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3 years ago

13

Every hour the number of users of a new smartphone app increases by 18 percent. At 1:00 p.m., there were 12,322 users. What expo

nential equation shows the number of users' x hours after 1:00 p.m.?

1 answer:

GaryK [48]3 years ago

5 0

Answer:

B

Step-by-step explanation:

Y is the starting point so it would be y=12322 and it becomes 1.18 because you add 100 to 18

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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

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4 0

3 years ago

Combine like terms to create an equivalent expression.<br><br> 17−3(37n−27)71 −3( 73 n− 72)

patriot [66]

Answer:

$\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7})=1-\frac{9}{7}n$

Step-by-step explanation:

Given : Expression $\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7})$

To find : Combine like terms to create an equivalent expression ?

Solution :

Step 1 - Write the expression,

$\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7})$

Step 2 - Apply distributive property, $a(b+c)=ab+ac$

$=\frac{1}{7}-3\times \frac{3}{7}n+3\times \frac{2}{7}$

$=\frac{1}{7}-\frac{9}{7}n+\frac{6}{7}$

Step 3 - Combine like terms,

$=\frac{1}{7}+\frac{6}{7}-\frac{9}{7}n$

$=\frac{1+6}{7}-\frac{9}{7}n$

$=\frac{7}{7}-\frac{9}{7}n$

$=1-\frac{9}{7}n$

Therefore, $\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7})=1-\frac{9}{7}n$

4 0

3 years ago

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