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A square is inscribed in a right triangle, as shown below. The legs of the triangle are 2 and 3. Find the side length of the square.

[asy]
unitsize(1.5 cm);

pair A, B, C, D, E, F, G;

A = (0,0);
C = (5,0);
B = (3^2/5,3*4/5);
D = extension(B, A + (0,-5), A, C);
G = extension(B, C + (0,-5), A, C);
E = extension(D, D + (0,1), A, B);
F = extension(G, G + (0,1), B, C);

draw(A--B--C--cycle);
draw(D--E--F--G);
[/asy]

 May 14, 2020
 #1
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Can you help me with this?

 

P and q are complex numbers such that |p| = 2/5x + 2, |q| = −3/4x − 1 , and |p+q| = 2x + 4 .

On what interval must x fall?

a) [-2, -4/3]

b) (-∞, -4/3]

c) [-2, ∞)

d) [-4/3, -60/47]

 

 

I got the first one, but I don't know if it's right. If someone could help, that would be greatly appreciated!

 May 14, 2020

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