40
There isnt a way the LCD can go lower, because 5 only counts by 5's and 5 and 8 meet at 40.
The first condition is for the perimeter of the equation so:
![P=2a+b=15.7](https://tex.z-dn.net/?f=P%3D2a%2Bb%3D15.7)
Now the secon condition is that the sum of two sides should be:
![\begin{gathered} a+b>b \\ b+b>a \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%2Bb%3Eb%20%5C%5C%20b%2Bb%3Ea%20%5Cend%7Bgathered%7D)
so the negative option and 0 don't make sence dor a distance, then we try with the value of b=0.5
So in the first equation will be:
![\begin{gathered} 2a+0.5=15.7 \\ 2a=15.2 \\ a=7.6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202a%2B0.5%3D15.7%20%5C%5C%202a%3D15.2%20%5C%5C%20a%3D7.6%20%5Cend%7Bgathered%7D)
So the condition:
![\begin{gathered} b+b>a \\ 0.5+0.5>7.6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20b%2Bb%3Ea%20%5C%5C%200.5%2B0.5%3E7.6%20%5Cend%7Bgathered%7D)
this is false, so the solution is
<h3>Given system :</h3>
![y = 5x - 7 \\ - 3x - 2y = - 12](https://tex.z-dn.net/?f=y%20%3D%205x%20-%207%20%5C%5C%20%20-%203x%20-%202y%20%3D%20%20-%2012)
<h3>Solution to the system :</h3>
Substitute the given value of y into the equation -3x-2y=-12
![- 3x - 2(5x - 7) = - 12](https://tex.z-dn.net/?f=%20-%203x%20-%202%285x%20-%207%29%20%3D%20%20-%2012)
Distribute -2 through the parentheses
![- 3x - 10x + 14 = - 12](https://tex.z-dn.net/?f=%20-%203x%20-%2010x%20%2B%2014%20%3D%20%20-%2012)
Collect like terms
![- 13x + 14 = - 12](https://tex.z-dn.net/?f=%20-%2013x%20%2B%2014%20%3D%20%20-%2012)
Move the constant to the right-hand side and change its sign
![- 13x = - 12 - 14](https://tex.z-dn.net/?f=%20-%2013x%20%3D%20%20-%2012%20-%2014)
Calculate the sum and divide both sides of equation by -13
![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
Now, Substitute the given value of x into y=5x-7
![y = 5(2) - 7](https://tex.z-dn.net/?f=y%20%3D%205%282%29%20-%207)
Multiply the numbers
![y = 10 - 7](https://tex.z-dn.net/?f=y%20%3D%2010%20-%207)
Subtract the numbers
![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
The possible solution of the system is the ordered pair (x,y)
![(x,y)=(2,3)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%282%2C3%29)
Answer:
The value of x = 9
Step-by-step explanation:
∵ The figure has right angle and a line ⊥ from the right angle to the hypotenuse
∴ There is a relation between the ⊥ line and the two parts of the hypotenuse
∴ (⊥)² = multiplication of the two parts of the hypotenuse
∴ (6)²= 4 × x
∴ 36 = 4 × x
∴ x = 36/4 = 9