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](https://tex.z-dn.net/?f=%28x-y%29%5E5)
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](https://tex.z-dn.net/?f=%28x-y%29%5E5%3D1%28x%29%5E5%2B5%28x%29%5E4%28-y%29%5E1%2B10%28x%29%5E3%28-y%29%5E2%2B10%28x%29%5E2%28-y%29%5E3%2B5%28x%29%5E1%28-y%29%5E4%2B1%28-y%29%5E5)
![(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](https://tex.z-dn.net/?f=%28x-y%29%5E5%3Dx%5E5%20-%205%20x%5E4%20y%20%2B%2010%20x%5E3%20y%5E2%20-%2010%20x%5E2%20y%5E3%20%2B%205%20x%20y%5E4%20-%20y%5E5)
Therefore, the coefficient of x²y³ is -10.
Answer:
see explanation
Step-by-step explanation:
The n th term ( explicit formula ) of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁₂ = - 95 and a₃₇ = - 270 , then
a₁ + 11d = - 95 → (1)
a₁ + 36d = - 270 → (2)
Subtract (1) from (2) term by term to eliminate a₁
25d = - 175 ( divide both sides by 25 )
d = - 7
Substitute d = - 7 into (1) and solve for a₁
a₁ + 11(- 7) = - 95
a₁ - 77 = - 95 ( add 77 to both sides )
a₁ = - 18 , thus
= - 18 - 7(n - 1) = - 18 - 7n + 7 = - 7n - 11
= - 7n - 11 ← explicit formula
--------------------------------------------------------------
The recursive formula allows a term in the sequence to be found by adding the common difference d to the previous term, thus
=
- 7 with a₁ = - 18 ← recursive formula
Answer: The number is 1.
Step-by-step explanation:
create the formula from the problem
4x -7 = 1
move the seven to the other side by adding seven to both sides
4x (+7) -7 = 1 (+7)
4x = 8
then to get the x by itself, divide both sides by 4
4x/4 = 8/4
x = 2
You can check your work by plugging the x back into the original problem
4 (2) -7 = 1
8 -7 = 1
1 = 1 (this means it is correct)
Answer:
Using the Pythagorean theorem
a^2 + b^2 = c^2
c = square root(a^2 + b^2)
c = square root(27^2 + 36^2)
c = square root(729 + 1296)
c = square root(2025)
c= 45
<u>Straight Line Distance = 45 miles</u>
Answer: no.
Step-by-step explanation:
3 cannot go into 2 equally.