Robert has built a mechanical model solar system with three balls representing planets at the ends of rods attached to the center representing the sun. The planets are aligned when he
turns on the motor. The innermost planet makes a revolution in 18 seconds, the middle
planet makes a revolution in 30 seconds, and the outermost planet makes a revolution in 42
seconds. After how many seconds will the planets be aligned again?

A. 1260 seconds
B. 630 seconds
C. 315 seconds
D. 945 seconds

according to egenuity the answer is

step-by-step explanation:

d. 344.22

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)