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3 years ago

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Leo wants to paint a mural that covers a wall with an area of 400 square feet. They height of the wall is 1/4 of its length. Wha

t is the length and the height of the wall?
So, the dimensions (length by height) of the wall are ___ feet by ___ feet.

1 answer:

Leya [2.2K]3 years ago

3 0

The height of the wall is 100 feet

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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

2x+2y=8<br> X+y=4<br> Which statement is true about the solution

laila [671]

Both x and y equal 2.

2•2=4 + 2•2=4

4+4=8

2+2=4

6 0

3 years ago

What is 4/1 + 3/4 = equal to?

kari74 [83]

4/1 is the same as 4.

So 4+3/4= 4 and 3/4

<u>Final Answer</u>= 4 and 3/4

3 0

3 years ago

Read 2 more answers

The ratio of art class to music class is 4:3. If there is 8 more students in art class, how many students are in music class

pishuonlain [190]

Answer:

9 students in music class.

Step-by-step explanation:

In art there are 4 and since there are 8 more 8 + 4 = 12. so there are 12 in Art.

4 x _ = 12. —> 4 x 3 = 12.
so we need to do the same for music class.

For music there are 3.
so we multiply by 3 like we did with the 4.

3 x 3 = _ —> 3 x 3 =9.
so there are 9 students in music class.

6 0

2 years ago

I need to know what X=

laila [671]

Answer:

Lol I learned about this today in class, but I couldnt pay attention cuz I started crying about something

Step-by-step explanation:

5 0

3 years ago