How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen ?

a 100
b 120
c 240
d 720

120

Step-by-step explanation:

Think about the eight letters A B C D E F G H, if A and B (or any two letters) are already chosen then you want to know how many ways 6 letters can fill 3 spaces when order matters, in other words the letters F G H are considered 1 outcome with the first two letters and G F H is considered another individual outcome with the first two letters.  If order didn't matter then F G H and G F H with the first two letters would be considered only one outcome.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

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