A, b,c, d,x, y,z, w are digits between 1-8. Find abcd and xyzw, both 4-digit numbers without any repeating numbers, such that

4*abcd = xyzw

git no. and how to prove it?

Lets say the number is written as ABCD (1000a+100b+10c+d).

Multiplying it by 4, gives you DCBA (1000d+100c+10b+a)

By divisibility of 4, BA is a two-digit number divisible by 4.

Now, the largest possible value of ABCD is 2499, because anything more will result in a five - digit number when multiplied by 4.

Out of the two possibilites 1 and 2 for A, [3] follows that A is even, so 2.

From [5], D is either 8 or 9. However, since D times 4 would end in 2, D is 8.

Using [2], 4000a+400b+40c+4d = 1000d+100c+10b+a, which would simplify to 2c-13b = 1 after substituting A = 2 and D = 8.

The only possible value of (b,c) where they would both be single - digit integers is (1,7). Also to note from [3], B is odd. And from [4], B is either 1 or 3.

The answer you're looking for is 2178, multiplied by 4 gives 8712.

Step-by-step explanation:

8

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.