Simplify. 1/4+4(1/2−3/4)^2
1 answer:
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To find x, first we'll split the triangle in two right triangles.
The first triangle will be the one with sides (8,x+4,y) and the second triangle will be the one with sides (12,2x+1,y).
As you can see, these two triangles share the side 'y'.
To solve we'll do the following; first solve for 'y' by applying the Pythagorean theorem in the second triangle, and finally solve for 'x' applying Pythagorean theorem in the first triangle.
From the second triangle (12,2x+1,y) we solve for 'y' by writing:
Now that we know 'y^2' we apply Pythagorean Theorem in the first triangle (8,x+4,y)
Now you solve the quadratic equation, you'll get a positive and negative value; as this are lengths, you take the positive and get:
The first triangle will be the one with sides (8,x+4,y) and the second triangle will be the one with sides (12,2x+1,y).
As you can see, these two triangles share the side 'y'.
To solve we'll do the following; first solve for 'y' by applying the Pythagorean theorem in the second triangle, and finally solve for 'x' applying Pythagorean theorem in the first triangle.
From the second triangle (12,2x+1,y) we solve for 'y' by writing:
Now that we know 'y^2' we apply Pythagorean Theorem in the first triangle (8,x+4,y)
Now you solve the quadratic equation, you'll get a positive and negative value; as this are lengths, you take the positive and get: