Solve ,nC2 = 4n+5 algebraically.

n = 10

Step-by-step explanation:

Using the definition of n =

where n! = n(n - 1)(n - 2)..... × 3 × 2 × 1

Given

n = 4n + 5 , then

= 4n + 5

Cancel the terms from (n - 2).... on numerator/denominator

= 4n + 5 ( multiply both sides by 2 )

n² - n = 8n + 10 ( subtract 8n + 10 from both sides )

n² - 9n - 10 = 0 ← in standard form

(n - 10)(n + 1) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 10 = 0 ⇒ n = 10

n + 1 = 0 ⇒ n = - 1

However n > 0 ⇒ n = 10

step-by-step explanation:

rectangles are made up of 4 right angles, which means that a side and a base meet perpendicular to one another.   their slopes then have to reflect perpendicular slopes.   perpendicular slopes are opposite reciprocals of one another.   for example, if the slope of one line is +2/3, then the perpendicular slope to that would be -3/2.   so we look for that combination in our choices.

all of them satisfy that condition (so what's the question, i guess? )