Answer:
The equation is
![f(x) = [\frac{x}{13}]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5B%5Cfrac%7Bx%7D%7B13%7D%5D)
Where x is the ribbon's length in ft and with [a] we denote the integer part of a real number a.
Step-by-step explanation:
In order to obtain how many pieces of ribbon Lei can make, we have to divide the length of the Ribbon by the length of each piece, which is 13 ft. This means that if we have x ft of ribbon, then Lei can make a total of x/13 pieces.
However, if the result we obtain is not an integer we need to discard the last part of the ribbon that couldnt form and entire piece of 13 ft, therefore, after we divide x by 13, we also need to take the integer part of that division, that is, the biggest integer that is not bigger than x/13. With this information in mind, we obtain that the amount of pieces Lei can make is given by the following formula:
Where [ a ] denotes the integer part of a real number a.
4/12= 2/6=1/3 So the answer is 1/3
6
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Answer:
The three numbers are 7 8 and 9
Step-by-step explanation:
Givens
- Let the first number be n - 1
- Let the second number be n
- Let the third number = n + 1
Equation
(n - 1)(n)(n + 1) - (n-1 + n + n+1) = 480
Solution
Multiply (n - 1) and (n + 1) = (n - 1)*(n + 1) = n^2 - 1
Multiply the second integer by the result of the first and third: n (n^2 - 1)
Add the three integers together: (x - 1) + (n - 1) + n = 3n Combine these 2 steps
n(n^2 - 1) - 3n = 480 Remove the brackets
n^3 - n - 3n = 480
n^3 - 4n = 480
n^3 - 4n - 480 = 0
Graph
The graph shows that the intercept point is n =8. This is the only way I can see to solve this cubic. There are no other real roots.
Answer
n - 1 = 7
n = 8
n + 1 = 9
Check
Product 7*8*9 = 504
Sum = 7 + 8 + 9 = 24
504 - 24 = 480 Which checks.
Answer:
(6x-5y)(20y-23x)
Step-by-step explanation:
x(6x - 5y) - 4(6x - 5y)^2
= (6x-5y)(x-4(6x-5y))
= (6x-5y)(x-24x+20y)
= (6x-5y)(20y-23x)
