Stoplight A changes color every 45 seconds and Stoplight B changes color every 80 seconds. Both stoplights changed color 60 seconds ago. After how many seconds will the stoplights change color at the same time again.​

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  660 seconds

Step-by-step explanation:

The least common multiple of 45 seconds and 80 seconds is ...

  45×80/GCF(45,80) = 45×80/5 = 720

The next change will be 720 seconds after the last one, so 720 -60 = 660 seconds from now.

Additional comment

You can find the least common multiple by looking at the factors of 45 and 80:

The LCM will include one copy of the common factor and all of the unique factors:

  LCM(45, 80) = 5×9×16 = 720

You can see that the greatest common factor is 5, and that the LCM is the product (5×9)(5×16) divided by 5:

  LCM(a, b) = a×b/GCF(a, b)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).