What is the absolute value of the complex number -4 - sqrt 2i ?

Step-by-step explanation:

Square (-4), obtaining 16.  Next, square [-sqrt(2)]i, obtaining 2.

Applying the Pythagorean Theorem, we get:

16 + 2 = 18, so that the absolute value of -4 - sqrt(2)i is sqrt 18, or 3sqrt(2).

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.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9