Part A: Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)
1 answer:
Answer:
x = 6
Step-by-step explanation:
Step 1 - Expand brackets via distributive property:
Step 2 - Combine like terms:
Step 3 - Use the addition property of equality to isolate the 9x:
Step 4 - Use the subtraction property of equality to move the 5x over and isolate the 24:
Step 5 - Use the division property of equality to simplify:
Hope this helps!
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Answer:
Step-by-step explanation:
<u>Regular Hexagon</u>
For the explanation of the answer, please refer to the image below. Let's analyze the triangle shown inside of the hexagon. It's a right triangle with sides x,y, and z.
We know that x is half the length of the side length of the hexagon. Thus
Note that this triangle repeats itself 12 times into the shape of the hexagon. The internal angle of the triangle is one-twelfth of the complete rotation angle, i.e.
Now we have , the height of the triangle y is easily found by
Solving for y
The value of z can be found by using
The area of the triangle is
The area of the hexagon is 12 times the area of the triangle, thus
