Geniuses please answer this.....step by step explanation

Is the number 4.333..... rational or irrational?

AleksAgata [21]

Answer:

Irrational number

7 0

2 years ago

A local hardware store sold 12 percent of its hammers on Saturday . If the hardware store sold 9 hammers on Saturday how many ha

Dmitrij [34]

$\frac{12}{100}$ = $\frac{9}{x}$ Cross multiply

12x=900 Divide both sides by 12.

x=75 hammers to begin with.

7 0

3 years ago

Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. X= 2.5 when y=

puteri [66]

Answer:constant of variation(k) is, 250.

Step-by-step explanation:

The inverse variation says that:

then, the equation is in the form of :

....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

Multiply 2.5 both sides we have;

or

k = 250

⇒

Therefore, the constant of variation is, 250 and the equation we get

Read more on Brainly.com - brainly.com/question/5991656#readmore

Step-by-step explanation:

4 0

2 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.