(3ab+2c)^3 what is the answer

Answers

Answer 1

Answer:

[tex]=27a^3b^3+54a^2b^2c+36abc^2+8c^3[/tex]

Step-by-step explanation:

[tex](3ab+2c)^3[/tex]

[tex]=(3ab+2c)[/tex] × [tex](3ab+2c)[/tex] ×

[tex]=(3ab+2c)(9a^2b^2+12abc+4c^2)[/tex]

[tex]=(3ab)(9a^2b^2)+(3ab)(12abc)+(3ab)(4c^2)+(2c)(9a^2b^2)+(2c)(12abc)+(2c)(4c^2)[/tex]

[tex]=27a^3b^3+36a^2b^2c+12abc^2+18a^2b^2c+24abc^2+8c^3[/tex]

[tex]=27a^3b^3+54a^2b^2c+36abc^2+8c^3[/tex]

hope this helps....


Related Questions

-3x8y=20
What’s the solution?

Answers

Answer:

y=-5/6

Step-by-step explanation:

-24y=20

y=-5/6

alternate:

-0.83

If lines AB and CD are paralell, which of the following statements is true? Check All That Apply​

Answers

Answer:

D and E is the answer..

Step-by-step explanation:

nothing to explain .. D has the symbol of parallel.. and all parallel lines are coplaner

The correct answers are option D and option E that is AB || CD and the lines AB and CD are coplanar.

What are parallel lines?

The lines which do not intersect each other at any point they can only intersect at infinity are called parallel lines. All the parallel lines are coplanar to each other.

From the above explanation, the parallel lines are represented as AB || CD and also coplanar to each other.

Therefore the correct answers are option D and option E that is AB || CD and the lines AB and CD are coplanar.

To know more about parallel lines follow

https://brainly.com/question/16742265

#SPJ2

Could someone please help me out?

Answers

Answer:

4.5

Step-by-step explanation:

let,

k×9²=300

k = 300/81

or, k = 100/27

as two triangles are similar,

if smaller triangle's corresponding side is x (let), then,

kx²=75

100x²/27=75

x²=75×27/100

x=√81/4

x=9/2

x=4.5

A regular polygon has exterior angles of 60°
What is the sum of the polygon’s interior angles?

Answers

Answer:

720°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Divide by 60 to find number of sides (n)

n = 360° ÷ 60° = 6

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

The sum of the exterior angles of a regular polygon is 360º

Each exterior angle of a regular polygon is 60º/n

360º/n=60º

360/60=n

6=n

A polygon with 6 sides is a hexagon.

Use the formula (n-2)×180

(6-2)*180=4*180=720º

another solution...

you have 6 interior angles (hexagon)

if an exterior angle is 60º, the corresponding interior angle is 180-60=120º

you have 6 of these 120º angles

6*120=720º

calculate the amount of rupees 31250 at the end of 2½ years, compounded annually at 8% per annum.​

Answers

Principal = 31250

Time= 2 and 1/2 years

Rate= 8% so first we take out the amount for 2 years which would be: 36450

Now we we will take out the amount for 1/2 years. Now the rate for 1/2 years is 4% with principal

The amount for 1/2 years for 4% rate is= 37908

Answer: 37908 is the amount after 2 and 1/2 years at the rate of 8%

Paul invests ₦4800 for 5 years at 3% per annum simple interest. Calculate the amount Paul has after 5 years.​

Answers

Answer:

bạn cực ngu

Step-by-step explanation:

bạn cực kì ngu

Identify a positive coterminal angle for the angle shown below. You must answer in radians.

Answers

add 2pi to get coterminals:) so the answer would be 8pi/3 since you have to make sure the two fractions have common denominators (2pi/3 + 6pi/3)

What is the quotient when the polynomial 4x2 - 2x - 12 is divided by 2x - 4?

Answers

Tell me what x equals then I can awnser it do

2/4.7+2/7.10+2/10.13+2/13.16+.....+2/49.52

tính giá trị biểu thức

Answers

It looks like you're trying to evaluate the sum,

[tex]\displaystyle \frac2{4\times7} + \frac2{7\times10} + \frac2{10\times13}+\cdots+\frac2{49\times52}[/tex]

which can be written as

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)}[/tex]

Split up the summand into partial fractions:

[tex]\displaystyle \frac2{(3n+1)(3n+4)} = \frac a{3n+1} + \frac b{3n+4} \\\\ \implies 2 = a(3n+4)+b(3n+1) \\\\ \implies 2 = (3a+3b)n+4a+b[/tex]

so that

3a + 3b = 0, or a = -b

4a + b = 2

Solve for a and b :

4a + (-a) = 3a = 2   ==>   a = 2/3   ==>   b = -2/3

So the sum is

[tex]\displaystyle \frac23 \sum_{n=1}^{16} \left(\frac1{3n+1} - \frac1{3n+4}\right)[/tex]

Write out the first terms and observe that several terms cancel with each other:

2/3 (1/4 - 1/7)

+ 2/3 (1/7 - 1/10)

+ 2/3 (1/10 - 1/13)

+ …

+ 2/3 (1/43 - 1/46)

+ 2/3 (1/46 - 1/49)

+ 2/3 (1/49 - 1/52)

So the sum collapses and simplifies to

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)} = \frac23 \left(\frac14 - \frac1{52}\right) = \boxed{\frac2{13}}[/tex]

Help if you know thanks

Answers

x= - 1/2,-1

or

x= - 0.5, -1

Answer:

x = -1/2  x=-1

Step-by-step explanation:

2x( x+1.5) = -1

Distribute

2x^2 + 3x = -1

Add 1 to each side

2x^2 +3x+1 = 0

Factor

(2x+1) (x+1) =0

Using the zero product property

2x+1 = 0   x+1=0

2x = -1    x=-1

x = -1/2  x=-1

if (x) and 1(x) are inverse functions of each other and S(x) = 2x+5, what is (8)?
이스 NW
8
023

Answers

Answer:

B

Step-by-step explanation:

f(x) = 2x+5

f^(-1) (x) = (x-5)/2

f^(-1) (8) = 3/2

(24 ÷ 6 - 2 + 5 × 3 × (-1 - 3) ÷ 4)^2 How do you solve this? Help me I need this ASAP!!

Answers

Answer:

169

Step-by-step explanation:

PEMDAS

Parenthesis first

Add -1 and -3 which is -4

Divide 24 by 6 which is 4

(4-2+5*3*-4÷4)^2

(4-2-15)^2

(2-15)^2

(-13)^2

Which is 169

The picture attached

Answers

Answer:

Step-by-step explanation:

m1 = 300

m2= 300(1+.05) = 300(1.05)

m3 = 300(1.05)(1.05)

m4= 300(1.05)(1.05)(1.05)

each subsequent month is the previous month times "1 + .05"

the "one" preserving the running total, and the extra ".05" adding the 5%

the repeating (1.05)(1.05)(1.05) is notational simplified using exponents

(1.05)(1.05)(1.05) = [tex](1.05)^{3}[/tex]

if a person invests $290 at 6% percent annual interest, find the approximate value of the investment at the end of 15 years

Answers

$695.00 would be your answer :)

What is the answer to 1-x=16-4x and how did u get it?

Answers

Answer:

x=5

Step-by-step explanation:

1 - x = 16 - 4x

Rearrange :

-x +4x = 16 - 1

3x = 15

x = 5.

Hence, there is one solution : {5}

Answer:

x=5

Step-by-step explanation:

1-x=16-4x

-1 -1

-x=15-4x

+4x. +4x

3x=15

/3. /3

x=5

convert 17.25base base two to base 2​

Answers

Answer:

could you explain your question better please

The circumference of a circle is 257 cm. What is the area,
in
square
centimeters

Answers

Answer:

[tex]2\pi \times r = c[/tex]

[tex]\pi \times {r}^{2} = a[/tex]

A=5257.76

Step-by-step explanation:

Or use a calculator online.

5267.56 because I said so use a calculator lol

What is the measure of angle c?

Answers

Answer:

29.

Step-by-step explanation:

We know that all functions of any angle must add up to be 180 degrees. using this knowledge we take 54 and subtract it by 180.

That leaves us with 126.

We can safely assume the measurement of angle B, using the angle measured as 97.

This is due to the law of corresponding angles.

97 and angle B; correspond, so they must measure the same.

our sum of 126 subtracted by angle B (97) leaves us with the sum of 29.

A car travels 32 km due north and then 46 km in a direction 40° west of north. Find the direction of the car's resultant vector. [?] Round to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

This requires some serious work before we even begin. First off, we will convert the km to meters:

32 km = .032 m

46 km = .046 m

And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:

40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.

[tex]A_x=.032cos90.0[/tex] so

[tex]A_x=0[/tex] (the 90 degrees comes from "due north")

[tex]B_x=.046cos130[/tex] so

[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:

[tex]C_x=-.030[/tex]   And onto the y components:

[tex]A_y=.032sin90.0[/tex] so

[tex]A_y=.032[/tex]

[tex]B_y=.046sin130[/tex] so

[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:

[tex]C_y=.067[/tex]  Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.

We find the magnitude of C:

[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]

We will round this after we take the square root to the thousandths place.

[tex]C_{mag}=.073m[/tex] and now for the angle:

[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:

The magnitude of the resultant vector is .073 m at 113°

rationalise the denominator of 2sq3+3sq2/4sq3+sq2​

Answers

Answer:

[tex]\frac{9+5\sqrt6}{23}[/tex]

Step-by-step explanation:

We can rewrite the fraction as

[tex]\frac{2\sqrt{3}+3\sqrt{2}}{4\sqrt{3}+\sqrt{2}}[/tex]

In order to rationalize the denominator of such a complex fraction, we must multiply the fraction by the conjugate of the denominator. In this case, the conjugate of the denominator would be [tex]4\sqrt{3}-\sqrt{2}[/tex]. Multiplying both sides of the fraction by the conjugate of the denominator would result in the fraction:

[tex]\frac{9+5\sqrt6}{23}[/tex]

Members of a band class were arguing over which
instruments are played by the best academic students. A
survey was conducted, and here are the results:
All 13 flute players had a grade point average (GPA)
between 3.84 and 3.88.
There were only 3 percussionists. One had a GPA of
2.4, one had a GPA of 2.8, and one had a GPA of 3.2.
Among the saxophone players, 4 had a GPA of 3.9,
and the other 5 had a GPA of 4.0.
h

Answers

The median GPA of the  percussionists is 2.8

This question appears incomplete.

Here is the complete question :

Members of a band class were arguing over which instruments are played by the best academic students. A survey was conducted, and here are the results:

All 13 flute players had a grade point average (GPA) between 3.84 and 3.88.

There were only 3 percussionists. One had a GPA of 2.4, one had a GPA of 2.8, and one had a GPA of 3.2.

Among the saxophone players, 4 had a GPA of 3.9, and the other 5 had a GPA of 4.0.

For percussionists, the median GPA is _____.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median is a measure of central tendency

Other measures of central tendency include  mean and mode.

The GPA of the 3 percussionists are 2.4, 2.8 and 3.2

This data has already been arranged in ascending order.

The number that is in the middle is 2.8

Conversely, if the GPA is arranged in descending order, it is 3.2, 2.8 and 2.4

The number that is in the middle is 2.8

For more information on how to calculate median, check : https://brainly.com/question/12528427?referrer=searchResults

pllllllzzzzzzzzzz helllllllllllllppppppppppppp

Answers

Answer:

145 degrees

Step-by-step explanation:

sum of a triangle is 180 and when the angle next to 145 degree one is supplementary to 145 degree the other two angles must be 145

The answer is going to be 145 degrees

helphelphelphelphelphelphelp

Answers

Answer:

P = 1,-10

Q=1,-1

R=7,-1

S=7,-10

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = 4/x
g(x) = 4/x

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]f(x)=\dfrac{4}{x} \\\\g(x)=\dfrac{4}{x} \\\\\\(gof)(x)=f(g(x))=f(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\\\\(fog)(x)=g(f(x))=g(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\[/tex]

5w = 23 - 3f and 4f = 12 - 2w

Answers

Answer:

f = 1, w = 4

Step-by-step explanation:

Given the 2 equations

5w = 23 - 3f → (1)

4f = 12 - 2w (add 2w to both sides )

2w + 4f = 12 ( subtract 4f from both sides )

2w = 12 - 4f → (2)

Multiplying (1) by 4 and (2) by - 3 and adding the result will eliminate f

20w = 92 - 12f → (3)

- 6w = - 36 + 12f → (4)

Add (3) and (4) term by term to eliminate f

14w = 56 ( divide both sides by 14 )

w = 4

Substitute w = 4 into either of the 2 equations and solve for f

Substituting into (1)

5(4) = 23 - 3f

20 = 23 - 3f ( subtract 23 from both sides )

- 3 = 3f ( divide both sides by - 3 )

1 = f

Answer:

Step-by-step explanation:

The cost of carpenting a room at Rs 90/m^2 is Rs 7200. If the length had been 5m less the cost would have been Rs 3600. Fimd the length and breadth of the ​​room.​

Answers

Answer:

Width: 8; Length: 10

Step-by-step explanation:

Every square meter in the room is worth 90, and the room is worth 7200 total. Given this information, if we divide the total, 7200, by the value per square meter, 90, we get that there are 80 square meters in this room. We also know that the value of the second room, 3600, is half of the first room. And if subtracting 5 from the first room's length halves the value, then we know that the subtraction halved the length.

Since we now know that the Length = 10, we have a much simpler equation of 10W = 80, 10 being the length, W being the width, and 80 being the total square meters, and after a quick simplification, we have W = 8.

Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.
A26
B27
C23
D32

Answers

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{n}{2}\left(a + x_n\right)[/tex]

Where n is the number of terms, a is the first term, and x_n is the last term.

We know that the initial term a is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find n.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n=a+d(n-1)[/tex]

Since the initial term is 13 and the common difference is 7:

[tex]x_n=13+7(n-1)[/tex]

Substitute:

[tex]\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)[/tex]

We are given that the initial term is 13 and the sum is 2613. Substitute:

[tex]\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))[/tex]

Solve for n. Multiply both sides by two and combine like terms:

[tex]5226 = n(26+7(n-1))[/tex]

Distribute:

[tex]5226 = n (26+7n-7)[/tex]

Simplify:

[tex]5226 = 7n^2+19n[/tex]

Isolate the equation:

[tex]7n^2+19n-5226=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 7, b = 19, and c = -5226. Substitute:

[tex]\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}[/tex]

Evaluate:

[tex]\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}[/tex]

Evaluate for each case:

[tex]\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}[/tex]

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

The cost of tickets of a comedy show of 'Gaijatra' is Rs 700 for an adult and Rs 500 for a child. If a family paid Rs 3,100 for 5 tickets, how many tickets were purchased in each category? ​

Answers

Answer:

Step-by-step explanation:

We need to create a system of equations here, one for the NUMBER of tickets sold and one for the COST of the tickets. They are very much NOT the same thing.

We have that the total number of tickets is 5, and that that total is made up of adult tickets and child tickets. The equation for the NUMBER of tickets, then, is:

a + c = 5

Now for the money.

If a child ticket costs Rc 500, the expression that represents that that is in fact the cost of the child ticket is 500c;

likewise for the adult ticket. If the adult ticket costs Rc 700, the expression that represents that is 700a.

And we know that a total of Rs 1300 was spent on the tickets. The equation for the COST is

700a + 500c = 1300

Now go back to the first equation and solve it for either a or c, it doesn't matter which. I solved for a:

a = 5 - c  and we will sub that into the second equation for a:

700(5 - c) + 500c = 1300 and

3500 - 700c + 500c = 1300 and

-200c = -400 so

c = 2 tickets. That means that there were

a = 3 tickets sold for the adults.

Find the value of x in the triangle shown below.(not a test just need help with khan academy)

Answers

Using angle sum property

[tex]\\ \sf\longmapsto x+44+29=180[/tex]

[tex]\\ \sf\longmapsto x+63=180[/tex]

[tex]\\ \sf\longmapsto x=180-63[/tex]

[tex]\\ \sf\longmapsto x=117°[/tex]

The angle sum property of a triangle:

The total measure of the three angles of a triangle is 180°

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: + \: 44 \degree \: + \: 29 \degree \: = \: 180 \degree[/tex]

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: + \: 73 \degree \: = \: 180 \degree[/tex]

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: = \: 180 \degree \: - \: 73 \degree \:[/tex]

[tex]\large\bf{\red{ \longrightarrow}} \: \tt \: x \: = \: 107 \degree[/tex]

⇛ Value of x is 107°

Convert the 7pi/5 to a degree measure

A=252
B=504
C=792
D=75

Answers

Answer:

252

Step-by-step explanation:

The conversion factor is

180/pi

7pi/5 * 180/pi = 7 *180/5 = 252 degrees

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