Consider the graph of the function , where .
1. For you have that and . This means that point (0,10) is y-intercept of this graph (the same as for function ).
2. For you have that , then and function is increasing. This means that the graph will increase at a slower rate and y-values will continue to increase as x-increases.
3. Not all y-values will be less than their corresponding x-values. For example, when b=1.5 and x=2,
.
As you can see x<y.
Answer: correct options are C and D, incorrect - A, B and E.
Answer:
9:10 P.M.
Step-by-step explanation:
The least common multiple (LCM) of 12 and 10 is 60. The lighthouses will blink together again 60 minutes later, at 9:10 P.M.
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<em>Comment on finding the LCM</em>
The LCM can be found several ways. One way is to factor out the greatest common factor (GCF) and write each number in terms of that:
12 = 2×6
10 = 2×5
Then the LCM is the product of the unique factors:
LCM(12, 10) = 2×6×5 = 60
This is equivalent to dividing the product of the two numbers by their GCF:
LCM(12, 10) = 12×10/GCF(12, 10) = 12×10/2 = 60
One can also write each number in terms of its prime factors, then form the product of each of those to its highest power:
12 = 2²×3
10 = 2×5
LCM(12, 10) = 2²×3×5 = 60