We have seen in the Triangle Sum<span> Conjecture that the</span>sum<span> of the </span>angles<span> in any triangle is 180 degrees. The</span>Quadrilateral Sum<span> Conjecture tells us the </span>sum<span> of the</span>angles<span> in any convex </span>quadrilateral<span> is 360 degrees. Remember that a polygon is convex if each of its</span>interior angles<span> is less that 180 degree.</span>
9514 1404 393
Answer:
305,645 base 10
1124755 base 8
Step-by-step explanation:
In expanded form, the number is ...
4×16^4 +10×16^3 +9×16^2 +14×16^1 +13
= (((4×16 +10)×16 +9)×16 +14)×16 +13 = ((74×16 +9)×16 +14)×16 +13
= (1193×16 +14)×16 +13 = 19102×16 +13 = 305,645 base 10
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If you want to convert this to base 8, that is easily done by writing the binary equivalents of the hex digits, then regrouping them by 3s.
4A9ED₁₆ = 0100 1010 1001 1110 1101₂ = 01 001 010 100 111 101 101₂
= 1124755₈
Answer:
about 252.78 ft
Step-by-step explanation:
Define angle QMP as α. Then ...
MN = 60·sin(α)
NP = 60·cos(α)
area MPN = (1/2)(MN)(NP) = 1800sin(α)cos(α)
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PQ = 60tan(α)
area MPQ = (1/2)(MP)(PQ) = 1800tan(α)
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The ratio of areas is 2.5, so we have ...
1800tan(α) = 2.5·1800sin(α)cos(α)
1 = 2.5cos(α)² . . . . . . divide by 1800tan(α)
cos(α) = √0.4 . . . . . . solve for cos(α)
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Then the perimeter is ...
Perimeter = MN +NP +PQ +QM = 60sin(α) +60cos(α) +60tan(α) +60/cos(α)
= 60(sin(α) +cos(α) +tan(α) +sec(α))
= 60(0.774597 +0.632456 +1.224745 +1.581139)
= 60(4.212936) = 252.776
The perimeter of the trapezoid is about 252.776 feet.
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With perhaps a little more trouble, you can find the exact value to be ...
perimeter = (6√10)(7+√6+√15)
Answer:
It decreases
Step-by-step explanation:
Given the expression: 70-3g
- When g=1, 70-3g=70-3(1)=70-3=67
- When g=2, 70-3g=70-3(2)=70-6=64
- When g=3, 70-3g=70-3(3)=70-9=61
- When g=4, 70-3g=70-3(4)=70-12=58
- When g=5, 70-3g=70-3(5)=70-3=55
From the above, notice that as g increases, the value of the expression decreases.
Um, I don't know if I actually answered the question, but I think that the second one is cheaper to rent.
