Answer: The point (5, 6) would divide the line segment so it is in the ratio of 3:5.
If the ratio of the line segment needs to be 3:5, that means the point will be at the 3/8 distance mark of the line segment. Because there are 8 total parts if the ratio is 3:5 (3 + 5 = 8).
The slope from (2, 9) to (10, 1) is -8/8. So our point would only move 3/8 of that distance. If we multiply -8 and 8 by 3/8, we have -3 and 3.
That means our point must fall 3 and move to the 3 spaces from our starting point of (2, 9). That will put us at (5, 6).
So we want to know how to write the inequality for Beth's jogging. The total number of miles Beth plans to jog cant go over 12, and she has already jogged for 3 miles, then she needs to jog for another m miles. This can be written mathematically like: 3 + m < 12. In other words: 3 miles + m miles Beth still plans to jog cant go over 12 miles.
Hello
sin ..... | 0° |30°|45°|60°|90°|
...........| 0...| 1..| 2..| 3..| 4..| write numbers
...........| 0...| 1..|√2.| √3 | 2..| take root square
...........| 0...|1/2|√2/2|√3/2|1| divide by 2
...........| 0...|1/2|√2/2|√3/2|1| .....
cos.....| 90°|60°|45°|30°| 0°|
sin (75°)
=sin(30°+45°)=sin 30°*cos 45° +cos 30°*sin 45°
.................... =1/2*√2/2 + √3/2*√2/2
.................... = √2(1+√3)/4
cos 75°
=cos(30°+45°)=cos 30°*cos 45°-sin 30°*cos 45°
=√3/2*√2/2-1/2*√2/2
=√6/4-√2/4=√2/4*(√3 -1 )
The work and answer provided are correct, the simpler way of doing it is
1)
1/6 page written in 1/12 of a minute
to write a full page, you would need to write 1/6, 6 times
so,
and
so it takes 1/2 of a minute to write a full page, there are 60 seconds in a minute, 1/2 of 60 seconds is 30 seconds
same process works for question 2(use 3 instead of 6 though)
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