Answer:
The length of river frontage for each lot are 96.55 ft. 98.85 ft, 101.15 ft and 103.45 ft.
Step-by-step explanation:
See the attached diagram.
The river frontage of 400 ft will be divided into 84 : 86 : 88 : 90 for each lot as AP, BQ, CR, DS and ET all are parallel.
Therefore, PQ : QR : RS : ST = 84 : 86 : 88 : 90 = 42 : 43 : 44 : 45
Let, PQ = 42x, QR = 43x, RS = 44x and ST = 45x
So, (42x + 43x + 44x + 45x) = 400
⇒ 175x = 400
⇒ x = 2.2988.
So, PQ = 42x = 96.55 ft.
QR = 43x = 98.85 ft.
RS = 44x = 101.15 ft and
ST = 45x = 103.45 ft
(Answer)
There are 16 on each layer and 96 in total
Answer:
2.2
Step-by-step explanation:
47/21 = 2.238095
round to tenth = 2.2
<h3>
Answers:</h3>
![f(g(x)) = \sqrt{x^2+5}+5\\\\g(f(x)) = x+30+10\sqrt{x-1}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Csqrt%7Bx%5E2%2B5%7D%2B5%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20x%2B30%2B10%5Csqrt%7Bx-1%7D)
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Work Shown:
Part 1
![f(x) = \sqrt{x-1}+5\\\\f(g(x)) = \sqrt{g(x)-1}+5\\\\f(g(x)) = \sqrt{x^2+6-1}+5\\\\f(g(x)) = \sqrt{x^2+5}+5\\\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7Bx-1%7D%2B5%5C%5C%5C%5Cf%28g%28x%29%29%20%3D%20%5Csqrt%7Bg%28x%29-1%7D%2B5%5C%5C%5C%5Cf%28g%28x%29%29%20%3D%20%5Csqrt%7Bx%5E2%2B6-1%7D%2B5%5C%5C%5C%5Cf%28g%28x%29%29%20%3D%20%5Csqrt%7Bx%5E2%2B5%7D%2B5%5C%5C%5C%5C)
Notice how I replaced every x with g(x) in step 2. Then I plugged in g(x) = x^2+6 and simplified.
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Part 2
![g(x) = x^2+6\\\\g(f(x)) = \left(f(x)\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}+5\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}\right)^2+2*5*\sqrt{x-1}+\left(5\right)^2+6\\\\g(f(x)) = x-1+10\sqrt{x-1}+25+6\\\\g(f(x)) = x+30+10\sqrt{x-1}\\\\](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%2B6%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20%5Cleft%28f%28x%29%5Cright%29%5E2%2B6%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20%5Cleft%28%5Csqrt%7Bx-1%7D%2B5%5Cright%29%5E2%2B6%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20%5Cleft%28%5Csqrt%7Bx-1%7D%5Cright%29%5E2%2B2%2A5%2A%5Csqrt%7Bx-1%7D%2B%5Cleft%285%5Cright%29%5E2%2B6%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20x-1%2B10%5Csqrt%7Bx-1%7D%2B25%2B6%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20x%2B30%2B10%5Csqrt%7Bx-1%7D%5C%5C%5C%5C)
In step 4, I used the rule (a+b)^2 = a^2+2ab+b^2
In this case, a = sqrt(x-1) and b = 5.
You could also use the box method as a visual way to expand out ![\left(\sqrt{x-1}+5\right)^2](https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%7Bx-1%7D%2B5%5Cright%29%5E2)
8X3 equals 24
3x 8 equals 24
Eight rows of 3 =24
3 rows of 8 = 24