The length of a rectangle is four times it's width and has an area of 1024cm squared. work out the width of the rectangle

Width = 16 cm

Step-by-step explanation:

Given that

Area of rectangle = 1024 cm²

Length of rectangle = four times the width

Let the width of rectangle be  W cm

Now we know that Area of rectangle = Length × Width

Or,                          Area of rectangle = (4 × width ) × width

                                1024 cm² = 4 × W²

                                = W²

                                256 = W²

∴                               W =

Or,                            W = 16 cm

Hence the width of given rectangle is 16 cm        Answer.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1