Find the 5th term of the expansion of (x + y)^9 a. 81x4y5 c. 81x5y4 b. 126x4y5 d. 126x5y4 select the best answer from the choices provided a b c d

Option d. .

Step-by-step explanation:

Based on binomial theorem we write down the binomial formula for all positive integer values of n as-

Now we calculate the 5th term of

From the given formula the fifth term of the binomial will be

=

Here the value of n = 9

Then the fifth term will be

1260=3*6*7*10=3^2*2^2*7*5 perfect cude = 3^3*2^

step-by-step explanation:

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3