Pls answer this question with steps (proof).

Step-by-step explanation:

Since triangle BCE is a right angle triangle, we would determine angle BEC by applying the tangent trigonometric ratio. Therefore,

Tan BEC = 6/3 = 2

Angle BEC = Tan^-1(2)

Angle BEC = 63.4°

The sum of the angles on a straight line is 180°. This means that

Angle AED + angle DEC + angle BEC = 180

Angle AED = 180 - (45 + 63.4) = 71.6°

Angle ADE = angle AED = 71.6°

Angle CDE + angle ADE = 180(sum of angles on a straight line)

Angle CDE = 180 - 71.6 = 108.4°

To get line EC, we would apply Pythagoras theorem. Therefore

EC² = 3² + 6² = 45

EC = √45 = 6.71 cm

The sum of the angles in a triangle is 180°

Therefore,

Angle ECD = 180 - (45 + 108.4) = 26.6°

By applying sine rule,

6.71/sin108.4 = ED/sin26.6 = DC/Sin45

6.71/sin108.4 = ED/sin26.6

Cross multiplying, it becomes

6.71sin26.6 = EDsin108.4

ED = 6.71sin26.6/sin108.4

ED = 3.00608/0.949 = 3.18cm

The area of a triangle is

Area = 1/2abSinC

Therefore, area of triangle EDC = 1/2 ×

ED × EC × SinDEC

Area = 1/2 × 6.71 × 3.18 × sin45

Area = 1/2 × 6.71 × 3.18 × 0.707

Area = 7.54 cm²

use substitution to solve each system of equations. y = x + 5 3x + y = 25 62/87,21 y = x + 5 3x + y = 25 substitute x + 5 for y in the second equation. substitute the solution for x into either equation to find y. the solution is (5, 10)

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step-by-step explanation: