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Slightly different approach using law of sines

x/sin30 = 50/sin10   yields x = 26.6044 (distance from 40 degree observer to island)

then 

26.044/sin 90 = x /sin40    yields   x = 17.1 m shortest distance to the beach....

SO he is paying (100%-7%) = 93% of the initial price in 12 payments

93% x L6500  /  12 =    .93 * 6500 / 12 = 6045/12 =  L 503.75/mo

ax + b + ax + ab = b   subtract b from both sides

2 ax + ab  = 0

2 a x   = -ab

x = -ab/(2a) = - 1/2  b   

1. This is an isosceles triangle, so 2x = 50º.  The sum of all the angles in a triangle must be 180º. These two bits of information are enough to allow you to calculate the value of y.

2. This is an isosceles triangle, with AB = AC. This allows you to find x and hence the size of BC.

3. Same as 2.

4.This is an equilateral triangle, so all the sides are the same length. Equate any two to find the value of x.

5. This is an equilateral triangle, so all the angles are equal to 60º.

1>   90   180   270 degrees

2>    (arc degrees)/360  x  pi  x d

3>  Cos is negative in Q2    Sin is positive in Q2

If the smallest angle is x, then we have x + 2x + 3x = 180º, So x = 30º.

This means the triangle is a 30/60/90 degree right angled triangle. The sides of this are in the ratio 1:root(3):2.  That is, the hypotenuse (the longest side) is twice as long as the shortest side.

All of the angles of ANY triangle add to 180 (degrees)

so   x   + (3x+25)  +  (x-5)  = 180

     5x + 20 = 180

     5x = 160

       x = 32

Angle G is   3x + 25 =  3 (32) + 25 = 121 degrees

2>  Same thing here    30 + 70 + x = 180     Think you can take it frome here? 

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thanks

Thanks! could you help me with the others i posted?

yes, i'm not sure

Here is a calculator for finding values of arithmetic increasing annuity...

https://www.mathcelebrity.com/arithannimmpv.php?fpmt=1000000&ap=1000000&n=241&i=5&check1=1&pl=Calculate

See bottom line,,,,,   53 trillion 681 billion 912 million 20 thousand  3hundred twenty four.    (using 241 payments)

it's very grey

Correct!

Express the number of centimeters in the length of  ???  in simplest radical form.

What is  ???       You accidentally omitted it! ......and did you mean to say m of A is 45 also?  Does not look like it from diagram....

1/6 + 1/4 x  = fraction of cake eaten     where x = # of friends each consuming 1/4 cake

Re-arrange:

x^2-2x-8 >0   Factor

(x-4)(x+2) >0

For this to be true, BOTH o these terms must be > 0   or they must BOTH be less than 0

    x-4>0

    x > 4

and   x+2 >0

         x > -2             so the only answer interval that will work is   x >4  for both >0

x-4 <0     x < 4

x+2<0    x<-2           so the only answer here that will work is x <-2

   combined

                          -2> x > 4  

Thanks very much Heureka :))

Whoops started before you sent...

Thanks anyway.

Nevermind I found out how to do it.

18 = 30

 x    100

cross multiply

30x=1,800

x=60