Answer:
27 mm
Step-by-step explanation:
The perimeter of the triangle is the sum of all sides lengths. In given triangle
first side has the length of 11 mm, the second side has the length of 35 mm.
If the perimeter is 73 mm, then
![73=11+35+x,\\ \\ x+46=73,\\ \\x=73-46,\\ \\x=27\ mm.](https://tex.z-dn.net/?f=73%3D11%2B35%2Bx%2C%5C%5C%20%5C%5C%20x%2B46%3D73%2C%5C%5C%20%5C%5Cx%3D73-46%2C%5C%5C%20%5C%5Cx%3D27%5C%20mm.)
![{ x }^{ 2 }-10x+9](https://tex.z-dn.net/?f=%7B%20x%20%7D%5E%7B%202%20%7D-10x%2B9)
First you should ask, which two numbers add up to -10 and multiply to 9.
-9 and -1 add up to -10 and multiply to 9.
![(-9)+(-1)=-10](https://tex.z-dn.net/?f=%28-9%29%2B%28-1%29%3D-10)
![(-9)(-1)=9](https://tex.z-dn.net/?f=%28-9%29%28-1%29%3D9)
So we can factor and rewrite like this ;
![(x-9)\cdot (x-1)](https://tex.z-dn.net/?f=%28x-9%29%5Ccdot%20%28x-1%29)
Let's equal it to 0 again.
![\\ (x-9)\cdot (x-1)=0](https://tex.z-dn.net/?f=%5C%5C%20%28x-9%29%5Ccdot%20%28x-1%29%3D0)
The multiplication of (x-9) and (x-1) is equal to 0
So we should equal them to 0 seperately to find the solution set
![x-9=0\\ \\ x=0+9\\ \\ x=9](https://tex.z-dn.net/?f=x-9%3D0%5C%5C%20%5C%5C%20x%3D0%2B9%5C%5C%20%5C%5C%20x%3D9)
and
![x-1=0\\ \\ x=0+1\\ \\ x=1](https://tex.z-dn.net/?f=x-1%3D0%5C%5C%20%5C%5C%20x%3D0%2B1%5C%5C%20%5C%5C%20x%3D1)
The solution set,
1) Diagonals of a rectangle bisect each other, so AW=13.
2) Since diagonals of a rectangle are congruent, AC=BD. Then, since diagonals of a rectangle bisect each other, DW=13.
3) Diagonals of a rectangle are congruent, so BD=26.
4) Opposite sides of a rectangle are congruent, so AD=10.
5) Using the Pythagorean theorem, BA=24.
You can turn them into improper fractions:
2 5/6 =
![\dfrac{17}{6}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B17%7D%7B6%7D%20)
8 4/7 =
![\dfrac{60}{7}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B60%7D%7B7%7D%20)
Multiply them: 170/7 =
24
Answer:
gradient = 3
Step-by-step explanation:
3/1 = 3
hope this helps