At the electronics store, television screens are sized by the lengths of their diagonals. the television that mrs. mallory wants to buy has a 25 inch diagonal. the width of the screen is 15 inches. what is the height of the screen?
group of answer choices

10 inches

15 inches

20 inches

25 inches

20 inches

Step-by-step explanation:

From the question, diagonal of the television screen is given to be 25 inch and the  width of the television set is given to be 15 inches and we are asked to find the height of the screen.

We can solve this question using the Pythagoras theorem.

The Pythagoras theorem states that in a right-angle triangle;

opposite²  +  adjacent²  = hypotenuse²

From the question, the width is given to be 15 inches, the with is  our adjacent. Also the diagonal is given to be 25 inches, the diagonal is  our hypotenuse. And we were ask to find the height, the height is our opposite.

so;

opposite = ?  

adjacent = 15

hypotenuse = 25

Let opposite = x

we can now substitute into our theorem;

opposite²  +  adjacent²  = hypotenuse²

x²     +    15²  = 25²

x²   =   25²  -   15²

x²    =  625  -  225

x²   = 400

x    =  √400

x     =  20

opposite  =  20 inches

Since opposite is the height of the screen, then the height of the screen is 20 inches.

Therefore the height of the screen is 20 inches.  

43

step-by-step explanation:

{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