There is a competition at the local movie theater for free movie tickets. you must guess all four employees’

ages given a few clues. the first clue is that when added together, their ages total 106 years. kirk is twice

ten years less than the manager’s age, brian is 12 years younger than twice the manager’s age, and matt is 6

years older than half the manager’s age. what are all four of their ages? it may to set up four let

statements, one for each employee (including the manager).

Kirk's age is 28 years.

The manager's age is 24 years.

Brian's age is 36 years.

Matt's age is 18 years.

Step-by-step explanation:

Let Kirk's age be = a

Let manager's age be = b

Let Brian's age be = c

Let Matt's age be = d

The first clue is that when added together, their ages total 106 years.

       .......(1)

Kirk is twice ten years less than the manager’s age.

   ..... (2)

Brian is 12 years younger than twice the manager’s age.

    ......(3)

Matt is 6 years older than half the manager’s age.

      ......(4)

=>

=>

=>

=>

=>

=>

b = 24

d = 18

a = 28

c = 36

Lets check:

=>   (checked)

Kirk's age is 28 years.

The manager's age is 24 years.

Brian's age is 36 years.

Matt's age is 18 years.

A figure is located at A(0, 0), B(−3, −4), and C(−3, 0) on a coordinate plane.

This form a right triangle ( because vector AC(3, 0) is perpendicular with vector BC(0, 4) at C. You can check it by take multiplication of vector AC and BC, you would get: vector AC x vector BC = 3 x 0 + 0 x 4 = 0)

And as you know a cone is created by rotating a right triangle around its side (not hypotenuse). Here, the right triangle ABC has AB as hypotenuse and AB is not lying on rotating axis (x axis).

=> The 3D-shape, which is created by rotating ABC around x-axis would be a cone.

Hope this helps!

:)