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natali 33 [55]
2 years ago
12

What is the slope of AC a.-3/2 b.-2/3 c.2/3 d.3/2

Mathematics
1 answer:
d1i1m1o1n [39]2 years ago
7 0

Answer: it is D and if it is wrong then it doesn’t look like this question was finished.

Step-by-step explanation:

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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
What is 251.327 rounded to the nearest whole number.
evablogger [386]

Answer:

251

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Solve the equation using square roots. x2 + 10 = 9
Oksana_A [137]
x^2 + 10 = 9

Subtract 10 from both sides.

x^2 = -1

Since the square of a number, x, equals a negative number, -1, the answer cannot be a real number because the square of a real number is always non-negative. Therefore, there is no real number solution to this equation.

Answer: <span>B. no real number solutions</span>
5 0
3 years ago
A ski lodge charges $26 per day for a pass and $1.50 for every ski lift ride. A second ski
malfutka [58]

Answer:

32=40

26=39

Step-by-step explanation:

8 0
3 years ago
A student factors a^6 - 64 to (a^2-4)(a^4 + 4a^2+ 16).
Neko [114]

Answer:

Option (b) is correct.

The expression is equivalent, but the term is not completely factored.

Step-by-step explanation:

edge 2020

4 0
3 years ago
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