1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artemon [7]
3 years ago
12

Explain how Pascal’s triangle allows you to compute the coefficient of x2y3 when (x − y)5 is

Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

-10

Step-by-step explanation:

Pascal’s triangle: It represents the binomial coefficients. If a binomial expression is (a+b)^n, then (n+1)th row of Pascal’s triangle represents the binomial coefficients or that binomial expression.

The given binomial expression is

(x-y)^5

The elements of 6th row are 1, 5, 10, 10, 5 and 1.

(x-y)^5=1(x)^5+5(x)^4(-y)^1+10(x)^3(-y)^2+10(x)^2(-y)^3+5(x)^1(-y)^4+1(-y)^5

(x-y)^5=x^5 - 5 x^4 y + 10 x^3 y^2 - 10 x^2 y^3 + 5 x y^4 - y^5

Therefore, the coefficient of x²y³ is -10.

You might be interested in
Help me please asap<br>​
Juliette [100K]

Answer:

5/6

Step-by-step explanation:

2/

3

: 4/

5

= 2/

3

· 5/

4

= 2 · 5/

3 · 4

= 10/

12

= 2 · 5/

2 · 6

= 5/

6

4 0
3 years ago
Read 2 more answers
Four times one number minus three times another number is 12. Two times the first number added to three times to the second numb
SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

x = first number, y = second number

4x - 3y = 12

2x + 3y = 6

------------------add

6x = 18

x = 18/6

x = 3

4x - 3y = 12

4(3) - 3y = 12

12 - 3y = 12

-3y = 12 - 12

-3y = 0

y = 0

solution : (3,0)

4 0
3 years ago
What is the value of the expression-2(3x-2)+x+9 when x= -3
nikitadnepr [17]

We know x=-3

Replace x with -3

-2(3[-3]-2)+(-3)+9

simplify

-2(-9-2)-3+9

-2(-11)-3+9

22-3+9

do math

22-12

Your Answer Is 10

4 0
3 years ago
Plz help meh (ASAP) question below
alisha [4.7K]

Answer:

It's D I believe.

Step-by-step explanation:

I had this question before.. hopefully this helps

8 0
2 years ago
The equation for the ellipse given is 4x^2+9y^2-16x+18y-11​
natita [175]

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

\dfrac{(x - h)^2}{a^2}  + \dfrac{(y - k)^2}{b^2} = 1

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) =  25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

\dfrac{4\cdot (x - 2)^2}{36}  + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}

\therefore \dfrac{ (x - 2)^2}{9}  + \dfrac{  (y + 1)^2}{4} =  \dfrac{ (x - 2)^2}{3^2}  + \dfrac{  (y + 1)^2}{2^2}  = 1

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

8 0
3 years ago
Other questions:
  • 270 is ninety percent of what number ?
    13·1 answer
  • Simplify 8^2 / 4 + 3(6 - 3) + 2^3.<br><br> show steps pls !!
    11·1 answer
  • Rectangles A and B have the same perimeter but are different shapes Rectangle S is 5 inches long and 3 inches wide. Rectangle B
    11·1 answer
  • a hockey team has 12 girls and 9 boys. Each week the coach chooses the player at random to play goalie for next game what is the
    8·1 answer
  • K is equal to l<br> m is equal to n<br> as the angles are marked, what's x and y
    8·1 answer
  • Can someone please answer. There is a picture. It is only one question. Thank you so much!
    6·1 answer
  • Solve for x.<br> -30 = 5(x + 1) <br>x=​
    8·1 answer
  • Kyle designs and conducts a computer simulation with 25 trials and uses the data to create the relative frequency bar graph show
    7·1 answer
  • Help help math math math
    5·2 answers
  • Nutritionists recommend that people eat
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!