<span>The long piece should measure 7.5 feet or 7'6" (7 foot 6 inches).
If x is the length of the short piece then the length of the long piece must be 3x. The total length of the uncut beam is 10 foot.
This can be represented by :
x + 3x = 10
4x = 10
x = 2.5
As x = 2.5 = length of short piece, then the long piece measures 3x = 3(2.5) = 7.5 feet.
There are 12 inches in a foot so 7.5 feet = 7'6"</span>
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Answer:
x = 65°
Step-by-step explanation:
Find the measure of the other two angles using the Supplementary Angles theorem:
180 - 105 = 75°
180 - 140 = 40°
The sum of all of the angles in a triangle is equal to 180°, therefore:
180 = 75 + 40 + x
180 = 115 + x
65 = x
x = 65°
Answer: x = 21; y = 29.5
because 2y° and 59° are 2 opposing angles ⇒ 2y° = 59° ⇔ y = 29.5°
we also have: (3x - 4)° = 59° ( because of 2 parallel lines)
⇔ 3x = 59 + 4 = 63
⇔ x = 63/3 = 21
Step-by-step explanation:
<span>First, we write an equation to represent that the fencing lengths add up to 568 feet. we call the side of the fence that has three segments of its length x and the side with only two segments y. We write 3x + 2y = 568. We also know that the area of the rectangle is equal to xy, so area = xy. We put y in terms of x using our first equation and find that y = (568 - 3x)/2. We plug this into our area equation and find that area = (568x - 3x^2)/2. To find the maximum we set the derivative equal to 0 and end up with 0 = 284 - 3x. We solve for x and get 94 and 2/3. We then put that into our first equation to find y = 142. So the dimensions that maximize the area are 94 2/3 x 142.</span>
Answer:
1. 32
2. 4.7
3. 3
Step-by-step explanation:
4*8=32
6.5-1.8= 4.7
18/6=3 or 18 divided by 6 = 3
