Answer:
1. 50 miles
2. 100 miles
3. 300 miles
4. 400 miles
5. 35th day
Step-by-step explanation:
1080 clothespins makes 90 chairs and we need to find out how many clothespins it takes to make 1 chair.
We can set up a proportion of the number of chairs to the number of clothespins because of the proportional relationship.
x is the number of clothes pins for 1 chair
![\frac{90 chairs}{1080 clothespins} =\frac{1 chair}{x clothespins}](https://tex.z-dn.net/?f=%5Cfrac%7B90%20chairs%7D%7B1080%20clothespins%7D%20%3D%5Cfrac%7B1%20chair%7D%7Bx%20clothespins%7D)
Cross multiply to get
90*x= 1080*1
Divide both sides by 90 to isolate x
x = 12 clothespins
It takes 12 clothespins to make 1 chair.
Answer:
36
Step-by-step explanation:
N = 6
S = 0 n = 1
2(1) - 1 = 1
S = 0 + 1 = 1
n = n + 1
n = 1 + 1
n = 2
S = 1 n = 2
2(2) - 1 = 3
S = 1 + 3 = 4
n = n + 1
n = 2 + 1
n = 3
S = 4 n = 3
2(3) - 1 = 5
S = 4 + 5 = 9
n = n + 1
n = 3 + 1
n = 4
S = 9 n = 4
2(4) - 1 = 7
S = 9 + 7 = 16
n = n + 1
n = 4 + 1
n = 5
S = 16 n = 5
2(5) - 1 = 9
S = 16 + 9 = 25
n = n + 1
n = 5 + 1
n = 6
S = 25 n = 6
2(6) - 1 = 11
S = 25 + 11 = 36
n = n + 1
n = 6 + 1
n = 7 > N
Stop
Answer:
![x^2 + 12x +36 = (x+6)^2](https://tex.z-dn.net/?f=x%5E2%20%2B%2012x%20%2B36%20%3D%20%28x%2B6%29%5E2)
Step-by-step explanation:
![x^{2} + 12x +36\\\\\\Step 1: Find\ factors \ of\ 36\ that \ add \ to \ +12.\\(1, 36)\ , \ ( 2, 18), \ (3, 12), \ (4, 9), \ (6, 6)\\\\Step2. \ From \ the \ pairs \ above \ (6 , 6) \ adds \ to \ +12.\\\\So \ the \ equation \ can\ be \ written \ as \\x^{2} + 6x +6x +36 = (x^{2} + 6x) + (6x + 36)](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%2012x%20%2B36%5C%5C%5C%5C%5C%5CStep%201%3A%20Find%5C%20factors%20%5C%20of%5C%2036%5C%20that%20%5C%20add%20%5C%20to%20%5C%20%2B12.%5C%5C%281%2C%2036%29%5C%20%2C%20%5C%20%28%202%2C%2018%29%2C%20%5C%20%283%2C%2012%29%2C%20%5C%20%284%2C%209%29%2C%20%5C%20%286%2C%206%29%5C%5C%5C%5CStep2.%20%5C%20From%20%5C%20the%20%5C%20pairs%20%5C%20%20above%20%5C%20%286%20%2C%206%29%20%5C%20adds%20%5C%20to%20%5C%20%2B12.%5C%5C%5C%5CSo%20%5C%20the%20%5C%20equation%20%5C%20can%5C%20be%20%5C%20written%20%5C%20as%20%5C%5Cx%5E%7B2%7D%20%2B%206x%20%2B6x%20%2B36%20%3D%20%28x%5E%7B2%7D%20%2B%206x%29%20%2B%20%286x%20%2B%2036%29)
![= x(x + 6) + 6(x+6)\\\\=(x+6)(x+6)\\\\=(x+6)^2](https://tex.z-dn.net/?f=%3D%20x%28x%20%2B%206%29%20%2B%206%28x%2B6%29%5C%5C%5C%5C%3D%28x%2B6%29%28x%2B6%29%5C%5C%5C%5C%3D%28x%2B6%29%5E2)