Answer:
The length of the diagonal HJ is 10.82 units
Step-by-step explanation:
* Lets revise the rule of the distance between two points
- 
, where
and 
are the two points
* Lets use this rule to find the length of the diagonal HJ
∵ The coordinates of point H are (-4 , 3)
∵ The coordinates of point J are (5 , -3)
∴ 
and 
∴ 
and 
- Lets find the length of the diagonal HJ by using the rule above
∴ HJ = 
∴ HJ = 
∴ HJ = 10.82
* The length of the diagonal HJ is 10.82 units
Work:
First department: (They have 9 possibilities for delegate and 8 for alternate)
9 * 8 = 72
Second department: (They have 7 possibilities for delegate and 6 for alternate)
7 * 6 = 42
Third department: (They have 10 possibilities for delegate and 9 for alternate)
10 * 9 = 90
Total possibilities:
72 * 42 * 90 = 272,160 possibilities
I hope this helps!
Not equivalent to any of the given expressions.
Step-by-step explanation:
Hence, 
is not equivalent to any of the given expressions.
For the first line we have a slope of (y2-y1)/(x2-x1)
(2--2)/(1--1)=4/2=2 so we have:
y=2x+b, now solve for b with either of the points, I'll use: (1,2)
2=2(1)+b
b=0 so the first line is:
y=2x
Now the second line:
(1-10)/(4--2)=-9/6=-3/2 so far then we have:
y=-3x/2+b, using point (4,1) we solve for b...
1=-3(4)/2+b
1=-6+b
b=7 so
y=-3x/2+7 or more neatly...
y=(-3x+14)/2
...
The solution occurs when both the x and y coordinates for each are equal, so we can say y=y, and use our two line equations...
2x=(-3x+14)/2
4x=-3x+14
7x=14
x=2, and using y=2x we see that:
y=2(2)=4, so the solution occurs at the point:
(2,4)
