What are three problems the have the sum of 4
1 answer:
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Well, you could assign a letter to each piece of luggage like so...
A, B, C, D, E, F, G
What you could then do is set it against a table (a configuration table to be precise) with the same letters, and repeat the process again. If the order of these pieces of luggage also has to be taken into account, you'll end up with more configurations.
My answer and workings are below...
35 arrangements without order taken into consideration, because there are 35 ways in which to select 3 objects from the 7 objects.
210 arrangements (35 x 6) when order is taken into consideration.
*There are 6 ways to configure 3 letters.
Alternative way to solve the problem...
Produce Pascal's triangle. If you want to know how many ways in which you can choose 3 objects from 7, select (7 3) in Pascal's triangle which is equal to 35. Now, there are 6 ways in which to configure 3 objects if you are concerned about order.
A, B, C, D, E, F, G
What you could then do is set it against a table (a configuration table to be precise) with the same letters, and repeat the process again. If the order of these pieces of luggage also has to be taken into account, you'll end up with more configurations.
My answer and workings are below...
35 arrangements without order taken into consideration, because there are 35 ways in which to select 3 objects from the 7 objects.
210 arrangements (35 x 6) when order is taken into consideration.
*There are 6 ways to configure 3 letters.
Alternative way to solve the problem...
Produce Pascal's triangle. If you want to know how many ways in which you can choose 3 objects from 7, select (7 3) in Pascal's triangle which is equal to 35. Now, there are 6 ways in which to configure 3 objects if you are concerned about order.
1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.
2)The solution for b² - 4b + 4 = 0 is x=2.
<u>Step-by-step explanation</u>:
The general form of quadratic equation is ax²+bx+c = 0
where
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
<u>To find the roots :</u>
- Sum of the roots = b
- Product of the roots = c
1) The given quadratic equation is m² - 5m - 14 = 0.
From the above equation, it can be determined that b = -5 and c = -14
The roots are -7 and 2.
- Sum of the roots = -7+2 = -5
- Product of the roots = -7
2 = -14
The solution is given by (x-7) (x+2) = 0.
Therefore, the solutions are x=7 and x= -2.
2) The given quadratic equation is b² - 4b + 4 = 0.
From the above equation, it can be determined that b = -4 and c = 4
The roots are -2 and -2.
- Sum of the roots = -2-2 = -4
- Product of the roots = -2
The solution is given by (x-2) (x-2) = 0.
Therefore, the solution is x=2.