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AnnZ [28]
3 years ago
15

Which equation has only one solution? A lx-5l=1 B l-6-2xl=8 C l5x+10l=10 D l-6x+3l=0​

Mathematics
1 answer:
dem82 [27]3 years ago
5 0

Answer:

D:  x = 1/2

Step-by-step explanation:

D is correct.  The solution here is the solution of -6x + 3 = 0, which is x = 1/2.

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3 years ago
Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.
-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

4^n+17 is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so 4^k+17 is divisible by 3

and we check what happens for k+1

4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17

3\cdot 4^k is divisible by 3 and

4^k+17 is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that 4^n+17 is divisible by 3 for all positive integers n.

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3 years ago
Simply the expression below, assume the denominator does not equal zero
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Step-by-step explanation:

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