Answer:
1, 2, 3, 6, 9, 18, 27, 54.
Step-by-step explanation:
factors:
1, 2, 3, 6, 9, 18, 27, 54.
Therefore, all the factor pairs for 54 is 1, 2, 3, 6, 9, 18, 27, 54..
This is tricky. Fasten your seat belt. It's going to be a boompy ride.
If it's a 12-hour clock (doesn't show AM or PM), then it has to gain
12 hours in order to appear correct again.
How many times must it gain 3 minutes in order to add up to 12 hours ?
(12 hours) x (60 minutes/hour) / (3 minutes) = 240 times
It has to gain 3 minutes 240 times, in order for the hands to be in the correct positions again. Each of those times takes 1 hour. So the job will be complete in 240 hours = <em>10 days .</em>
Check:
In <u>10</u> days, there are <u>240</u> hours.
The clock gains <u>3</u> minutes every hour ==> <u>720</u> minutes in 240 hours.
In 720 minutes, there are 720/60 = <u>12 hours</u> yay !
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If you are on a military base and your clocks have 24-hour faces,
then at the same rate of gaining, one of them would take 20 days
to appear to be correct again.
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Note:
It doesn't have to be an analog clock. Cheap digital clocks can
gain or lose time too (if they run on a battery and don't reference
their rate to the 60 Hz power that they're plugged into).
Let b and s be the velocity of the boat and stream respectively....
3(b-s)=27
b-s=9
b=9+s we will use this in the second equation....
2(b+s)=30
b+s=15, now use b found above in this to get:
9+s+s=15
2s+9=15
2s=6
s=3, and since from earlier b-s=9, b=9+s so
b=12
So the speed of the boat is 12mph and the stream is 3 mph
To solve a system of equations by graphing, you must first graph both equations. The solution is the point of intersection of the lines.
To plot these two equations, do this.
First equation.
y = 3x + 1
y = mx + b
b = 1, so plot point (0, 1), the y-intercept.
Now starting at point (0, 1), use the slope, m = 3 = 3/1, to go up 3 units and 1 unit to the right. Plot that point which is (1, 4). Now connect points (0, 1) and (1, 4) with a straight line and extend the line in both directions. That is how you graph the first equation.
Second equation.
Solve it for y.
x - 2y = 8
-2y = -x + 8
y = (1/2)x - 4
y = mx + b
b = -4. Plot point (0, -4) which is the y-intercept. Now from that point, go up 1 unit and right 2 units to point (2, -3), and plot that point. Connect the two points with a straight line and extend it in both directions. That is how you plot the second equation.
The point of intersection of both lines is the solution of the system of equations. Read that point.
Answer: 8
Step-by-step explanation: 8(15-4)/4^2-5 8(11)/16-5 88/11 = 8