What is the size of the TV, to the nearest inch, as measured along its diagonal?

The size of the TV along it's diagonal is 47 inches

Step-by-step explanation: The rectangle shaped Television has it's dimensions given as,

Length = 41 in

Width = 23 in

The length of the diagonal is also the Hypotenuse, since the the diagonal line divides the rectangle into two right angled triangles. With that bit of information, we can calculate the hypotenuse by using the Pythagoras theorem which states that

AC² = AB² + BC²

Where AC is the hypotenuse (or diagonal) and AB and BC are the other two sides.

Therefore, AC² = 23² + 41²

AC² = 529 + 1681

AC² = 2210

Add the square root sign to both sides of the equation

AC = √2210

AC = 47.0106

(The approximate value is 47)

Therefore the size of the TV to the nearest inch equals 47 inches

answer: $201

step-by-step explanation: to get the answer, you first get 3 nieces that he sold and multiply it by 67 and get $201, so he earned $201 selling his nieces.

{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