If sin (x) =2/5 and tan(x) > 0, what is sin(2x)?

sin2x =

Step-by-step explanation:

Given sinx = =

Then the third side, the adjacent is found using Pythagoras' identity, that is

adj² + opp² = hyp²

adj² + 2² = 5²

adj² + 4 = 25 ( subtract 4 from both sides )

adj² = 21 ( take the square root of both sides )

adj = , then

cosx = =

Using the double angle identity

sin2x = 2sinxcosx

         = 2 × ×

         =

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315