The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
2 answers:
We know that for each triangle made up by dashed line segment forms 30° angles, so, for example, ∠GOH is 30° and then ∠HOI is 30°
Rotating the shape 240° around the centre is the same as counting in 30°
The triangle GOH will first fit the triangle HOI then triangle IOJ and so on until it has completed 8 times 30° turn. Its final position is shown in the diagram below
Rotating the shape 240° around the centre is the same as counting in 30°
The triangle GOH will first fit the triangle HOI then triangle IOJ and so on until it has completed 8 times 30° turn. Its final position is shown in the diagram below
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Answer:
Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old.
Step-by-step explanation:
Let be Kirk's age.
Let be Brian's age.
Let be Matt's age.
Let be the boss/manager's age.
From the information given, we can set up 4 equations:
Rewrite the first equation, substituting ,
, and
in terms of
to get:
Open up the parentheses using the distributive property (which is ) and combine like terms to get:
Add 26 to both sides to reach:
Thus, . Substitute
for
in the second, third, and fourth original equations to find that
,
, and
. Therefore, Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. To check, you can add up all of the ages to get 106.
Hope this helps :)