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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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tatyana61 [14]

Answer:

looks pretty hard

Step-by-step explanation:

4 0
3 years ago
point q is located in ( -4 , 6) point r is located in ( 8,6) . what is the distance from pint q to point r
Hoochie [10]

Answer: 12

Step-by-step explanation: It’s on the same y axis and -4 to 8 is going to the right on a graph.

5 0
3 years ago
Which equation represents the line that passes through the points (-3, 7) and (9,-1)? oy--3x+5 o y=-x-7 o y=zx-7 oy - 12 2x+5​
olchik [2.2K]

Answer:

The answer is

<h2>y =  -  \frac{2}{3} x + 5</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation we must first find the slope of the line.

So the slope of the line using points (-3, 7) and (9,-1) is

<h3>m =  \frac{ - 1 - 7}{9 + 3}  =  -  \frac{8}{12}  =  -  \frac{2}{3}</h3>

Now we use the formula

<h3>y - y1 = m(x - x1)</h3>

where

m is the slope

( x1 , y1) is any of the points given

So the equation of the line using point

( - 3 , 7) and slope - 2/3 is

<h3>y - 7 =  -  \frac{2}{3} (x + 3) \\ y - 7 =  -  \frac{2}{3} x - 2 \\ y =  -  \frac{2}{3} x - 2 + 7</h3>

We have the final answer as

<h3>y =  -  \frac{2}{3} x + 5</h3>

Hope this helps you

5 0
3 years ago
Read 2 more answers
STANDARD DEVIATION
givi [52]

Answer:

0.1527

Step-by-step explanation:

Standard Deviation = √p × q/n

Reynolds: 63%

Bachmann: 37%

n = 100

Standard Deviation = √0.63 × 0.37/100

= √(0.02331)

= 0.1526761278

≈ 0.1527

4 0
3 years ago
find the least perfect square that is exactly divisible by each of the numbers 5 , 18 , 25 and 27 . ​
Dimas [21]
<h3>☂︎ Answer :- </h3>

  • 8100
<h3>☂︎ Solution :- </h3>

  • LCM of 5 , 18 , 25 and 27 = 2 × 3³ × 5²
  • 2 and 3 have odd powers . To get a perfect square, we need to make the powers of 2 and 3 even . The powers of 5 is already even .

In other words , the LCM of 5 , 18 , 25 and 27 can be made a perfect square if it is multiplied by 2 × 3 .

The least perfect square greater that the LCM ,

☞︎︎︎ 2 × 3³ × 5² × 2 × 3

☞︎︎︎ 2² × 3⁴ × 5²

☞︎︎︎ 4 × 81 × 85

☞︎︎︎ 100 × 81

☞︎︎︎ 8100

8100 is the least perfect square which is exactly divisible by each of the numbers 5 , 18 , 25 , 27 .

7 0
2 years ago
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