How many ways are there for six dogs and four cats to sit in a row in a strawberry field so that no two cats sit next to each ot
1 answer:
Answer: 5,760
Step-by-step explanation:
It was given that each dog is distinct from other dogs and each cat is distinct from other cats, Also from the hint given, the First position is for the dogs.
Let D represent the dogs and C represent the Cat , then we have
D C D C D C D C D D or
D D C D C D C D C D or
D C DD C D C D C D or
D C D C D D C D C D or
D C D C D C DD C D
Each of the arrangements above could be done in
2 x 4! x 4! ( it is constant that D is starting , so I am only left with the arrangement of the remaining 5 D's , out of the remaining 5 D's it is also constant that tow of them will be together and this could be done in 2 ways, so I have 4! left for the D's and 4! also for the C's )
= 2 x 24 x 24
= 1 , 152
The total arrangement = 5 x 1 , 152
= 5,7 60 ways
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Answer: a = 2 b = 3 c = 5
Literally a+ b+c = 10, but I don't think that's what the question means to ask.
the equation is 2x² +3x + 5
Step-by-step explanation: Substitute the values of the given coordinates into the formula and use algebra (solve a system of equations by substitution and elimination) to get the values of a,b & c
y=ax²+bx+c using (0,5), (1,10), and (2,19)
5=a(0)²+b(0)+c becomes 5= 0+0 + c .so we find c = 5
10=a(1)²+b(1)+c becomes 10 = a + b + c
19=a(2)²+b(2)+c . becomes 19 = 4a + 2b + c
Substitute the 5 for c. Then rewrite
10 = a + b + 5 becomes 5 = a+ b to eliminate b multiply this be (-2)
(-2)( 5 = a+ b) .to get -10 = -2a - 2b
19 = 4a + 2b + 5 becomes 14 = 4a + 2b
_______________ Add these two
14 = 4a + 2b
<u>-10 = -2a - 2b</u><u> </u> this will eliminate the "b" term
4 = 2a divide both sides by 2 so you have a = 2
substitute in 10=a(1)²+b(1)+5 to find b
10=2(1)²+b(1)+5 .becomes 5 = 2 + b Subtract 2 from both sides
b = 3
So now you have all three values:
a = 2 b= 3 c = 5
I am attaching the graph. I hope this deserves Brainiest.
Best wishes in your studies!
