1. area of a pentagon when 1 side is x is
![\frac{x^2}{4}\sqrt{5(5+2\sqrt{5})}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B4%7D%5Csqrt%7B5%285%2B2%5Csqrt%7B5%7D%29%7D)
so if perimiter is 100 then one side is 100/5 or 20
area will be
![\frac{20^2}{4}\sqrt{5(5+2\sqrt{5})}](https://tex.z-dn.net/?f=%5Cfrac%7B20%5E2%7D%7B4%7D%5Csqrt%7B5%285%2B2%5Csqrt%7B5%7D%29%7D)
≈<span>688.2 square yards
2. area of a hexagon when 1 side is length x is
![\frac{3x^2\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%5E2%5Csqrt%7B3%7D%7D%7B2%7D)
so if permiter is 100 then length of one side is 100/6 or about 16.666666666666
the area will be
![\frac{3(16.6666666)^2\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2816.6666666%29%5E2%5Csqrt%7B3%7D%7D%7B2%7D)
≈721.7 square yards
3. area of a regular octagon with side lenghts x is
![2(1+\sqrt{2})x^2](https://tex.z-dn.net/?f=2%281%2B%5Csqrt%7B2%7D%29x%5E2)
so if 8 sides then side length of each is 100/8 or 12.5
area will be
![2(1+\sqrt{2})12.5^2](https://tex.z-dn.net/?f=2%281%2B%5Csqrt%7B2%7D%2912.5%5E2)
≈754.4 square yards
octagon wil have most space
you can tell because the more sides it has, the more it gets to a circle and the more area it encloses with a given perimiter
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21. There are 4 aces and 4 fours. p = 8/52 = 2/13
23. There are 26 black cards and 6 red picture cards. p = 32/52 = 8/13
25. There are 13 clubs and 15 more cards 5 or less. p = 28/52 = 7/13
He is false the equation should be as follows
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
Answer:
Step-by-step explanation:
(0^209 + 1(209)/(209))^0 + 208