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
Blizzard [7]
3 years ago
12

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Mathematics
1 answer:
Sloan [31]3 years ago
5 0

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

You might be interested in
Plzzzzzzzzzzzzzzz<br> aaaaaaaaaaaaaaaaaaaaa
kvasek [131]

Answer:

C. 7x + 11

Step-by-step explanation:

(13x-4)+(-6x+15)

13x-4-6x+15

7x+11

4 0
3 years ago
Read 2 more answers
How To Write ten hundredths in standard form
jekas [21]

Answer:

Ten hundredths in standard from is 0.1.

5 0
3 years ago
Can someone please explain to me the difference between SAS and SSS in Geometry when dealing with triangle proofs?
ANTONII [103]

Hello from MrBillDoesMath!

Answer:   SAS = side - angle -side    congruence

              SSS  = side - side - side     congruence


Discussion :

In Plane Geometry,  identical triangles are said to be "congruent". There are several ways, depending upon the information you have, to prove 2 triangles are congruent.

In one approach ("SSS") if you can show that 2 triangles have identical side lengths,  then the triangles are congruent. (A triangle has 3 sides, hence "SSS" -- 3 S's; 3 sides, get it?)

In another approach ("SAS") if you can show that 2 sides, and the angle included between those sides, in one triangle are identical to the sides and included angle in another triangle,  then the triangles are congruent

It's easier to understand this with a picture or diagram than in words. Please review the SSS, SAS picture in your textbook

Regards, MrB

7 0
3 years ago
What is the least common multiple of 15 and 6?<br><br> Take notes and show your work.
Mariulka [41]
Hello!

The least common multiple is 3

Hope this helps!
4 0
3 years ago
Somebody, please help
SashulF [63]
F(x) can be written as:
f(x) = Asin(2x); where A is the amplitude and the period of the function is half that of a normal sin function.
f(π/4) = 4
4 = Asin(2(π/4))
4 = Asin(π/2)
A = 4
Amplitude of g(x) = 1/2 * amplitude of f(x)
A for g(x) = 2
g(x) = 2sin(x)
5 0
3 years ago
Other questions:
  • A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g and 3.14 for π. If you ente
    6·1 answer
  • Factor the expression completely over the complex numbers.<br><br> x4−625
    7·1 answer
  • Uncle Drew scored 28 points in 5 5/6 minutes during a game of basketball.
    9·1 answer
  • The place value of the 7 in 0.724
    14·2 answers
  • 0.4 divided by 0.08 show your work
    6·2 answers
  • Uh, uh, uh, uh
    7·2 answers
  • 1. 6x - 29 = 115<br> 2. 3y - 1 = 29<br> 3. 4z - 32 = 36<br><br> find x, y, and z
    10·1 answer
  • I dont think I can write this out via phone; any help?
    12·2 answers
  • Karina is driving from her house to her cottage. If she drives at 10 kilometers per hour, she will arrive at 6 PM. If she drives
    15·1 answer
  • How many planes are in this figure?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!