Please answer It is very easy<br><br> what value will make the equation true -2.1-?=-1 1/2

PLEASE HELP, 30 POINTS<br> what system of equations is equivalent to this system?

Elena L [17]

The answer I got was The third one

5 0

3 years ago

Joe paid x dollars for a pair of jeans. Dennis bought the same pair of jeans for half as much as Joe. If they paid a total of $6

drek231 [11]

Joe spent 44. Denis spent 22

6 0

3 years ago

Read 2 more answers

Lina has 12 coins in her purse. D of them are dimes and the rest are quarters. How many quarters does Lina have? How much money

andrey2020 [161]

D=dimes
q=quarters
if she has 12 coins then
12-d=q she has 12-d quarters
we dont know how much money she has unless we know d.
she could have 12 dimes and 0 quarters or 11 dimes and 1 quarter etc. we need more information to solve.

3 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.