Answer: ∠ABE=20°
Step-by-step explanation:
∵ AB=BC
∴ ΔABC is a isosceles triangle
∵ ∠A=30
∴ ∠C=30
∵ The interior angle sum of triangle is 180°
∵ ∠A+∠B+∠C=180
     30+∠B+30=180
            ∠B+60=180
                   ∠B=120 (∠ABC)
∵ ∠EBD+∠ABE+∠ABC=linear pair
∴∠EBD+∠ABE+∠ABC=180°
                   4x+2x+120=180
                         6x+120=180
                                 6x=60
                                   x=10
∠ABE=2x=2(10)=20°
Hope this helps!! :)
Please let me know if you have any question
 
 
        
             
        
        
        
Answer:

Step-by-step explanation:
The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:


The numerical value of the slope is:

The component of the y-axis is:

Now, the tangent line has the following mathematical model:

The value of the intercept is found by isolating it within the equation and replacing all known variables:


Thus, the tangent line is:

The vertical distance between a point of the tangent line and the origin is given by the intercept.

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:




The area of the triangle is computed by this formula:



 
        
             
        
        
        
Cross multiply to find your answer
x/250 = 20/100
250 X 20= 5000
5000=100x 
x = 50
250 - 50 = 200