Can someone please help me with math

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.

Thanks

4 0

3 years ago

Which is greater 11/16 or 3/4

Anettt [7]

To compare fractions, we need to have the same denominator
The least common multiple is 16
$\frac{11}{16}$
to change $\frac{3}{4}$ , we should multiply the numerator and denominator by 4
$\frac{3*4}{4*4}$ = $\frac{12}{16}$

$\frac{11}{16}$ < $\frac{12}{16}$

so basically, $\frac{12}{16}$ is greater than $\frac{11}{16}$
which means $\frac{3}{4}$ is greater

$\frac{3}{4}$ is greater

6 0

2 years ago

The data plots represent the hours students study each week in two different classrooms.

Oduvanchick [21]

Tu profesor esta loco cámbiate de clases

5 0

2 years ago

Read 2 more answers

Triangles ABC and XYZ are similar. Find side x.

lesantik [10]

Answer is 6. because 3x6 is 18

6 0

2 years ago

Read 2 more answers

WHOEVER DOES ALL OF THIS GETS BRAINLYEST AND 5 STARS PLS HELP!!!!!!!!!!!!!!

laila [671]

Answer:

1. B

2. D

3. B

4. D

5. C

6. A

7. What is the estimated sum of "?" what are we estimating?

8. C

9. C

10. B

Step-by-step explanation:

1st question

1/4 ≤ 8/19 ≤ 3/4, so round it to 1/2.

1/4 ≤ 6/13 ≤ 3/4, so round it to 1/2.

Estimating:

1/2 + 1/2 = 1

2nd question

220 9/11 divided by 6 19/20 = 2.99542184434

Rounded/estimated = 3

3rd Question

Estimate 8 1/8 (common sense)

8 1/8 = 8.

4th Question

Assuming cups = 2.

2x24 = 48.

5th Question

3

6th Question

Add and estimate

7th question

What is the estimated sum of "?" what are we estimating?

8th question

6/7 > 3/4, so round it to 1.

1/4 ≤ 4/7 ≤ 3/4, so round it to 1/2.

Estimating:

1 + 1/2 = 1 1/2

9th Question

Round 7 to 8. It is over half, so it would be 8, which = 1

10th Question

Half of 20 = 10, 9 isn't above 10.

So round backwards to 24.

3 0

2 years ago

Read 2 more answers