Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.

Answers

Answer 1

Answer:

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

Step-by-step explanation:

(2x + 3)⁵

₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵

Use Pascal's triangle to find nCr.

[tex]\left\begin{array}{c}1\\1\ 1\\1\ 2\ 1\\1\ 3\ 3\ 1\\1\ 4\ 6\ 4\ 1\\1\ 5\ 10\ 10\ 5\ 1\end{array}\right[/tex]

1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵

(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243


Related Questions

Help THIS IS DUE IN LESS THAN A HOUR

Answers

Take that back, please delete this question.

Answer:

i beleive its b or d

Step-by-step explanation:

mostly b

solve.
5-(x-6)=-7+3(-x+2)

Answers

Answer:

x=-6

Step-by-step explanation:

For this equation, when we remove the parenthesis, we get 5-x+6=-7+-3x+6.

Then we simplify both sides of the equation, so we get 11-x=-1-3x. When we separate the numbers and variables, we get -12=-2x. -12/2 = -6.

5-x+6=-7-3x+6
combine like terma
11-x=-1-3x
add 3x to both sides
11+2x=-1
subtract 11 from both sides
2x=-12
x=-6

solve the equation. 4.6g +9+1.6g +21 what is g

Answers

Answer:

= 6.2g+9

Step-by-step explanation:

6.2g + 30 I cant solve for g since you didn’t provide what it equals

.4 ÷ 28.08 Dividing Decimals , Divide to the nearest Tenth??
I Will Give You 10 Points

Answers

Answer:

0

Step-by-step explanation:

The answer is 0.01424, but if you round it to the nearest tenth, you would end up with 0.

What is the value of the expression (x – 2y) (x + 2y) when x= 4 and y=1/2

Answers

Answer:

15

Step-by-step explanation:

First you would plug in the 4 and 1/2 in the x and y's places, making the expression (4 - 2 (1/2))*(4 + 2 (1/2). Then you solve (below).

(4 - 2 (1/2))*(4 + 2 (1/2)

(4 - 1)*(4 + 1)

(3)*(5)

15

Hope this helped! If you have any questions, feel free to message me :)

1/3 kilograms 2/3 what is the unit rate

Answers

Idk I download this app so other ppl can help me

320÷b∙20 and 320÷(b∙20) for b=4

Answers

Answer:

Step-by-4vttbrbwtetbb4tbtb44tny4ny4nyn4tbryn4y

step explanation:

Please help I need to get this answered!

Answers

Answer:

4  1/9

Step-by-step explanation:

so if we make the fraction the same having 7 4/9 and 3 1/3

we would then make 1/3 into 3/9 (its the smae thing not simplified)

subtract 7-3=4

4-3=1

and then simplify the fraction

The exact form would be 37/9
But in mixed number form, it would be 4 1/9

WILL MARK BRAINLIEST PLZ ANSWER FAST GUYS AND GIRLS. Don't mind the second question. You can answer it if you want that will help me.

Answers

Answer:

1. 10d + 5n = 85

2. look at graph  or graph coordinates (0, 17) and (8.5, 0) and make a line through them

3. 17 nickels since its only nickels, on the graph you see where the line hits the y-axis which is 17.

4. 8.5 dimes since its only dimes, on the graph you see where the line meets the x-axis which is 8.5

Step-by-step explanation:

y-axis is nickels

x-axis is dimes

What strategy would be the best to solve this problem? Ann-Marie bought apples. She kept one-third for herself and gave the rest to 4 friends. Each friend got 2 apples. How many apples did Ann-Marie buy? A. guess, check and revise B. work backwards C. use a formula D. look for patterns

Answers

Answer:

D. Look for patterns

Step-by-step explanation:

To solve :

Assume number of apples bought = x

Fraction kept = 1/3 of x

Fraction shared = (x - x/3) = (3x - x) /3 = 2x/3

Number of people who shared (2x/3) = 4 with each getting 2

Total number shared = 4 * 2 = 8

Fraction shared = total shared

2x/3 = 8

Multiply both sides by 3

(2x/3) * 3 = 8 * 3

2x = 24

x = 12

Hence, Anne-Marie purchased 12 apples

A car increases, then decreases, its speed. Which table could represent the speed of the car? A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 5, 6, 7, 8, 9. The second column is labeled speed (miles per hour) with entries 45, 43, 41, 42, 43. A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 5, 6, 7, 8, 9. The second column is labeled speed (miles per hour) with entries 45, 47, 49, 48, 47. A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 5, 6, 7, 8, 9. The second column is labeled speed (miles per hour) with entries 45, 45, 45, 43, 41. A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 5, 6, 7, 8, 9. The second column is labeled speed (miles per hour) with entries 45, 43, 41, 41, 41.

Answers

Answer:

The speed increases (45—>47—>49) then decreases (48—>47) over time.

Step-by-step explanation:

HOPE THIS HELPED ✨

Answer: The speed increases (45—>47—>49) then decreases (48—>47) over time.

Solve [X + 8) = 5
With steps

Answers

Answer:

X=(-3)

Step-by-step explanation:

1.Subtract 8 from both sides of the equation.-(x+0)=5-8-the 0 is there because the 8 on the left side is canceled out.

2.5-8 is all you have to look at.-when you look at this you know that it will be negative because 8 is on the right of the minus sign and it is greater than 5.

3.Use a calculator or you fingers to find answer.-(4,3,2,1,0,-1,-2,-3)

HOPE THIS HELPS!!!

HELP BAD DAY
Write as an expression:twice the product of the squares of x and y
with the product of the cube of a and the square of b

Answers

Answer:

the square root of 2(x^3 * x^2)

Step-by-step explanation:

twice means 2 and product means either division or multiplication (multiplication in this scenario because twice means multiply).  cubed means to the third power

25-2z-10z=-3(4z+8)-1
solve and how many solutions ?

Answers

distribute first
25-2z-10z=-12z-24-1
combine like terms
25-12z=-12z-25
add 12z to both sides
25=-25
no solution because the right side has a negative

Answer:

No Solutions

Step-by-step explanation:

Step 1:

25 - 2z - 10z = - 3 ( 4z + 8 ) - 1       Equation/Given

Step 2:

25 - 12z = - 12z - 25        Combine Like Terms/Multiply

Step 3:

25 = - 25       Add 12z on both sides

Answer:

No Solutions

Hope This Helps :)

Help it’s homework!!!!

Answers

Answer:

(3x - 3)(x + 2)

Step-by-step explanation:

3x^2 + 3x - 6

(3x^2 + 6x)(-3x - 6)

3x(x + 2) -3(x + 2)

(3x - 3)(x + 2)

Twice a number increased by 4 is at least 10 more than the number

Answers

Answer:

the twice as number increased by 4 is at least 10 more than a number .

2x + 4 ≥ x + 10

x ≥ 6

Step-by-step explanation:

Mark Brainliest

Answer:

2n+4 >= 10 + n

Step-by-step explanation:

solve for n , but remember the rules of dealing with inaqualities

What is the pyhtagoream thereom and how can you use it to slove right triangles

Answers

Answer:

Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

a is one leg of the right triangle.

b is another left of the right triangle.

c is the hypotenuse of the right triangle.

We use the Pythagorean Theorem to help us solve for missing side lengths of a right triangle.

how do you solve u = 3a/2 solving for a

Answers

Answer:

Step-by-step explanation:

a=2a/3. ✌️

The answer that I got is 2a/3


P(5. - 5), y=3x+3
Write an equation for the line in point-slope form

Answers

Answer:

M= 3

Step-by-step explanation:

l2ecdnienofnweucon fuovnewdionsdv wqueijncqodi

Answer:

y+5 =3(x-5)

Step-by-step explanation:

The point slope form of an equation is : y-y₁ = m(x-x₁)

Given in the question ;

x₁= 5

y₁ = -5

y= 3x+3 where m=3

The equation is :

y-y₁ = m(x-x₁)

y--5 =3(x-5)

y+5 =3(x-5) ----equation of the line in point-slope form.

What is the y intercept of this graph?. What is the slope?

Answers

Answer:

y intercept is -3

slope is 4

y=4x-3

Step-by-step explanation:

The difference between a number x and 3 is at least nine Write an inequality for the following sentence.

Answers

Answer:

3 - x ≥ 9

Step-by-step explanation:

At least in inequality means greater than or equal to (≥)

Difference in mathematics means subtraction

The difference between a number x and 3

3 - x

is at least nine

3 - x ≥ 9

The inequality for the sentence is

3 - x ≥ 9

Answer please 1st and second

Answers

1/9 x 12 is 4/3 or 1.333 repeated
The correct answer is 1.333

Filling up a tank of gas costs $36.96. If the tank holds 16.5 gallons of gas, then how much d
each gallon cost?

Answers

Answer:

$2.24 per Gallon

Step-by-step explanation:

36.96 divided by 16.5 is 2.24, then to check that multiple 2.24 by 16.5 and you get the total cost of 36.96. Hope this helps.


The annual profit at a chain of stores is normally distributed with a mean of $61,000 and a standard
deviation of $23,000. The stores in the top 5% of annual profit were rewarded with a celebration. What
was the annual profit required to have a party?

Answers

Answer: $98,835.

Step-by-step explanation:

Given: Annual profit at a chain of stores is normally distributed with a mean ([tex]\mu[/tex]) of $61,000 and a standard  deviation([tex]\sigma[/tex]) of $23,000.

Let [tex]x[/tex] denoted the profit.

Let [tex]x_0[/tex] be the minimum profit required to have a party.

The stores in the top 5% (i.e. 0.05) of annual profit were rewarded with a celebration.

i.e. [tex]P(x>x_0)=0.05[/tex]

[tex]\Rightarrow\ P(\dfrac{x-\mu}{\sigma}>\dfrac{x_0-61000}{23000})=0.05\\\\\Rightarrow\ P(z>\dfrac{x_0-61000}{23000})=0.05\ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\\Rightarrow\ \dfrac{x_0-61000}{23000}=1.645\ \ [\text{critical z-value for p-value 0.05=1.645}]\\\\\Rightarrow\ x_0-61000 =1.645\times 23000\\\\\Rightarrow\ x_0-61000 =37835\\\\\Rightarrow\ x_0=37835+61000\\\\\Rightarrow\ x_0=98835[/tex]

Hence, the annual profit required to have a party was $98,835.

Find the equation of the line that passes through (2,8) and (6,48)

Answers

Answer: m = 10

.........................

What is the missing reason in the proof?

given
transitive property
alternate interior angles theorem
converse alternate interior angles theorem

Answers

Answer:

c, alternate interior angles theorem

Step-by-step explanation:

if 1 is equal to 3, and 3 is equal to 2 by alternate interior angles theorem, then that should also apply to angle 1.

15 points!
What is the correct answer for Claire's problem? Explain where she went wrong.

Answers

Answer:

it would be y=50+25x

Step-by-step explanation:

There is an extra $25 per room, and since we dont know how many rooms she has cleaned, we can use x to represent that amount. So for x amount of rooms, it will be an extra $25

Solve the equation given
x = - 4.
5 = x + 9

Answers

Answer:

x=-4

Step-by-step explanation:

You wrote the answer in the question, so there is really no question.

How it helps :)

Lincoln Cook has a check for $295.50 and a check for $6.25. He also has a $10.00 bill
He would like to receive $5.00 in cash and deposit the rest of the money in his say-
ings account. What is the total deposit?

Answers

Step-by-step explanation:

First, we need to add all the checks and money he has.

295.50

 10.00

   6.25

+________

  3   6  1  . 7 5

Total- $361.75

Now, we have to subtract 5 from this.

361.75

   5.00

-______

3 5 6 . 7 5

The total deposit is $356.75

Answer:

$306.75 is the right answer i just took the test.

Step-by-step explanation:

Help please
And thank you so much

Answers

Answer:

$0.1 /lb.

Step-by-step explanation:

First, divide 1.99 by 19. You get 0.1047368421. To round it to the nearest hundred, look to the number 3 points away from the decimal, which is number 4. Since it is not 5 or greater, we round it down, and it would round down to 0.1.

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