Answer:
The single transformation that fully maps triangle A onto triangle B is the reflection of triangle A across the line y = x
Step-by-step explanation:
The coordinates of the vertices of triangle A are
1) (4, -1)
2) (1, -3)
3) (4, -3)
The coordinates of the vertices of triangle B are
1) (-1, 4)
2) (-3, 1)
3) (-3, 4)
Therefore, we have the points (x, y) in triangle A becoming the points (y, x) in triangle B, which is a reflection across the line y =x.
Hence, the single transformation that fully maps triangle A onto triangle B is the reflection of triangle A across the line y = x.
<span>4(c+2)= -28
Use distributive property
4c+8=-28
Subtract 8 from both sides
4c=-36
Divide 4 on both sides
Final Answer: c=-9</span>
Greetings!To find the length of any side of a
right triangle, you can use the
Pythagorean Thereom. It states that the squares of two sides are equal to the square of the hypotenuse:
Input the information from the diagram into the formula:
Expand each term:
![(x)^2+(x+7)^2=(13)^2](https://tex.z-dn.net/?f=%28x%29%5E2%2B%28x%2B7%29%5E2%3D%2813%29%5E2)
![x^2+((x+7)(x+7))=169](https://tex.z-dn.net/?f=x%5E2%2B%28%28x%2B7%29%28x%2B7%29%29%3D169)
![x^2+(x(x+7)+7(x+7))=169](https://tex.z-dn.net/?f=x%5E2%2B%28x%28x%2B7%29%2B7%28x%2B7%29%29%3D169)
Combine like terms:
Add -169 to both sides:
![(2x^2+14x+49)+(-169)=(169)+(-169)](https://tex.z-dn.net/?f=%282x%5E2%2B14x%2B49%29%2B%28-169%29%3D%28169%29%2B%28-169%29)
Factor out the Common Term (2):
Factor the Complex Trinomial:
![2(x^2-5x+12x-60)=0](https://tex.z-dn.net/?f=2%28x%5E2-5x%2B12x-60%29%3D0)
![2(x(x-5)+12(x-5))=0](https://tex.z-dn.net/?f=2%28x%28x-5%29%2B12%28x-5%29%29%3D0)
![2(x-5)(x+12)=0](https://tex.z-dn.net/?f=2%28x-5%29%28x%2B12%29%3D0)
Set Factors to equal
0:
![x-5=0](https://tex.z-dn.net/?f=x-5%3D0)
![x=5](https://tex.z-dn.net/?f=x%3D5)
or
![x+12=0](https://tex.z-dn.net/?f=x%2B12%3D0)
![x=-12](https://tex.z-dn.net/?f=x%3D-12)
However, since we are solving for the side length, the only possible answer is 5 (a shape can't have a side with a negative length.)
The Solution Is:
![\boxed{x=5}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%3D5%7D%20)
I hope this helped!
-Benjamin
Answer:
2/3
Step-by-step explanation:
So we have 10%+5%=15% of clients under the condition "permanent", and we can find the probability that a client in that group requested a haircut:
P(haircut | permanent)=10%/15%=2/3
It changes it into negative