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Katyanochek1 [597]
3 years ago
15

Please help me on this. you need to match the terms to the correct number.

Mathematics
1 answer:
Gnom [1K]3 years ago
5 0

Answer:

64=8

49=7

36=6

25=5

100=10

16=4

9=3

20=4.5

4=2

1=1

67=8.2

81=9

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Which expression is equivalent to (a^-3 b/a^-5 b3)^-3? Assume a=0, b=0.
prohojiy [21]
Use:\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\dfrac{1}{a^n}\\\\(ab)^n=a^nb^n

\left(\dfrac{a^{-3}b}{a^{-5}b^3}\right)^{-3}=\left(a^{-3-(-5)}b^{1-3}\right)^{-3}=\left(a^{-3+5}b^{-2}\right)^{-3}=\left(a^2b^{-2}\right)^{-3}\\\\=(a^2)^{-3}(b^{-2})^{-3}=a^{2(-3)}b^{-2(-3)}=a^{-6}b^6=\dfrac{b^6}{a^6}
7 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
Write an equation of the line that passes through the point(-6,-9) with slope -5
LUCKY_DIMON [66]

Answer:

  y = -5(x +6) -9

Step-by-step explanation:

The point-slope form of the equation for a line can be written as ...

  y = m(x -h) +k

for a line with slope m through point (h, k).

You have m=-5 and (h, k) = (-6, -9). Filling in these values gives ...

  y = -5(x -(-6)) -9

Simplifying a bit, you get ...

  y = -5(x +6) -9

4 0
3 years ago
7y = 14 -28x to standard form
MissTica

Answer:

28x + 7y = 14.

Step-by-step explanation:

Just add the 28x to each side.

4 0
3 years ago
Read 2 more answers
What is the correct way to write 1/4% as a decimal
WINSTONCH [101]

Answer:

1/0.04 = 25

Step-by-step explanation:

5 0
3 years ago
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