to find the radius of x^2+y^2-10x+6y+18=0, we must complete the square:
x^2 - 10x + y^2 + 6y = -18
Then:
x^2 - 10x + 5^2 - 5^2 + y^2 + 6y + 9 - 9 = -18
Collecting all three constants on the right-hand side, r^2 = -18 + 25 + 9 = 16
Then r = +sqrt(16) = +4 (answer)
The answer would be 60, if you add 13,15, and 12 up you get 40. Those numbers would be considered 2/3 of all the marbles. Divide 40 by 2 to get how many marbles is 1/3. You would get 20 being a third if the marbles. Add that to the original 40 and you’ll get a total of 60.
6x+y=24
-6x to both sides
y=-6x+24
divide by 6
y=-4
I am sorry if this is wrong.
Answer:
1?
Step-by-step explanation:
I think its one...
Answer:
97.98
Step-by-step explanation:
The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;
Area of the parallelogram = |PQ×PS|
PQ = Q-P and PS = S-P
Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)
PQ = (4,-5,3) - (0,0,0)
PQ = (4,-5,3)
Also, PS = S-P
PS = (8,-12,4)-(0,0,0)
PS = (8,-12,4)
Taking the cross product of both vectors i.e PQ×PS
(4,5,-3)×(8,-12,4)
PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k
PQ×PS = -16i - 40j -88k
|PQ×PS| = √(-16)²+(-40)²+(-88)²
|PQ×PS| = √256+1600+7744
|PQ×PS| = √9600
|PQ×PS| ≈ 97.98
Hence the area of the parallelogram is 97.98
