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Naddika [18.5K]
2 years ago
5

Show that 3/8 ÷ 7/12 =9/14

Mathematics
1 answer:
myrzilka [38]2 years ago
4 0
3/8*12/7 = 36/56 = 9/14 (simplify)
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A rope 8 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a functi
shtirl [24]
<span>1st piece: x feet
2nd piece: 8-x feet
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Use the "x" piece to form a circle:
Circumference = "x".
2(pi)*radius = x

radius = x/(2pi)
So, Area = pi[x/(2)]^2 = x^2/(4pi) = (1/4pi)x^2
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Use the 10-x piece to form square:
side = (1/4pi)(10-x)
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8 0
2 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.

Thanks

4 0
3 years ago
Factorise :x^2y^2-16​
Lyrx [107]

Answer:

(xy - 4)(xy + 4).

Step-by-step explanation:

The is the difference of 2 squares.  

a^2 - b^2 = (a - b)(a + b: so we have:

x^2y^2 - 16​ = (xy - 4)(xy + 4)

5 0
3 years ago
Rearrange the equation so a is the independent variable.<br><br> 3a-7= -4b+1<br><br> Please help! :)
Aleksandr-060686 [28]

Answer:

Hiii the answer would be a= -4b+8/3

7 0
3 years ago
Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find h
Pavel [41]

Answer:

$13.75

Step-by-step explanation:

Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution. 5 3.5 = 12 x 3.5x = 60 x = $17.14

<u>5x2=10+3.75=13.75</u>

6 0
3 years ago
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