The answer is of course E -340
Answer:
![S=(\frac{9}{2},-\frac{3}{2})](https://tex.z-dn.net/?f=S%3D%28%5Cfrac%7B9%7D%7B2%7D%2C-%5Cfrac%7B3%7D%7B2%7D%29)
Step-by-step explanation:
The missing details are:
![T= (0,4)](https://tex.z-dn.net/?f=T%3D%20%280%2C4%29)
--- Midpoint of ST
Required
Determine the coordinates of S
To do this, we apply the mid-point formula:
![M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x_1%2Bx_2%2Cy_1%2By_2%29)
Where
![M(x,y) = (\frac{9}{4}, \frac{5}{4})](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%20%28%5Cfrac%7B9%7D%7B4%7D%2C%20%5Cfrac%7B5%7D%7B4%7D%29)
![T(x_1,y_1) - (0,4)](https://tex.z-dn.net/?f=T%28x_1%2Cy_1%29%20-%20%280%2C4%29)
The equation becomes:
![M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)](https://tex.z-dn.net/?f=M%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x_1%2Bx_2%2Cy_1%2By_2%29)
![(\frac{9}{4},\frac{5}{4}) = \frac{1}{2}(0+x_2,4+y_2)](https://tex.z-dn.net/?f=%28%5Cfrac%7B9%7D%7B4%7D%2C%5Cfrac%7B5%7D%7B4%7D%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%280%2Bx_2%2C4%2By_2%29)
![(\frac{9}{4},\frac{5}{4}) = \frac{1}{2}(x_2,4+y_2)](https://tex.z-dn.net/?f=%28%5Cfrac%7B9%7D%7B4%7D%2C%5Cfrac%7B5%7D%7B4%7D%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x_2%2C4%2By_2%29)
Multiply through by 2
![2*(\frac{9}{4},\frac{5}{4}) = 2*\frac{1}{2}(x_2,4+y_2)](https://tex.z-dn.net/?f=2%2A%28%5Cfrac%7B9%7D%7B4%7D%2C%5Cfrac%7B5%7D%7B4%7D%29%20%3D%202%2A%5Cfrac%7B1%7D%7B2%7D%28x_2%2C4%2By_2%29)
![(\frac{9}{2},\frac{5}{2}) = (x_2,4+y_2)](https://tex.z-dn.net/?f=%28%5Cfrac%7B9%7D%7B2%7D%2C%5Cfrac%7B5%7D%7B2%7D%29%20%3D%20%28x_2%2C4%2By_2%29)
By comparison:
![x_2 = \frac{9}{2}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B9%7D%7B2%7D)
![4 + y_2 =\frac{5}{2}](https://tex.z-dn.net/?f=4%20%2B%20y_2%20%3D%5Cfrac%7B5%7D%7B2%7D)
![y_2 =\frac{5}{2}-4](https://tex.z-dn.net/?f=y_2%20%3D%5Cfrac%7B5%7D%7B2%7D-4)
![y_2 =\frac{5-8}{2}](https://tex.z-dn.net/?f=y_2%20%3D%5Cfrac%7B5-8%7D%7B2%7D)
![y_2 =-\frac{3}{2}](https://tex.z-dn.net/?f=y_2%20%3D-%5Cfrac%7B3%7D%7B2%7D)
Hence, the coordinates of S is:
![S=(\frac{9}{2},-\frac{3}{2})](https://tex.z-dn.net/?f=S%3D%28%5Cfrac%7B9%7D%7B2%7D%2C-%5Cfrac%7B3%7D%7B2%7D%29)
isoscele triangle, equalateral triangle, and scalene triangle
In a deck of cards there are total of 52 cards.
But in our case we have to check the probability of red 8, which is either the 8 of diamond or of heart.
So the number of events of which we have to find probability is 2. And total number of events is 52.
So the probability will be
2/52 = 1/26 = 0.0384615
This is the lower part of the shape, we must find the height of both shapes
The heights of both shapes are the same since the opposite sides are equal
for th lower shape drawn h, the height =
The
so MN = 1/2(AB + DC)
MN = 27
AB = ?
DC = 32
Substituting
27 = 1/2(AB + 32)
27 = AB/2 + 32/2
27 = AB/2 + 16
2 x 27 = 2 x AB/2 + 2x16
54 = AB + 32
AB = 54-32
AB = 22