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3 years ago

It’s real simple just answer it

Mathematics

2 answers:

sladkih [1.3K]3 years ago

6 0

Answer:

-6 and negative 1 with the bio

Step-by-step explanation:

-Dominant- [34]3 years ago

5 0

-6 and -1 Would be the answer

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A jar contains 10 blue marbles, 3 red marbles, and 7 white marbles.

finlep [7]

Answer:

50% chance because (10)/(20)=1/2=0.5=50%

Step-by-step explanation:

hope this helps

8 0

3 years ago

△ABC @ △DEF. Find the measures of the given angles or the lengths of the given sides

brilliants [131]

Answer:

BC = EF = 8

Step-by-step explanation:

Assuming you mean BC ≅ EF, then ...

... 3z +2 = z +6

... 2z = 4 . . . . . . . . add -2-z

... z = 2 . . . . . . . . . divide by 2

BC = EF = 2+6 = 8

7 0

3 years ago

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.