Multiply (3)(−4)(2). −48 −24 24 48

real estate values in a town are increasing at a rate of 7% per year. ms. keen purchased a building for $245,000 in 2015. how mu

Lunna [17]

Answer:

367,679

Again someone helped me with this question so you get the answer too.

4 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

Please help... no links

iris [78.8K]

If I get a uniform then I make the team.

4 0

3 years ago

If you place a 17-foot ladder against the top of a 8-foot building, how many feet will the bottom of the ladder be from the bott

Goshia [24]

Answer:

15 feet

Step-by-step explanation:

This problem involves using the Pythagorean theorem, since the figure made with the ladder, building, and ground would make a right triangle. You are given the values 17ft and 8ft, which is enough to plug into the Pythagorean theorem.

The ladder, 17ft, would be the longest side (hypotenuse). The 8ft building would be one of the legs of the right triangle.

1. Plug your given values correctly into the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

$8^{2} + b^{2} = 17^{2}$

2. Now solve for b, which is your unknown distance (the distance the bottom of the ladder is from the bottom of the building).

$8^{2} + b^{2} = 17^{2}$ --> Square 8 and 17

$64 + b^{2} = 289$ --> Subtract 64 from both sides

$b^{2} = 225$ --> Square root both sides to get b by itself

b = 15

3. The distance is 15 feet

*Note: to make solving this problem easier, try drawing out the given situation, namely the building and the ladder

7 0

3 years ago

In timara math class there are, 12 boys and 15 girls which of the following in the ratio to boys and girls in timaras math class

tiny-mole [99]

Answer:

4:5

Step-by-step explanation:

If there are 12 boys and 15 girls, the ratio of boys to girls will be 12:15.

However, this can be simplified by dividing each number by 3. This can be done since both 12 and 15 are divisible by 3.

12:15

= 4:5

So, the ratio of boys to girls in Timara's class is 4:5

7 0

3 years ago