Answer:
B. 97.2
Step-by-step explanation:
The sequence of positive terms is ...
54, 24, 10 2/3, 4 20/27, ...
This sequence has first term 54 and common ratio 24/54 = 4/9. The sum of the infinite series is ...
S = a1/(1 -r) = 54/(1 -4/9) = 54(9/5)
S = 97.2
The sum of the positive terms in the infinite series is 97.2.
Answer:
90 degrees
Step-by-step explanation:
Angle BGD is supplementary with angle DGE.
BGD + DGE = 180
Since angle DGE is a right angle, then Angle BGD must also be a right angle:
BGD + 90 = 180
BGD = 90
Subtracting the second equation by 18 on both sides, we have xy=-18. Next, we divide both sides by x to get y=-18/x Plugging that into the first equation, we have x+2(-18/x)=9. Multiplying both sides by x, we get x^2-36=9x. After that, we subtract both sides by 9x to get x^2-9x-36=0. Finding 2 numbers that add up to -9 but multiply to -36, we do a bit of guess and check to find the answers to be -12 and 3. Factoring it, we get
x^2-12x+3x-36=x(x-12)+3(x-12)=(x+3)(x-12). To find the x values, we have to find out when 0=(x+3)(x-12). This is simple as when you multiply 0 with anything, it is 0. Therefore, x=-3 and 12. Plugging those into x=-18/y, we get x=-18/y and by multiplying y to both sides, we get xy=-18 and then we can divide both sides by x to get -18/x=y. Plugging -3 in, we get -18/-3=6 and by plugging 12 in we get -18/12=-1.5. Therefore, our points are (-3,6) and (12, -1.5)
