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Lady bird [3.3K]
2 years ago
6

HELLPP!! Find the value of x that makes line m parallel to line n:

Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
7 0

Answer:

x = 6

Step-by-step explanation:

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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
PLEASE HELP GIVING BRAINLIST
melisa1 [442]
I’m pretty sure it’s the number of wrenches in the toolbox because that gonna affect the amount of space he has left
3 0
2 years ago
Find the distance between the points (4,3) and (-1,4) round answer to the nearest tenth
scZoUnD [109]

Answer:

The distance between those points rounded to the nearest tenth is 5.1

Step-by-step explanation:

1.   (x2-x1) = (-1 - 4) = -5

2.   (y2-y1) = (4 - 3) = 1

3.   (-5^)2 + (1)^2 = 25 + 1 = 26

4.   √26 = √26

5.   5.099 ---> Rounded to the nearest tenth = 5.1

5 0
2 years ago
George bought 7 quarts of cleaning fluid: x quarts at $3.00 per quart & y quarts at $2.00 per quart. Find x & y if the t
PolarNik [594]

Answer:

3x + 2y = 16

x = 2 , y = 5

Step-by-step explanation:

Given that George bought x quarts at $3.00 per quart & y quarts at $2.00 per quart and he bought 7 quarts for $16.00

Considering the total cost

3x + 2y = 16

For the cost of each

x + y = 7

solving the 2 equations simultaneously be substitution

x = 7 - y

3(7 - y) + 2y = 16

21 - 3y + 2y = 16

-3y + 2y = 16 - 21

-y = - 5

Divide both sides by -1

y = 5

x = 7 -y

x = 7 - 5

= 2

7 0
2 years ago
I need serious help with this equation.​
garri49 [273]

Answer:

First, it’s already telling you that you need to find d, which is the opposite of degree 59. This means you have to do the exact thing for degree 37. Since it’s already telling you to use sine, you need to look at the opposite side of 37 which is 98.4.

So ? is 98.4

Now, you need to find sin 59 / d.

First, plug in sin 98.4 sin (37) in your calculator (make sure it’s in degree setting)

The result is 59.2.

Now, 59.2 = sin 59 / d.

Switch sides like this: d = 59.2 sin (37)

And the answer is approximatley d = 35.6

? = 98.4

d = 35.6

8 0
3 years ago
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