Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the trigonometric ratios with their values based on the triangle shown in the diagram.

 A-2, B-DNE*, C-3, D-DNE, E-4, F-1

The first attachment shows the solutions to A and C.

The second attachment shows the solutions to E and F.

There are no real number solutions to systems B and D.

In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.

A.

 (3-x) +12 = x^2 +x

 15 = x^2 + 2x

 16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root

 ±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A

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B.

 (x -1) -15 = x^2 +4x

 -16 = x^2 +3x

 -13.75 = x^2 +3x +2.25 = (x +1.5)^2

roots are complex: -1.5 ±i√13.75

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C.

 (1-2x) +5 = x^2 -3x

 6 = x^2 -x

 6.25 = x^2 -x + .25 = (x -.5)^2

 ±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C

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remaining problems are done in a similar way.

* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.

Hope this helps!

Brainliest would be great!

With all care,

07x12!