What is the smaller angle formed by the minute and hour hands at 3:30pm?

75 degrees

Step-by-step explanation:

360/60=6 degrees per minute on a clock face

minute hand, from 12 o'clock position is 30 minutes so 30x6=180 degrees

hour hand, from 12 o'clock position is 17.5 minutes so 17.5x6=105 degrees

180-105=75 degrees

75 degrees.

Step-by-step explanation:

The angles between 2 consecutive  numbers on the clock are 360 /12 = 30 degrees.

The hour hand is half way between the 3 and 4 so this = 15 degrees,

So the required angle = 2*30 + 15

= 75 degrees.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1