Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4

Answers

Answer 1

Answer:

Step-by-step explanation:

Binomial Expansion:

[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]

Pascal's Triangle:

  Zero row                        1

 First row                  1                 1

 Second row          1           2             1

 Third  row         1         3              3          1

 Fourth row    1       4            6           4          1


Related Questions

Someone pls help me ill give out brainliest pls don’t answer if you don’t know

Answers

Answer:

(1/3) r2 =(1/3) r +14

1/6 divided by 83 r + 14

97r

i think...

I hope this helps you!

XoXo Mashayla

Step-by-step explanation:

find the next four terms of the sequence 5, 4, 9, 13, 22

Answers

Hello,

It is the Fibonacci 's suit.

[tex]u_1=5\\u_2=4\\u_3=u_1+u_2=5+4=9\\u_4=u_2+u_3=4+9=13\\u_5=u_3+u_4=9+13=22\\u_6=13+22=35\\u_7=22+35=57\\u_8=35+57=92\\u_9=57+92=149\\\\\\\boxed{u_{n+2}=u_{n}+u_{n+1}}\\[/tex]

Can someone help me with this math homework please!

Answers

Answer:

Step-by-step explanation:

The sum of a father's and his son's age is 60. Eight years ago, the father's age was 3 times that of his son. How old is each of them?​

Answers

Answer:

Father=41

Son=19

Step-by-step explanation:

Father=f

Son=s

f+s=60

Eight years ago would mean that 16 is subtracted from 60 since there is both of them

3s+s=4s

4s=44

s=11

11+8=19

33+8=41

A boutique was having a 20% storewide sale.Erica bought 2 dresses which originally cost $80 each.How much savings did Erica enjoy?

Answers

Answer: $32

Step-by-step explanation:

Since the boutique was having a 20% storewide sale and Erica bought 2 dresses which originally cost $80 each, therefore the sale for each dress will be:

= $80 - (20% × $80)

= $80 - (0.2 × $80)

= $80 - $16

= $64

Therefore, on each dress Erica saves $16. The amount of savings enjoyed will then be:

= $16 × 2

= $32

Find the x of a triangle.

Answers

This triangle is an isosceles triangle because it has two congruent sides. Therefore, the two bottom angles are also congruent. And, the sum of the interior angles of a triangle is 180 degrees.

180 = 104 + (9x - 25) + (9x - 25)

180 = 104 + 18x - 50

180 = 54 + 18x

126 = 18x

x = 7

Hope this helps!

Evaluate the expression.
32 + 6 x 22-42 - 23

Answers

Answer:

25

Step-by-step explanation:

You need to simplify

.

.

.

.

................... :)

Answer:

D

Step-by-step explanation:

9+24-16+8= 25

Cans of soda at a local store a six-pack of soda costs $2.59 and indivdual cans cost $0.80. What is the maximum of cans of soda that can be purchased for $15​

Answers

Answer:  30 cans (buy them by the six-pack; so you'd buy 5 six-packs)

==============================================================

Explanation:

Let's say you buy six-packs only. Divide the amount of money you have over the cost per six-pack.

15/(2.59) = 5.7915 which rounds down to 5.

If you buy six-packs only, then you can buy a max of 5 of them. That gets you 5*6 = 30 cans of soda.

-------------

Now let's say you buy individual cans only. We'll use the same idea mentioned earlier but this time divide over 0.80

15/(0.80) = 18.75 which rounds down to 18

We round down because we can't buy that 19th can of soda (note how 19*0.80 = 15.2 which is larger than 15).

So if you buy individual cans only, then you can get a max of 18 cans.

We see that it's better to go with the six-pack option (in the first section) since we can get 30 cans compared to 18 cans.

Which statement is not always true for a parallelogram?
A. Consecutive angles are supplementary.
B. Diagonals are congruent.
C. Opposite sides are congruent.
D. Opposite angles are congruent.

Answers

Answer: B. Diagonals are congruent.

Explanation:

If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.

If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.

Choices A, C and D are true for any parallelogram (rectangle or not).

Find the product

14/4 • 33/10 =

Answers

Answer:

Step-by-step explanation:

[tex]\frac{14}{4}*\frac{33}{10}=\frac{7}{2}*\frac{33}{10}\\\\ =\frac{7*33}{2*10}\\\\=\frac{231}{20}\\\\=11\frac{11}{20}[/tex]

The cost of having a window fixed is $175 plus $30 per hour of labor. Using h for the number of hours of labor, write an expression that represents the total cost.

Answers

Answer:

175 + 30h

Step-by-step explanation:

Hope this helps

Answer:

total cost = 175+30h

Step-by-step explanation:

Total cost = fixed cost + cost per hour * hours

total cost = 175+30h  where h is the number of hours

What conclusion would be true given the hypothesis?

Answers

Answer:

4th option

Step-by-step explanation:

If ∠ 1 = ∠ 2 = ∠ 3

Then ∠ 1 = ∠ 3 is true

Answer:

The second one the measure of angle?1 is less then angle 3 is the correct answer.

A movie rental store gives free popcorn to every 40th
customer and a free movie rental to every 45th
customer. Which customer was the first to win both​ prizes?

Answers

Answer:

360th customer

Step-by-step explanation:

To find the customer that will receive both the free popcorn and the free movie rental, we have to list the multiples of 40 and 45 until we get a multiple that is the same for both of them.

Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440

Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360

360 is the first multiple that is same for multiples of 40 and 45

So the 360th customer will receive both items.

(Sorry if my explanation is hard to understand. I haven't done this kind of math in a while)

Hope it helps (●'◡'●)

In the history of Major League Baseball, the most valuable player award has been won by players from 7 different countries. which countries were they

Answers

Answer:

United States, Canada, Dominican Republic, Cuba, Venezuela, Japan, Panama

Step-by-step explanation:

Taking a look at a list of Major League Baseball most valuable players, the countries are:

United States(most players are US-born).

Canada(Joey Votto in 2010).

Dominican Republic(Albert Pujols and Vlad Guerrero Sr. for example).

Cuba(last Jose Abreu in 2020)

Venezuela(last Jose Altuve in 2017)

Japan(Ichiro in 2001).

Panama(Rod Carew)

Can someone help me with this math homework please!

Answers

Answer:

1. [tex]x=2[/tex]

2. Simplify by combining like terms

3. [tex]x=1[/tex]

4. [tex]k=0.5[/tex]

5. [tex]y=3[/tex]

Step-by-step explanation:

1. [tex]2.5(6x-4)=10+4(1.5+0.5x)[/tex]

Distribute within the parenthesis

[tex]15x-10=10+6+2x[/tex]

Combine like terms

[tex]15x-10=16+2x[/tex]

Isolate the variable expression by using the addition/subtraction properties of equality

[tex]13x=26[/tex]

Isolate the variable by using the division/multiplication properties of equality

[tex]x=2[/tex]

2. Like terms are always combined as soon as possible but never before the distributive property is applied.

3. You can find the solution by comparing the tables.

4. [tex]6k+10.5=3k+12[/tex]

Apply the addition/subtraction properties of equality

[tex]3k=1.5[/tex]

Apply the division/multiplication properties of inequality

[tex]k=0.5[/tex]

5. [tex]y+3=-y+9[/tex]

Addition/subtraction properties

[tex]2y=6[/tex]

Division/Multiplication properties

[tex]y=3[/tex]

Jill has just moved to a new town and wants to share plates of baked goods with her neighbors. She has 20 cookies and 12 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates she can make to share?

Answers

Answer:

4

Step-by-step explanation:

The greatest number of plates Jill can split the 20 cookies and 12 brownies into can be determined by calculating the highest common factor and 20 and 12

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 20 = 1, 2,4, 5, 10, 20

50 pts pls help
What is the range of the function shown on the graph above?

Answers

572^ the answer above is correct!!!!!

Answer:

[0, 7]

Step-by-step explanation:

The range is the set of y-values.

The graphed function has its range between 0 and 7, both inclusive.

So the range is:

y ∈ [0, 7]

Solve for X (line a and b parallel)

Answers

Answer:

x=29°

Step-by-step explanation:

as lines are parallel.

external alternate angles are equal.

7x-86=4x+1

7x-4x=1+86

3x=87

x=87/3=29

Between the numbers 15/20 and 35/40 , the greater number is
a. 15/20 b. 20/15 c. 35/40 d. 45/30

Answers

Answer:

35/40

Step-by-step explanation:

To compare, both denominator should be same.

[tex]\frac{15}{20}=\frac{15*2}{20*2}=\frac{30}{40}\\\\\\\frac{30}{40} \ < \ \frac{35}{40}\\\\\\\frac{15}{20} \ < \ \frac{35}{40}[/tex]

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

⠀the numbers 15/20 and 35/40⠀⠀⠀

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

⠀⠀⠀⠀

the greater number is

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

we have to find the greater number between 15/20 and 35/40

To do this,

we have to compare the denominator same.

[tex]\sf{\dfrac{35}{40}=\dfrac{35×1}{40×1}=\dfrac{35}{40} }[/tex]

[tex]\sf{\dfrac{15}{20}=\dfrac{15×2}{20×2}=\dfrac{30}{40} }[/tex]

According to the question,

we have to find the greatest one

[tex]\sf{\dfrac{35}{40} > \dfrac{30}{40} }[/tex]

[tex]\sf{\dfrac{35}{40}>\dfrac{15}{20} }[/tex]

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

⠀⠀

[tex]\therefore\mathrm{\dfrac{35}{40} > \dfrac{15}{20} }[/tex]

⠀⠀

plss, help me!!!

Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 wich are blend. Each one orders a different color ( no repeats) at random. What is the probability that the friends order only cotton sweatshirts?​

Answers

Answer:  B) 1/52

===========================================================

Explanation:

Let's label the friends as A,B,C,D.

Person A has a probability of 7/16 when it comes to ordering a certain color of cotton sweatshirt.

Then 6/15 is the probability for person B. Note how the 7 and 16 drop by 1 for each. This is because no repeats are allowed. If person A goes for a blue sweatshirt, then person B cannot select blue as well.

Person C's probability is 5/14 and person D has a probability of 4/13

-------------------------

So we have these fractions: 7/16, 6/15, 5/14, 4/13

Once again, we have the numerators and denominators counting down by 1 each time.

Multiplying those fractions gets us...

(7/16)*(6/15)*(5/14)*(4/13)

(7*6*5*4)/(16*15*14*13)

840/43680

(1*840)/(52*840)

1/52

So if you did 52 trials of this, then you should expect about 1 of those trials is where each friend orders a different color cotton sweatshirt.

1/52 = 0.0192 = 1.92% approximately

So this happens about 1.92% of the time.

Does anyone know what graph is correct?

Answers

First graph is the correct one.

when x= 1

y=f(x) = -√1 = -1

when x= 2

y= -√2

The third wait no the first actuality it’s the second one

Which number line represents the solution set for the inequality-1/2x>_4

Answers

Answer:

B

Step-by-step explanation:

Firstly, we solve for x

-x ≥ 2 * 4

-x ≥ 8

Multiply both sides by -1

x ≤ -8

So we look at the inequality represented by this;

We can see that the correct inequality is option B;

PLZ HELPPP!!! whoever answers first with a good answer ill mark as brainliest

Answers

Answer:  B. F(53)

This is because the nth term is found by adding the previous two terms

F(n) = nth term

F(n-1) = term just before the nth term

F(n-2) = term before the F(n-1) term

F(n) = F(n-1) + F(n-2)

We can re-index values of n to say this equivalent statement

F(n+2) = F(n+1) + F(n)

Based on either equation mentioned, adding F(51) and F(52) will get us F(53). In other words, the 51st and 52nd terms add to the 53rd term.

Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women

Answers

Answer:

The number of ways is 26,400 ways

Step-by-step explanation:

Given;

total number of men, M = 10

total number of women, W = 12

number of committees to be formed = 6

If there must be equal gender, then it must consist of 3 men and 3 women.

[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]

Therefore, the number of ways is 26,400 ways

(a+1)(b+2)
please help me!!!

Answers

Answer:

(a + 1) (b + 2 ) = 2a + b + ab + 2

Step-by-step explanation:

[tex](a +1 )(b + 2) \\\\= a( b+ 2) + 1 (b +2) \\\\= ab + 2a + b + 2\\\\=2a + b + ab + 2[/tex]

Answer:

[tex](a + 1)(b + 2) \\ = a(b + 2) + 1(b + 2) \\ = ab + 2a + b + 2[/tex]

Answer ↦ [tex]\boxed{\tt{ab + 2a + b + 2}}[/tex]

Method Used:

↦ Distributive Property.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Write using exponents. Rewrite the expression below in the same sequence.

Answers

Answer:

[tex]10^2a^2b[/tex]

Step-by-step explanation:

Exponents are a way of shortening multiplication statements. The exponent represents how many times a term is being multiplied by itself. So, when two terms have the same base it can be written with exponents. For example. 10*10 can be written as [tex]10^2[/tex] because 10 is being multiplied 2 times. Therefore, if we do this with every term you get [tex]10^2a^2b[/tex].

The ratio of keepers to animals in the city zoo is 2 : 7. The table shows the current numbers of animals and keepers in the zoo. If 21 more animals are added, how many total keepers are needed to maintain the ratio of keepers to animals?

City Zoo
Number of Keepers Number of Animals
12 42

Answers

Answer:

18

Step-by-step explanation:

42+12= 63

63/7=9

9*2=18

Answer:

18

Step-by-step explanation:

plato/edmentum

can someone help me with this?​

Answers

Answer:

-64 is the 26th number

it's an arithmetic sequence because the difference between the number is constant : -3

they are all -3 in difference

Step-by-step explanation:

an = a1 + (n-1)d

an = the nᵗʰ term in the sequence

a1=the first term in the sequence

d=the common difference between terms

-64 = 11 + (n - 1)-3

-64=11 -3n+3

-78 = -3n

n = 26

Find the area

Help me please

Answers

Answer:

143

Step-by-step explanation:

to find the area we multiply half of the sum of the bases with height

(18+8)/2*11 = 143

Evaluate the expression 2

Answers

2^5 = 32

Hope this helps! :)

Answer:

32

Step-by-step explanation:

[tex]2^{5}[/tex]

= 2 × 2 × 2 × 2 × 2

= 4 × 4 × 2

= 16 × 2

= 32

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