Mathematics, 20.09.2020 16:01, JoJo3671

The average weight of a newborn panda is 0.2, or 2/10 pound. Between what two integers is the weight of a newborn panda?

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answered: Ellafrederick

$\frac{2}{10}$ lies between 0 and 1.

Step-by-step explanation:

We must have in mind that given average weight of a newborn panda is a non-integer rational number, such that lies between two integer rational number. In other words, this number must satisfy the following condition:

$n < \frac{a}{b} < n +1$ , $n, a, b \in \mathbb{N}_{O}$

$\mathbb{N}_{O} = \mathbb{N}\,\cup\,{\{0\}}$

Which is now developed mathematically to deduce a useful expression to find integers:

1) $n < \frac{a}{b} < n +1$ Given

2) $n \cdot 1 < \frac{a}{b} < n\cdot 1 + 1$ Modulative property

3) $n \cdot (b\cdot b^{-1}) < a\cdot b^{-1} < n \cdot (b\cdot b^{-1}) + b\cdot b^{-1}$ Existence of Multiplicative inverse/Definition of division.

4) $(n\cdot b)\cdot b^{-1} < a\cdot b^{-1}< [(n+1)\cdot b] \cdot b^{-1}$ Commutative, Associative and Distributive properties.

5) $n\cdot b < a < (n+1)\cdot b$ Compatibility with Multiplication/Existence of Multiplicative Inverse/Modulative Property/Result.

If we know that a = 2 and b = 10 , the following inequation is formed:

$10\cdot n < 2 < 10\cdot (n+1)$

It is quite evident to conclude that $\frac{2}{10}$ lies between 0 and 1.

answered: Guest

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2: