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3 years ago

Prove that in any pythagorean triple, one of the side lengths is divisible by 5

1 answer:

7 0

The trick is to realize what your choices are.

if m or n or both are divisible by 5, then 2mn will be divisible by 5
I don't know if you know about x mod(5), but in that case there can only be 4 possibilities for m and n
m mod (5) = +/- 2 or m mod(5) = +/- 1
In the first case m^2 = 4 mod(5) and in the second case m^2 = 1 mod(5) N has the same considerations.
If m and n have the same modular results (both are [say] 2 ) then m^2 - n^2 which be 0
If they are different, then (m^2 + n^2) mod 5 = 0

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A toy box contains eight green balls and four purple balls. Suppose you choose a ball at random and then replace it by putting i

dedylja [7]

Answer: C. $\dfrac{1}{3}$

Step-by-step explanation:

Given: Box contains 8 green balls and 4 purple balls.

Total balls = 8+4 = 12

event 1 = first picking green ball

event 2 = second picking purple balls.

As first ball was replaced, that means both events are independent.

Probability that you have selected a green ball and then a purple ball = P(purple ball )

Formula for probability = $\dfrac{\text{favorable outcomes}}{\text{total outcomes}}$

Probability of selecting a purple ball (second pick)= $\dfrac{4}{12}$

$=\dfrac{1}{3}$

The required probability $=\dfrac{1}{3}$ , so C is correct option.

3 0

3 years ago

Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. E

Elenna [48]

Answer:

Step-by-step explanation:

a₃ = -2

a₇ = -10

The nth term of an arithmetic sequence is:

a = a₁ + d (n − 1)

Therefore:

-2 = a₁ + d (3 − 1) = a₁ + 2d

-10 = a₁ + d (7 − 1) = a₁ + 6d

Subtract the equations:

8 = -4d

d = -2

Plug into either equation to find the first term.

-2 = a₁ + 2(-2)

a₁ = 2

5 0

3 years ago

A pet shop had 8 identical fish tanks in the shape of rectangular prisms. The width and height of each tank was (x - 7) inches a

kipiarov [429]

The area of rectangular base of each tank

7 0

3 years ago

Jose wants to build a rectangular kennel for his dog. His dad will let him use a spot in the corner of the yard that is 12 feet

Varvara68 [4.7K]

The answer is 42 ft 4 in

The perimeter of a rectangle with length l and width w is:
P = 2l + 2w

l = 12 ft 3 in
w = 8 ft 11 in

1 ft = 12 in
l = 12 * 12 in + 3 in = 144 in + 3 in = 147 in
w = 8 * 12 in + 11 in = 96 in + 11 in = 107 in

P = 2 * 147 + 2 * 107 = 294 + 214 = 508 in
P = 508 in = 504 in + 4 in = 42 * 12 in + 4 in = 42 ft 4 in

7 0

3 years ago

Mattias gets dressed in the dark one morning and chooses his clothes at random. He chooses a shirt (green, red, or yellow), a pa

Oliga [24]

Answer:

So, the number of ways in which the dress can be chosen

= 3 × 2 × 2

= 12.

And the combinations are

(Green shirt, black pant, checkered shoes),

(Green shirt, black pant, red shoes),

(Green shirt, blue pant, checkered shoes),

(Green shirt, blue pant, red shoes),

(Red shirt, black pant, checkered shoes),

(Red shirt, black pant, red shoes),

(Red shirt, blue pant, checkered shoes),

(Red shirt, blue pant, red shoes),

(Yellow shirt, black pant, checkered shoes),

(Yellow shirt, black pant, red shoes),

(Yellow shirt, blue pant, checkered shoes),

(Yellow shirt, blue pant, red shoes).

The tree diagram is below.

Step-by-step explanation:

7 0

3 years ago