Answer:
k = 9
Step-by-step explanation:
Consider the pattern on the right side , that is
= k(k + 2) + 1 = k² + 2k + 1
Equating
k² + 2k + 1 = 100 ( subtract 100 from both sides )
k² + 2k - 99 = 0 ← in standard form
(k + 11)(k - 9) = 0 ← in factored form
Equate each factor to zero and solve for k
k + 11 = 0 ⇒ k = - 11
k - 9 = 0 ⇒ k = 9
But k > 0 , then k = 9
Answer: 15
Step-by-step explanation:
(r+1)th term of 
is given by:-
For 
, n= 6
![=\ \dfrac{6!}{4!2!}a^4b^2\ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{6\times5\times4!}{4!\times2}a^4b^2\\\\=3\times5a^4b^2\\\\ =15a^4b^2](https://tex.z-dn.net/?f=%3D%5C%20%5Cdfrac%7B6%21%7D%7B4%212%21%7Da%5E4b%5E2%5C%20%5C%20%5C%20%5B%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D%5D%5C%5C%5C%5C%3D%5Cdfrac%7B6%5Ctimes5%5Ctimes4%21%7D%7B4%21%5Ctimes2%7Da%5E4b%5E2%5C%5C%5C%5C%3D3%5Ctimes5a%5E4b%5E2%5C%5C%5C%5C%20%3D15a%5E4b%5E2)
Hence, the coefficient of the third term in the binomial expansion of is 15.
Answer:
15 in
Step-by-step explanation: It would be 15 in because 12+12 equals 24 and 50-24=30 and 30 divided by 2 equals 15 in.
1 pound is 16 ounces
32 ounces is 32 ÷ 16 = 2 pounds
1 pound of Botcoil ⇒ 1.5
2 pounds = 1.5 × 2 = 3
Answer:
$X = $12y
Step-by-step explanation:
In this question, we are asked to give an expression to represent the amount of money charged to a man who stayed in a motel for a particular number of days.
Firstly, we need to know the amount of money charged per day. This is visible from
the question and it is equal to $y.
Secondly, the number of days/night stayed is 12 days. This means that the amount of money he was charged is 12 * y = $12y
Since the amount of money charged is equal to $x, the amount to pay can be expressed in terms of y and x to be
$X = $12y
