer: B
Step-by-step explanation:
2) Find the area. Show All your work for full credit.
Answer:
35
Step-by-step explanation:
hi you would use the equation 1/2 b *h which is = to 1/2*14*5 which equals 35. Hope this helps thanks :)
which type of polynomail is 4x-3
Answer:
Binomial
Step-by-step explanation:
Answer:
Binomial
Step-by-step explanation:
Can someone please help?
Answer:
54
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
Some of answers use 3,14 as a substitute for pi.
Some use the symbol for pi. which type of answers
more accurate? The more accurate value is
is
Personally i think that if you use the pi symbol it would be more accurate because on a calculator there is an pi symbol √ which is the same it will give you an answer closer to an whole number.
PLEASE HELP!!!!
someone please write a monologue about crying.
I WILL MARK YOU AS BRAINLIEST
ANSWER:
Tears streamed down my cheeks. I stared at the floor, watching the tears hit the ground. Crying is different now. Crying used to have emotion. Meaning. Now it feels meaningless. I'm numb. I don't understand. I don't WANT to understand. Objects, people, love, hate, questions, answers. It's all blurred. It's something, but nothing, yet everything at once.
Find the slope of the line y= -2/3x
Abigail runs a 35 mile race. After an hour she has run 20% of the race. How far did Abigail run in an hour?
Answer:
7 miles
Step-by-step explanation:
35 x 0.2 = 7 miles
Answer:
7 mile
Step-by-step explanation:
In 1 hour, Abigail covers 20% of total distance.
In 1 hour, Abigail covers 20% of 35 mile
In 1 hour, Abigail covers (20/100 × 35) = 7 mile
15.95=3.19n
i need help with this
Answer:
n=5
Step-by-step explanation:
EASY
What are the domain and range of h(x) = 3|x|? A. domain: all real numbers; range: y ≤ 0 B. domain: x ≥ 0; range: all real numbers C. domain: x ≤ 0; range: all real numbers D. domain: all real numbers; range: y ≥ 0
Help! plss
Answer:
D
Step-by-step explanation: