How to simplify 5 square
2 answers:
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Answer:
60
Step-by-step explanation:
The problem will be solved by looking for the least common multiple (LCM) of the amounts of all four kinds since they want equal amounts of each.
LCM is defined as the smallest positive integer that is divisible by each of the integers (spring flowering bulbs in this case) involved in the operation.
therefore, we are looking for the LCM of the following integers:
Crocus: 6
Tulip: 4
Daffodil: 3
Hyacinth: 5
The first step to calculate the LCM is to factor each integer (to break it up into numbers that can be multiplied together to get the original number) and express them in terms of powers:
Crocus: 6=2*3
Tulip: 4=2*2=
Daffodil 3 = 3 (prime numbers only have themselves as factors)
Hyacinth 5=5 (prime numbers only have themselves as factors)
Now, To calculate the LCM we need to multiply all factors we have found ( in this case 2, 3, and 5) but only once and with the maximum power.
This means the least number of each spring flowering bulbs that they can buy to buy equal amounts is 60.
Now this will cost:
Crocus:
Tulip:
Daffodil:
Hyacinth:
Answer:
(x, y) = (1/2, -1)
Step-by-step explanation:
Subtracting twice the first equation from the second gives ...
(2/x +1/y) -2(1/x -5/y) = (3) -2(7)
11/y = -11 . . . . simplify
y = -1 . . . . . . . multiply by y/-11
Using the second equation, we can find x:
2/x +1/-1 = 3
2/x = 4 . . . . . . . add 1
x = 1/2 . . . . . . . multiply by x/4
The solution is (x, y) = (1/2, -1).
_____
<em>Additional comment</em>
If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.
A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).
