Answer:
(3,2)
Step-by-step explanation:
I graphed the two lines using a graphing tool. The lines intercept at (3,2). Therefore, the solution to the system is (3,2).
Answer: The dimensions are 8 and 3
Step-by-step explanation:
So 8*3=24 which corresponds with the formula for area l*w= Area
And perimeter means we add up all 4 sides so
8+8+3+3= 22
So the dimensions are 8 and 3
It is convenient to do part b first, then use that result to do part a.
b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end.
Adding (a, b) to the above equation gives
2(a, b) - (x1, y1) = (x2, y2)
Adding (x1, y1) then gives
2(a, b) = (x1, y1) + (x2, y2)
Finally, dividing by 2 gives a formula for (a, b):
(a, b) = ((x1, y1) + (x2, y2))/2
The midpoint is the average of the end points.
a. Using the result from part b, the midpoint is
midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2
midpoint = (4, 5)
Answer:
5040
Step-by-step explanation:
There are 7 options for the 1st song, 6 options for the 2nd song, 5 options for the 3rd song, 4 options for the 4th song, 3 options for the 5th song, 2 options for the 6th song, and 1 option for the 7th song. We get:
(<em>Note: when you have a number n, where it is multiplied by every number until one (ex. 7. 7*6*5*4*3*2*1), then the number in the result is n! (n factorial). So we get that 7*6*5*4*3*2*1 is 7! is 7 factorial. So 5040 is 7! </em>)
