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masha68 [24]
3 years ago
6

Prove that if an integer is a perfect square and a perfect cube, simultaneously, then it is either of the form 7k or 7k+1

Mathematics
1 answer:
Bogdan [553]3 years ago
5 0
If an integer is both a square and a cube, it can be of the form:
<span>(<span>a3</span><span>)^2</span></span>
Now,
since a cube can be of the form 7k or 7k+-1(thanks to FoolForMath),
 we write
<span><span>a^3</span>=7k</span>
and get the no to be
49k^2
, which is in the form of 7 times something
<span>49<span>k^2</span>=7×(7<span>k^2</span>)</span>
Now put
<span><span>a^3</span>=7k+−1</span> Square it
and you'll get a number in the form of (7times something +1)
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What is 649,284,143 rounded to the nearest hundred million
zysi [14]
The answer is 600,000,000
4 0
3 years ago
Please help.. no links​
neonofarm [45]

Answer:

Its 9.0 units

Step-by-step explanation:

For the side mostly to the left, its gonna be 3 units, since we can easlily count it

Now, for the diagonals, we have to use the formula for the area of a triangle, which is (l * w) / 2 = a.

For the bottom side, its 3 along the x axis and 1 along the y axis. 3 * 1 is 3, now divide that by 2 and you got 1.5

Now, for the right side, its 5 on the y, 1 on the x. Multiply 1 by 5, you got 5. Now divide that by 2 and you have 2.5

Finally, for the top side, its 4 on the x, and 1 on the y. 4 * 1 is 4, divided by 2 and its 2.

Alright, now we have to add 'em all together. 3 + 1.5 + 2.5 + 2 is 9 units

Theres your answer :)

6 0
2 years ago
The following list shows the items and prices for a restaurant order. Calculate the total amount if there is a 7% tax and the cu
ziro4ka [17]

Answer :  b. $65.10

1 appetizer: $7.39=7.39

2 entrees: $16.99 each=  2 * 16.99=33.98

1 dessert: $5.29= 5.29

2 drinks: $2.30 each=4.6

cost = 7.39 + 33.98 + 5.29 + 4.6 =$51.26

7% tax = 51.26 * 0.07 = 3.5882

20% gratuity = 51.26 * 0.2= 10.252

Total cost = 51.26 + 3.5882 + 10.252 =65.1002

the total amount = $65.1

6 0
3 years ago
Read 2 more answers
Given ƒ(x) = −10x + 45, find x when ƒ(x) = 15.
Temka [501]

Answer:

x = 3

Step-by-step explanation:

Given

f(x) = - 10x + 45 and f(x) = 15, then equating gives

- 10x + 45 = 15 ( subtract 45 from both sides )

- 10x = - 30 ( divide both sides by - 10 )

x = 3

5 0
3 years ago
Please help me with this question. I will also give brainliest!
Alekssandra [29.7K]
What question? I don’t see no question
3 0
3 years ago
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