VIrene takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 7 inches long and 6 inches wide, how long is the diagonal cut that Irene made? If necessary, round to the nearest tenth.
Please help with me with this phytagareon theorem problem please. i really appreciate it.

Virene?  

The Old Babylonians didn't really think about right triangles like we do.  They thought about the diagonal of a rectangle, which is essentially the same thing.  We get the Pythagorean theorem with the sides of the rectangle the legs and the diagonal of the rectangle is the hypotenuse.  In our case diagonal d satisfies

d² = 6² + 7² = 36 + 49 = 85

d = √85

d ≈ 9.219

9.2

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.