Let T: set of real numbers R squaredright arrowset of real numbers R squared be a linear transformation such that Upper T (x 1 comma x 2 )equals(x 1 plus x 2 comma 2 x 1 plus 4 x 2 ). Find x such that T(x)equals(3 comma negative 2 ).

The pair (7,-4) maps to the pair (3,-2) under T.

Step-by-step explanation:

We are given that . The questions asks for the pair (x,y) such that T(x,y) = (3,-2). So, knowing the behaviour of the transformation T, we know that

T(x,y) = (x+y, 2x+4y) = (3,-2). So, we have the following equations

From first equation, we have that x = 3-y. REplacing this result in the second equation, we have that

Which implies that y = -4. Then, x=3-(-4) = 7.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.