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.

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)