# Match the trigonometric ratios with their values based on the triangle shown in the diagram.

sin D = 4/5 sin C = 3/5 sin D x cos D = 12/25 cos C x tan D = 16/15 Step-by-step explanation: sin x = opposite/hypotenuse cos x = adjacent/hypotenuse tan x = opposite/adjacent then sin D = 4/5 sin C = 3/5 sin D x cos D = 4/5 x 3/5 = 12/25 cos C x tan D = 4/5 * 4/3 = 16/15

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, 07×12!

Also Read :   Which is true about the polynomial y2 – 3y + 12?

Step-by-step explanation:

Sin D = 4/5 Sin C = 3/5 Sin D x Cos D = 12/25 Tan C x Tan D = 1 Cos C x Tan D = 16/15