Binomial Theorem

The constant term in the expansions of
[tex](px^{3} + \frac{q}{x ^{3} } )^{8} [/tex]
and
[tex](p {x}^{2} + \frac{q}{ {x}^{2} } ) ^{4} [/tex]
are equal, and p and q are both greater than zero. Express p in terms of q.

Answers

Answer 1

Answer:

[tex]\frac{p^{4} x^{24}+6p^{2}q^{2}x^{12}+q^{4}+4p^{3}qx^{18}+4pq^{3}x^{6}}{x^{12} }[/tex]

Step-by-step explanation:


Related Questions

a) John wants to buy a house and is trying to figure out how much money he needs for the down payment. If the house
costs $275,000 and the down payment is 15% of the price of the house, how much will the down payment be? $

Answers

Answer:

$41 250

Step-by-step explanation:

15% * $275 000 = $41 250

2
3250 m + 1,662 km =

Answers

Answer:

1,665.25 km

Step-by-step explanation:

Rearrange the equation so q is the independent variable 9q - 4 = 3r - 6

Answers

3r = 9q - 4 + 6

r = (9q + 2)/3

Answer: r = (9q + 2)/3

Answer:

q = [tex]\frac{3}{9}[/tex]r -[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

9q - 4 = 3r - 6

+4 on both sides

9q = 3r - 2

Divide both sides by 9

q = [tex]\frac{3}{9}[/tex]r -[tex]\frac{2}{9}[/tex]

What is the area of the composite figure?

Answers

Answer:

208

Step-by-step explanation:

16x13

HELP please!!!!!!!!!!!

Answers

All real numbers are greater than or equal to 0.

8th grade math solution problem. Please help

Answers

3x + 2y = 12
x = y - 1

3x + 2y = 12
3 (y - 1) + 2y = 12
3y - 3 + 2y = 12
5y - 3 = 12
5y = 15
y = 3

x = y - 1
x = (3) - 1
x = 2

answer:
(2, 3)

If there are 125 boxes of prescription bottle labels at the beginning of inventory cycle, and 25 3/4 remain ,how many boxes of labels remain?

Answers

Answer:

Rounded to the nearest integer, 32 boxes of labels remain at the end of the inventory cycle.

Step-by-step explanation:

Given that there are 125 boxes of prescription bottle labels at the beginning of the inventory cycle, and 25 3/4 remain at the end of it, to determine how many boxes of labels remain the following calculation must be performed:

3/4 = 0.75 + 25 = 25.75

125 x 25.75 / 100 = X

3218.75 / 100 = X

32.1875 = X

Thus, rounded to the nearest integer, 32 boxes of labels remain at the end of the inventory cycle.

A. Find the product. Rewrite +
5.67 X 1.25

Answers

Answer:

Multiply

5.67 by 1.25.

7.0875

What is the sum of -3/7

Answers

Answer:

-0.4285714286

Step-by-step explanation:

-3/7 = -0.4285714286

0.42. Bun. Ufitb. G up ggivhh

5) Un pedazo de pizza cuesta $30, un jugo cuesta $15. ¿Cuánto de deben sobrar de
$500 al comprar 5 pedazos de pizza y 5 jugos?​

Answers

275
Explicación: 30 por 5 es 150 por la pizza
15 por 5 es 75. 150+75=225.
500-225=275

Answer:

I think it is 275 if you are subtracting

QUESTION:
Rachelle is offered a new job with Big Time Book-Sellers. Her starting wage is $10.00
per hour, and she will receive a $0.50 raise after the first year. For each year that she
stays with the company after that, her raise will be $0.50 more than it was the year
before. How much will Rachelle make per hour in her 7th year working at Big Time
Book Sellers?
A) How would you solve this problem? Explain the steps you would take. What is
your answer?
B) What is one important detail from this problem that you think people might
commonly miss?

Answers

Answer:

Step-by-step explanation:

multiplicas 0.50 por 7 , el resultado es 3.5, 3.5 lo sumas a 10 y eso es el resultado de lo que ella ganaría 13.50 dólares por hora después de trabajar 7 años con ellos.

a)You multiply 0.50 by 7, the result is 3.5, 3.5 l add to 10 and that is the result of what she would earn, $ 13.50 per hour after working 7 years with them.

During a charity walk, lunch was served from 12:00 PM until 2:10 PM. How long was lunch served?

Answers

Answer:

2 hours and 10 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 hours and 10 mins!

If Dave drove one-third of the distance of his trip on the first day, and 60 miles on the second day, he figured out that he still had 1/2 of the trip to drive. What was the total length, in miles, of his trip?
360

180

120

60

90

Answers

Answer:

180

Step-by-step explanation:

Answer:

The answer is 180

Step-by-step explanation:

To check the answer:

Since 60 is part of a half then 60 * 60 = 120

Now we have to find the other 60 remaining from 180 because 180-120 is 60.

1/2 of 180 is 90.

90-60 = 30

if one half is equal to 90 then the other half is equal to 90.

A man ears $15.50 per hour with time and a half for overtime and he worked 46 hours during a recent week. Find his gross pay for the week
The man's gross pay for the week was $
(Round to the nearest cent as needed)

Answers

Answer:

525267262525226

Step-by-step explanation:

594944+757548484-848484%

If IM is reflected across the x-axis and then translated along the vector <4, 1>, in
which quadrant is the final image?

Answers

Answer:

Final image L"M" will lie in the fourth quadrant.

Step-by-step explanation:

Coordinates of the ends of segment LM,

L  → (-3, 4)

M → (-3, 2)

Rule to reflect a point across x-axis is,

(x, y) → (x, -y)

By this rule, coordinates of the image point of L and M will be,

L(-3, 4) → L'(-3, -4)

M(-3, 2) → M'(-3, -2)

Further these image points are translated along the vector <4, 1>

Rule for this translation will be,

(x, y) → (x + 4, y + 1)

Now the image points of the points L' and M' will be,

L'(-3, -4) → L"(-3 + 4, -4 + 1)

             → L"(1, -3)

M'(-3, -2) → M"(-3 + 4, -2 + 1)

              → M"(1, -1)

Therefore, final image L"M" will lie in the fourth quadrant.

Write an equation and solve.
8 less than a number is 24

Answers

8 less than a number can be written as

x-8

when you see the word is you should think of = sign

so the equation will be x-8=24

Now solve adding 8 to both sides.

x=24+8

x=32

Answer:

a-8=24

Step-by-step explanation:

Answer is 32. add 8 to other side, making it 32

there are 70 students in the school band. 40% of them are sixth graders, 20 % are seventh graders, and the rest are eight graders. How many band members are sixth graders? How many band members are Seventh graders? What percentage of the band members are eighth graders?​

Answers

Answer:

28 are 6th

14 and 7th

40% are 8th

Step-by-step explanation:

Answer:

28= 6th grader

14= 7th grader

28= 8th grader

40% were 8th graders

Step-by-step explanation:

28= 6th grader

14= 7th grader

28= 8th grader

40% were 8th graders

Find the product of largest 4 digit number and

smallest 3 digit number.​

Answers

Largest 4 digit number =9999
Smallest 3 digit number= 100
So the product of 9999 x 100 = 999,900

Answer:

Largest 4-digit number is 9999 and smallest 3-digit number is 100 and product is 10000.

Step-by-step explanation:

hope it's helpful to you

PLEASE HELP ME
Amelia burns 10 calories for each minute that she spends running. How many calories will she burn if she runs for 20 minutes?
SHOW YOUR WORK

Answers

Answer:

She will burn 200 calories

Step-by-step explanation:

10(number of calories)x20(minutes)=200

Answer:

amelia is running for 20 minutes. so

10 calories per minute

x

20 minutes of running

=

200 calories burned.

10 x 20 = 200

In ΔOPQ, o = 5.2 inches, p = 8.4 inches and q=8.7 inches. Find the measure of ∠Q to the nearest 10th of a degree.

Answers

Answer:

75.475667

Step-by-step explanation:

Answer:75.5

Step-by-step explanation:

Multiply the sum 5 and 3 and the sum of 8 and 9

Answers

Answer:

136

Step-by-step explanation:

Sum of 5 and 3: 8

Sum of 8 and 9: 17

17 * 8 is 136

Answer: The sum of 5 and 3 is 8 and the sum of 8 and 9 is 17.

In ΔTUV, v = 49 inches, u = 47 inches and ∠U=65°. Find all possible values of ∠V, to the nearest degree.

Answers

Answer: 16

Step-by-step explanation:

sin M/6.3=sin 21/8.2

6.3 sin 21/8.2=0.27533147

sin^-1(0.27533147)=15.981=16

HELP PLEASE!!!! WILL GIVE BRAINLIEST :)))

Answers

Answer:

4(x + 9) = 76

Hope that helps!

Btw, x = 10

Step-by-step explanation:

(giving brainiest)

Susie has 4 gallons of juice. How many cups of juice does she have?

A. 2 cups
B. 16 cups
C. 32 cups
D. 64 cups

Answers

Answer:

D

Step-by-step explanation:

Answer:

You'll know that she has 64 cups of juice by multiplying 4 gallons x 16 cups.

Step-by-step explanation:

simply xsquared +5x +3x +15​

Answers

Answer:

5x+3x+15=8x+15

.................... ;)

The answer would be 8x + 15. This is the answer because you can add 5x and 3x, but not 15 to the coefficients.

If x=−1and y=−3, then 5(x2−7+y)=

Answers

my answer would be -60

ANSWER THEM PLEASEE I HAVE 20 MINSS

Answers

GIRLL I DONT SEE YOUR PIC

plz give work below​

Answers

Answer:

m < -6 or m > 8

Step-by-step explanation:

m - 2 < -8

Add 2 to both sides of the inequality.

m < -8 + 2

m < -6

m/8 > 1

Multiply both sides of the equation by 8

m/8 ⋅ 8 > 1 ⋅ 8

Simplify.

m > 8

good luck, i hope this helps :)

The table shows a linear relationship between x and y. What is the rate of change of y with respect to x.
A. -9/2
B. 2/9
C. -2/9
D. 9/2

Answers

Answer:

A. -⁹/2

Step-by-step explanation:

Using any two pairs of values form the table, say (-12, 60) and (-6, 33),

Rate of change = ∆y/∆x

= (33 - 60) / (-6 -(-12))

= -27/6

= -9/2

Rate of change = -⁹/2

The rate of change of y with respect to x is -9/2

Option A is correct

For a linear relationship, the rate of change of y with respect to x is given by the formula:

[tex]\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1} \\[/tex]

From the table:

[tex]x_1=-20, x_2=-12, y_1=96, y_2=60[/tex]

Substitute [tex]x_1=-20, x_2=-12, y_1=96, y_2=60[/tex] into the equation [tex]\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1} \\[/tex]

[tex]\frac{\triangle y}{\triangle x} =\frac{60-96}{-12-(-20)} \\\\\frac{\triangle y}{\triangle x} =\frac{-36}{8}[/tex]

Reduce the expression to the lowest term by dividing the numerator and denominator by 4

[tex]\frac{\triangle y}{\triangle x} =\frac{-9}{2}[/tex]

The rate of change of y with respect to x is -9/2

Learn more on rate of change here: https://brainly.com/question/8728504

Find the area of the following figure:

Answers

Answer:

138

Step-by-step explanation

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