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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

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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3 years ago

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Simplify; 5a+3b-7a+4b

serg [7]

Combine like terms:

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2 years ago

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Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove to get to the

lara31 [8.8K]

Answer:

$D(t)=-24t+166$

Step-by-step explanation:

Let

D(t) = the distance to the safe zone (measured in meters)

t = time (measured in seconds)

<u>Given:</u>

Rachel's rate = 24 meters per second

At $t_1=4$ seconds $D(t_1)=70$ meters

<u>Find:</u> D(t)

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative.

Hence, the function expression is

$D(t)=-24t+b$

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3 years ago

Solve equation 3x-5y=7 5x-2y=-1 by elimination

kakasveta [241]

Answer:

x = -1, y = -2.

Step-by-step explanation:

Using the elimination method,

multiply the first eqn by 2 and the 2nd eqn by 5.

6x - 10y = 14

25x - 10y = -5

Subtract one of the new equations from the other

-19x = 19

x = -1

Sub x=-1 into the 2nd eqn

-5 - 2y = -1

y = -2

Hence x = -1, y = -2.

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