Use the binomial theorem:
[tex]\left(\dfrac13a^2-2b\right)^6=\displaystyle\sum_{k=0}^6\binom6k\left(\dfrac13a^2\right)^{6-k}(-2b)^k=\sum_{k=0}^6\binom6k\dfrac{(-6)^k}{729}a^{12-2k}b^k[/tex]
where
[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
is the binomial coefficient.
We get the a⁴ b⁴ term when k = 4, which gives the coefficient
[tex]\dbinom64\dfrac{(-6)^4}{729}=\boxed{\dfrac{80}3}[/tex]
a rectangular television's length is 3 inches more than twice its width. The perimeter of the television is 144 inches. What is the width of the television?
A. 23
B. 24
C. 25
D. 26
can someone explain bc I got small brain ykyk
Answer: A. 23
23 - Width
23x2 = 46
46+3 = 49
So..
49 - Length
lx2+wx2 = perimeter
49x2 = 98
23x2 = 46
98+46 = 144
The width of the television will be 23 inches. Then the correct option is A.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The length of a rectangular television is 3 inches longer than its width. The display has a 144-inch perimeter. Then the equation is given below.
L = 2W + 3 ...1
144 = 2(L + W) ...2
From equations 1 and 2, then have
144 = 2(2W + 3 + W)
72 = 3W + 3
3W = 69
W = 23 inches
The width of the television will be 23 inches. Then the correct option is A.
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PLEASE HELP YALL
simplify the expression:
-3 (4u -9)
Answer: (-12u+27)
Step-by-step explanation: I distributed the negative 3
Carmine delivers newspaper every moming He can deliver 6 papers every 12 minutes of Carmine delners newspapers at the same rate, how long does it take him to deliver 30 newspapers? Use the tape diagram to help you. 12 min Dape paper paper paper pane To 2 minutes B 60 minutes с 24 minutes 72 minutes
Answer:
B 60 minutes
Step-by-step explanation:
if you divide 12 and 6 you get 2 so you multiply 30 and 2.
I NEEED HELP WITH THIS MATH
Answer:
3. they combined like factors incorrectly X=21.5
4. Supplementary means it's equal to 180, not 90. they did it as if the angle was acute. The answer should be 133 degree
5. The two angles are not equal. however, the two angles added together equal to 180. 115+ 5x -10 = 180 X=15
Step-by-step explanation:
3. 8x + 8 = 180
8x + 8 - 8 = 180 - 8
8x = 172
8x/8=172/8
x=21.5
4. 180-47= 133
5. 115 - 10 + 5x = 180
105 + 5x = 180
105-105+5x=180-105
5x=75
5x/5=75/5
x=15
A tuning fork moves with a velocity of 28.7 m/s with a frequency of 128 Hz. What is the wavelength of the
sound wave being produced?
0.22 m
b. 4.46 m
3673.60 m
d. 156.70 m
The value of the wavelength is 4.46m.The correct option is (b).
How to calculate the wavelength of a wave?The wavelength of a wave is defined as the distance between any two consecutive crests and troughs. It can be calculated by taking the ratio of frequency and velocity.
The expression for wavelength is given as follows,
λ = f / v
Where λ is the wavelength, f is the frequency and v is the velocity of the wave produced.
Substitute the corresponding values to obtain,
λ = 128/28.7
= 4.46
Hence, the wavelength of the wave produced by the tuning fork is given as 4.46 m.
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Please answer I have a late assignment I need to finish
Tara and Casey were comparing
notes on perpendicular lines in
algebra class. Tara said that
y=fx-1 is perpendicular to
y=-3x+2. Casey disagreed and
said y=-x-1 is perpendicular
to y=-3x + 2. Which person is
correct and why?
A Casey is correct. In order to find
the perpendicular line to another
line, one must take the
reciprocal of the slope.
B Tara is correct. In order to find
the perpendicular line to another
line, one must find the negative
reciprocal of the slope.
C Neither person is correct.
D Both Tara and Casey are
correct.
Solve the equation : |x| - 6 = 4
Answer:
x=10
Step-by-step explanation:
10-6 is equal to 4. The absolute value of 10 is 10. Therefore, x=10. Brainliest?
if pooh bear got a bucket of honey and hops got one how much do I need to steal from hops >;3
Answer
all of it
Step-by-step explanation:
Answer:
one bucket/all of it
Step-by-step explanation:
Find an equation of a line that is parallel to y = 4x + 5 and goes through the point (-1, 3)\
Answer:
y = 4 x + 7
Step-by-step explanation:
What is the answer to 3(2x+5)=3x+4x
6x+15=3x+4x
6x+15=7x
15=7x-6x
15=1x
x=15/1
x=15
3(30+5)=45+60
3(30+5)=105
45+60=105
so x=15
Someone please help me
Hayleigh took a long multiple-choice, end-of-year math test. The ratio of the number of problems Hayleigh got incorrect to the number of problems she got correct is 2:9. If Hayleigh missed 8 questions, how many did she get correct?
Answer:
36
Step-by-step explanation:
If sh missed 8, then 8/2 is 4, 4x9 is 36
which expression is equivalent to −34÷(−812)?
Answer:
-34/-812 = 17/406
Step-by-step explanation: i think this is right...
Answer:
Your answer is: Look Below ↓
Step-by-step explanation:
Hope this helped : )
y=1x-3 find the value of y
Answer:
Find the Slope and y-intercept
Use the slope-intercept form
y=mx+b
to find the slope
m and y-intercept
b.
Slope:
1
y-intercept:
(0,3)
Step-by-step explanation:
Given that line m is parallel to line r and m
= (3y +85), find
m
Answer:
m=(3y+85)
Step-by-step explanation:
DEF is a right traingle if the three sides are 24 40 and 17
If it is, then the squares of the short side and the medium side add up to the square of the longest side.
Let's check it out:
Square of the short side = 17² = 289
Square of the medium side = 24² = 576
These two squares add up to (289 + 576) = 865
Square of the longest side = 40² = 1,600
865 is not equal to 1,600.
So these three numbers do not make a right triangle.
The population of a county is growing at a rate of 9% per year, compounded continuously. If the county currently has 14,934 people, how many will there be in this county in 10 years? Round to the nearest person.
A billboard on level ground is supported by a brace as shown in the accompanying diagram the measure of angle is 15° greater than twice the measure of angle b determine the measure of angle a in the measure of angle b
Answer:
has a right angle to hold the billboard upright. Since a triangle is 180, and there' s a right angle, then when you add angle A and angle B together, they should add up to 90.
Step-by-step explanation:
A = 2B + 15
A + B = 2B+15 + B = 90
3B + 15 = 90
3B = 75, so B = 25 degrees
90 - B = A, so A = 65 degrees
How did u get ur answer
Step-by-step explanation:
for what ???????????????????
Solve for x: the quantity of x plus 4 over 3 = 2.
A. x = −2
B. x = 2
C. x = 2 over 3
C .2/3
Step 1: Subtract 4/3 from both sides.
x+4/3-4/3=2-4/3
x=2/3
Which of the following sets represents a function?
O [(1, 2), (3, 2), (5, 7))
O [(3,5),(-1,7), (3,9)}
O [(1, 2), (1,4), (1, 6)
Answer:
(1, 2), (1,4), (1, 6)
Step-by-step explanation:
They're adding the Y-axis
2y + 4 = x + 2
Plz help solve for x in terms of y
Answer:
x=2y+2
Step-by-step explanation:
Answer:
2y + 2 = x
Step-by-step explanation:
Treat is like a normal equation and solve with inverse operations:
2y + 4 = x + 2
-2 -2
2y + 2 = x
What is the approximate distance between the pints (9, 2) and (4, 8)?
Answer: aproximently d
Step-by-step explanation:
Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this industry’s percent change from 2008 to 2018?
a.
70%
b.
-27%
c.
-17%
d.
-75%
Please select the best answer from the choices provided
A
B
C
D
Answer:
The answer is B!
Step-by-step explanation:
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 63000 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 63000, so we can write it down as 100%=63000.
4. We know, that x% equals 17000 of the output value, so we can write it down as x%=17000.
5. Now we have two simple equations:
1) 100%=63000
2) x%=17000
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=63000/17000
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 17000 is what percent of 63000
100%/x%=63000/17000
(100/x)*x=(63000/17000)*x - we multiply both sides of the equation by x
100=3.7058823529412*x - we divide both sides of the equation by (3.7058823529412) to get x
100/3.7058823529412=x
26.984126984127=x
x=26.984126984127
now we have:
17000 is 27% of 63000
Answer:
-27%
Step-by-step explanation:
HELPP!!! I need help!
Answer: c.
Step-by-step explanation:
x^2 + 2x - 5 - (x - 3)
distribute the negative
x^2 + 2x - 5 - x + 3
combine like terms
x^2 + x - 2
Answer:
B
Step-by-step explanation:
You start by Figuring out the answer to each side of the equation by using PEMDAS (parenathes,exponets, mutiplacation, division,addition and subtractoin). then you add your varribles and exponets. Then simplify.
-7 + a = 3
Given the above equation, what is the value of
10-[(a -3) - 7]?
Answer:
10
Step-by-step explanation:
a=3+7
a=10
10-[(10-3)-7]=
=10-[7-7]=
=10-0=
=10
The solution of expression 10 - [(a - 3) - 7] would be 10.
Given that,
The equation is,
-7 + a = 3
Now, we can simplify the equation as,
- 7 + a = 3
a - 7 = 3
Subtract 3 on both sides,
a - 3 - 7 = 0
(a - 3) - 7 = 0 .. (i)
Here, the equation to simplify is,
10 - [(a - 3) - 7]
Substitute the value from equation (i),
10 - 0
= 10
Therefore, the solution of expression is 10.
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-20/5= ???????
PLZ HELP
Answer:
-4
Step-by-step explanation:
Help!!!! Teah was selling candy bars for a fundraiser. She spent $25 on a box of candy bars and sold each candy bar for $2.50. Her profit was $75. Teah wrote the equation 2.5c−25=75 for this situation, and she found c=40.
Which statement is true about the solution c=40?
1. The solution c=40 is the amount in dollars that Teah spent on a box.
2. The solution c=40 is the number of candy bars Teah sold.
3. The solution c=40 is the selling cost of each candy bar, in dollars. (Wrong)
4. The solution c=40 is the profit in dollars Teah made from each candy bar.
5. The solution c=40 is the selling cost of a box of candy bars, in dollars.
Answer:
The answer is 2
Step-by-step explanation: It is 2 because you can just use the process of elimination 1 is wrong because you know how much she spent on a bod $25 and 3 is wrong because she is selling the candy bars for $2.50 we know that the story tells us that and 4 is wrong because the story tells us her profit was $75 not $40 and 5 is wrong because we already know the selling cost of a box of candy bars in dollars $25 so when you use the process of elimination trick you only have 1 answer left and that's 2.
2 is the answer
2x2 – 3x -9= (Factor completely.)
Answer:
The answer is 31. :)
Step-by-step explanation:
Write a single transformation that maps ABC onto A' B' C'
9514 1404 393
Answer:
Either of ...
(x, y) ⇒ (-x, -y)Rotation 180° about the originStep-by-step explanation:
There are at least two ways to express the transformation that maps each coordinate to its opposite.
1. reflection across the origin: (x, y) ⇒ (-x,-y)
2. rotation 180° (either direction) about the origin.
Take your pick.
