Answer:
   24/325 m ≈ 7.38 cm
Step-by-step explanation:
The equilibrium position of the package is the distance at which the package weight is balanced by the spring force. That distance is ...
   (12 N)/(325 N/m) = 12/325 m
Since the package is placed suddenly on the pan and there are no losses in the system, the position of the package will oscillate about this distance with an amplitude equal to this distance. That is, the maximum compression will be to a distance that is twice this amount, or ...
   24/325 m
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This is the depth at which all of the potential energy of the package due to its height is transformed into the potential energy of the spring due to its compression.
 
        
             
        
        
        
Answer:  The answer is (2,9) and (6,3).
Step-by-step explanation:  Given that Juan sells 2 sizes of dried wreaths. He takes 3 hours to make each large one and tales 2 hours to make each small one. Also, he has material for maximum 6 large wreaths or maximum 9 small wreaths.
Let, 'x' and 'y' be the number of number of large wreaths and number of small wreaths respectively made by Juan.
So, according to the given information, we have the following relations - 

We tried plotting these inequalities in the graph paper (please see the attached figure), and found that the following two solutions will fit the situation perfectly.
Point A (x = 2, y = 9)   and   point B (x = 6, y = 3).
Thus, the two possible combinations are
(i) 2 large wreaths and 9 small wreaths, and
(ii) 6 large wreaths and 3 small wreaths.
 
        
             
        
        
        
9514 1404 393
Answer:
   (x, y) = (-3, -13) or (-8, -23)
Step-by-step explanation:
The values for y can be equated and the resulting quadratic solved by factoring.
   2x -7 = x^2 +13x +17
   0 = x^2 +11x +24 . . . . . . subtract 2x-7
   0 = (x +8)(x +3) . . . . . . . .factor*
The values of x that make these factors zero are x=-8 and x=-3. The corresponding values of y are ...
   y = 2(-8) -7 = -23
   y = 2(-3) -7 = -13
The solutions are ...
   (x, y) = (-8, -23) and (-3, -13)
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* The constants in the binomial factors are factors of 24 that total 11. You know that ...
   24 = 1×24 = 2×12 = 3×8 = 4×6
The sums of these factors are 25, 14, 11, 10. The factors 3 and 8 are the constants in the binomial factors of the quadratic.
"24" is the constant in the quadratic. "11" is the coefficient of the x term.
 
        
             
        
        
        
Answer:
Jane is 9 1/4 years old
Step-by-step explanation:
Camden is 10 1/2 years old and Jane is (10 2/4 - 1 1/4) which equals 9 1/4 years
 
        
             
        
        
        
Answer: 100/25 and 4/1 and 60/15
Step-by-step explanation: 
20/5=4, 100/25=4, 4/1=4, and 60/15=4