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3 years ago

There are 30 colored circle's on a rug 1/5 of the circles are red how many red circles are on the rug

Mathematics

2 answers:

Zinaida [17]3 years ago

4 0

Answer:

Step-by-step explanation:

30/5 = 6. 30 circles, 5 of which are red

Ivan3 years ago

3 0

1/5 of 30 is 6.
There are 6 red circles

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Multi step equation 3x+3-x+12=x+5

dlinn [17]

Answer:

x= -10

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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.

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

Helppppppp pleaseeeeee

LenKa [72]

Answer:

Step-by-step explanation:

5 0

3 years ago

Part C

makvit [3.9K]

A hope this helps :)

3 0

3 years ago

Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.

Vitek1552 [10]

The answer is 3/4 ft² = 0.75 ft²

The area (A) of the parallelogram with altitude a and base b is:
A = a * b

We have:
A = ?
a = 6 in
Since 1 inch is 0.083 feett, then 6 inches is
a = 6 * 0.083 ft = 0.498 ft ≈ 0.5 ft = 1/2 ft
b = 1 1/2 ft = 1 + 1/2 ft = 2/2 + 1/2 ft = 3/2 ft
_______
A = a * b
a = 1/2 ft
b = 3/2 ft
A = 1/2 * 3/2 = 3/4 ft² = 0.75 ft²

4 0

3 years ago