A rectangular window is 4x inches wide and 8x inches long. What is an expression for the distance from one corner of the window to the opposite corner? Give your answer as a simplified radical.

Step-by-step explanation:

Pythagorean theorem

a² + b² = c²          a = 4x     b=8x

c = √(a² + b²)

c =√((4x)² + (8x)²)

  = √(16x² + 64x²)

  = √80x²

  = √(16×5)x²

  = 4x√5

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.