Kate just bought a tv that measures 42 inches diagonally, and is 18 inches tall. She wants to place the tv into a 40 inch wide cabinet. Will the tv fit and if so, how much room will be left (width) in the cabinet after the tv is placed?

9514 1404 393

  yes, about 2.05 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the width of the TV.

  w^2 +h^2 = d^2

  w = √(d^2 -h^2)

  w = √(42^2 -18^2) = √1440 = 12√10

  w ≈ 37.95 . . . inches

This dimension is less than 40 inches by a margin of ...

  40 -37.95 = 2.05 . . . inches

The TV will fit, with 2.05 inches of space remaining.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.