we know that
In a right triangle we have
two legs and one hypotenuse
Let
a,b -----> the legs of the right triangle
c-----> the hypotenuse of the right triangle (the greater side)
Applying the Pythagoras Theorem
therefore
<u>the answer is</u>
The length of the hypotenuse squared is the length of one leg squared plus the length of another leg squared
The value placed in the box that makes the system of equation with infinitely many solution is 12.
<h3>How to solve an infinitely many solution equation?</h3>An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If we simplify the equation we will notice both sides are equal. This means the equation has an infinitely many solution.
Hence,
y = -2x + 4
Therefore,
6x + 3y = 12
divide the equation(ii) by 3
2x + y = 4
y = -2x + 4
Therefore, both equation are equal if the the box is filled with 12. This means for the value placed in the box that makes the system of equation with infinitely many solution is 12.
learn more on equation here: brainly.com/question/13116557
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