Answer:
Step-by-step explanation:
90 + 34 = (l)
(l) = 124
Answer:
a. ![M(x,y) = (-1,-1)](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28-1%2C-1%29)
b. ![D(-4,-9)](https://tex.z-dn.net/?f=D%28-4%2C-9%29)
Step-by-step explanation:
Given
A(-8,7) and B(6,-9).
Solving (a):
Determine the Midpoint M;
This is calculated as follows;
![M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Where
![(x_1,y_1) = (-8,7)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-8%2C7%29)
![(x_2,y_2) = (6,-9)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%286%2C-9%29)
Substitute these values in the formula
![M(x,y) = (\frac{-8+6}{2},\frac{7-9}{2})](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28%5Cfrac%7B-8%2B6%7D%7B2%7D%2C%5Cfrac%7B7-9%7D%7B2%7D%29)
![M(x,y) = (\frac{-2}{2},\frac{-2}{2})](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28%5Cfrac%7B-2%7D%7B2%7D%2C%5Cfrac%7B-2%7D%7B2%7D%29)
![M(x,y) = (-1,-1)](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28-1%2C-1%29)
<em>Hence; the midpoint is (-1,-1)</em>
Solving (a):
Here, we have
C = (2,7)
M; Midpoint = (-1,-1)
Required: Determine D
This is calculated as follows;
![M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Where
![(x_1,y_1) = (2,7)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C7%29)
![(x,y) = (-1,-1)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28-1%2C-1%29)
Substitute these values in the formula
![(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})](https://tex.z-dn.net/?f=%28-1%2C-1%29%20%3D%20%28%5Cfrac%7B2%2Bx_2%7D%7B2%7D%2C%5Cfrac%7B7%2By_2%7D%7B2%7D%29)
Solving for x2
![-1 = \frac{2 + x_2}{2}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B2%20%2B%20x_2%7D%7B2%7D)
Multiply both sides by 2
![-2 = 2 + x_2](https://tex.z-dn.net/?f=-2%20%3D%202%20%2B%20x_2)
Subtract 2 from both sides
![x_2 = -2 - 2](https://tex.z-dn.net/?f=x_2%20%3D%20-2%20-%202)
![x_2 = -4](https://tex.z-dn.net/?f=x_2%20%3D%20-4)
Solving for y2
![-1 = \frac{7 + y_2}{2}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B7%20%2B%20y_2%7D%7B2%7D)
Multiply both sides by 2
![-2 = 7 + y_2](https://tex.z-dn.net/?f=-2%20%3D%207%20%2B%20y_2)
Subtract 7 from both sides
![y_2 = -2 - 7](https://tex.z-dn.net/?f=y_2%20%3D%20-2%20-%207)
![y_2 = -9](https://tex.z-dn.net/?f=y_2%20%3D%20-9)
Hence, the coordinates of D is
![D(-4,-9)](https://tex.z-dn.net/?f=D%28-4%2C-9%29)
Answer:
x ≈ 50.8°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin x =
=
=
, then
x =
(
) ≈ 50.8° ( to the nearest tenth )
I don't understand exactly what you mean lolol