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kati45 [8]
3 years ago
10

Express the fraction 1/15 as a decimal

Mathematics
1 answer:
worty [1.4K]3 years ago
7 0
1/15 = 0.06
1 divided by 15 = 0.066666666666667
The best way to write the answer would be 0.06
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Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
kogti [31]

Answer:

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if (x+y)^{2} = x^{2} + 2\cdot x\cdot y  + y^{2}. From statement, we must fulfill the following identity:

a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}

By Associative and Commutative properties, we can reorganize the expression as follows:

a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2} (1)

Then, we have the following system of equations:

x = a (2)

(b^{2}-1) = 2\cdot x\cdot y (3)

y = c (4)

By (2) and (4) in (3), we have the following expression:

(b^{2} - 1) = 2\cdot a \cdot c

b^{2} = 1 + 2\cdot a \cdot c

b = \sqrt{1 + 2\cdot a\cdot c}

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, a, b, c > 1. If a, b and c are prime numbers, then  2\cdot a\cdot c must be an even composite number, which means that a and c can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, b must be a natural number, which means that:

1 + 2\cdot a\cdot c \ge 4

2\cdot a \cdot c \ge 3

a\cdot c \ge \frac{3}{2}

But the lowest possible product made by two prime numbers is 2^{2} = 4. Hence, a\cdot c \ge 4.

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Example: a = 2, c = 2

b = \sqrt{1 + 2\cdot (2)\cdot (2)}

b = 3

4 0
3 years ago
Determine whether 5, 226 is divisible by 2,3,4,5,6,9, or 10.
uranmaximum [27]

Answer:

2,3,6

Step-by-step explanation:

5,226   ...(1)

unit digit=6

6 is divisible by 2,

so (1) is divisible by 2.

last two digits=26 ,not divisible by 4,

so (1) is not divisible by 4.

5+2+2+6=15 divisible by 3 but not divisible by 9.

so (1) is divisible by 3 but not divisible by 9.

2×3=6,so (1) is divisible by 6.

unit digit=6≠0 or 5

so (1) is not divisible by 5 or 10.

8 0
2 years ago
Read 2 more answers
The sum of three consecutive odd integers is 153. what is the value of the largest of the integers?
Lelechka [254]
The answers would be 49,51,and53!
6 0
3 years ago
There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Write a system of equations tha
olga55 [171]

Answer:

well

Step-by-step explanation:

44 legs and 15 animals you have to subtract

7 0
3 years ago
How does a translation 7 units up change the coordinates of a shape?
Salsk061 [2.6K]

You add 7 to the y coordinates. (x,y+7)


3 0
3 years ago
Read 2 more answers
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