<span>Given the diagram, where AB and EF are horizontal lines and CB is a vertical line segment.
Given that FB : FC = 4 : 3,
From the diagram, the coordinate of A is (-10, -8) and the coordinate of C is (-3. -1).
We can also see that the coordinate of B is (-3, -8) (since CB is a vertical line means that B is the same x-value as C and AB is a horizontal line means that B is the same y-value as A)
Recall that the coordinate of a point dividing a line segment in the ratio m:n is given by (x1 + m/(m+n) (x2 - x1), y1 + m/(m+n) (y2 - y1))
Thus, since FB : FC = 4 : 3, this means that point F divides the line segment BC in the ratio 4 : 3.
Thus, the coordinate of F is given by (-3 + 4/(4+3) (-3 - (-3)), -8 + 4/(4+3) (-1 - (-8))) = (-3 + 4/7 (0), -8 + 4/7 (7)) = (-3, -4).
Also, given that FB : FC = 4 : 3, this means that point D divides the line segment AC in the ratio 4 : 3.
Thus, the coordinate of D is given by (-10 + 4/(4+3) (-3 - (-10)), -8 + 4/(4+3) (-1 - (-8))) = (-10 + 4/7 (7), -8 + 4/7 (7)) = (-6, -4).
Therefore, the coordinates of point D is (-6, -4).</span>
Answer:
12.3
Step-by-step explanation:
You will use cosine to solve for y because you are given the hypontenuse and need to find the adjacent side.
cos 35 degrees = adjacent/hypontenuse
cos 35 = y/ 15
15( cos35 ) = y
y=12.287
=12.3
Answer:
3/20
Step-by-step explanation:
You have velocity 1 of 5 km per hour after 1 hour and velocity 2 of 3 km per hour after 2 hours.
Part A)
Let Velocity = a +bt, with t being the time in hours.
For velocity 1 you have a +b = 5
For velocity 2, you have a + 2b =3
Now subtract velocity 1 from velocity 2:
a +2b - (a+b) = 3-5
Simplify to get b = -2
Now solve for a in the first equation:
a + b =5
Replace b with -2:
a - 2 = 5
a = 7
Now replace a and b in the original formula:
Velocity = 7 -2t
Part B)
Create a table with x and Y values to graph.
X axis would be the time and the velocity would be the Y axis
Your time would be 0 , 1, 2 3 and 4 hours.
Using the final equation from part A, replace t with the hours ans solve for the velocities, which become the y axis:
7 - 2(0) = 7-0 = 7
7 - 2(1) = 7-2 = 5
7 - 2(2) = 7-4 = 3
7 - 2(3) = 7-6 = 1
7-2(4) = 7-8 = -1
Now you have your x and y coordinates to plot on a graph:
(0,7) (1,5) (2,3) (3,1) and (4,-1)
Answer:
44x +56y = 95
Step-by-step explanation:
To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.
The midpoint is the average of the coordinate values:
((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)
The differences of the coordinates are ...
(3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)
Then the perpendicular bisector equation can be written ...
Δx(x -h) +Δy(y -k) = 0
5.5(x -0.25) +7(y -1.5) = 0
5.5x -1.375 +7y -10.5 = 0
Multiplying by 8 and subtracting the constant, we get ...
44x +56y = 95 . . . . equation of the perpendicular bisector
