How to factor the trinomial 3 x^{2} + 8 -3

A large carton of milk is 72 ounces. How

agasfer [191]

Answer: not here!

Step-by-step explanation: 72 ounces is 9 cups! (Divide by 8) (Assuming you mean US cups)

6 0

2 years ago

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Need help asap pls and ty.

Anastasy [175]

Answer:

D

Step-by-step explanation:

8 0

2 years ago

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Prove that if x is an positive real number such that x + x^-1 is an integer, then x^3 + x^-3 is an integer as well.

Shkiper50 [21]

Answer:

By closure property of multiplication and addition of integers,

If $x + \dfrac{1}{x}$ is an integer

∴ $\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot \left (x + \dfrac{1}{x} \right )$ is an integer

From which we have;

$x^3 + \dfrac{1}{x^3}$ is an integer

Step-by-step explanation:

The given expression for the positive integer is x + x⁻¹

The given expression can be written as follows;

$x + \dfrac{1}{x}$

By finding the given expression raised to the power 3, sing Wolfram Alpha online, we we have;

$\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot x + \dfrac{3}{x}$

By simplification of the cube of the given integer expressions, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot \left (x + \dfrac{1}{x} \right )$

Therefore, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )= x^3 + \dfrac{1}{x^3}$

By rearranging, we get;

$x^3 + \dfrac{1}{x^3} = \left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )$

Given that $x + \dfrac{1}{x}$ is an integer, from the closure property, the product of two integers is always an integer, we have;

$\left ( x + \dfrac{1}{x} \right) ^3$ is an integer and $3\cdot \left (x + \dfrac{1}{x} \right )$ is also an integer

Similarly the sum of two integers is always an integer, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 + \left(- 3\cdot \left (x + \dfrac{1}{x} \right ) \right )$ is an integer

$\therefore x^3 + \dfrac{1}{x^3} = \left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )= \left ( x + \dfrac{1}{x} \right) ^3 + \left(- 3\cdot \left (x + \dfrac{1}{x} \right ) \right )$ is an integer

From which we have;

$x^3 + \dfrac{1}{x^3}$ is an integer.

4 0

3 years ago

Please do the agree or disagree part and justification

Jlenok [28]

Answer:

<em>We disagree with Zach and Delia and agree with Alicia</em>

Step-by-step explanation:

The domain of a function is the set of values of the independent variable that the function can take according to given rules or restrictions.

The range is the set of values the dependent variable can take for every possible value of the domain.

The graph shows a continuous line representing the values of the function. We must take a careful look to the values of x (horizontal axis) where the function exists. It can be done by drawing an imaginary vertical line passing through the value of x. If that line touches the graph of the function, it belongs to the domain. It's clear that every value of x between -5 and 3 (both inclusive because there are solid dots in the extremes) belong to the domain:

Domain: $-5\leq x \leq 3$

The range is obtained in a similar way as the domain, but the imaginary lines must be horizontal. That gives us the values of y range from -7 to 5 both inclusive:

Range:

$-7\leq y \leq 5$

Thus we disagree with Zach and Delia and agree with Alicia

8 0

3 years ago

HELP

serg [7]

Answer:

5 percent monthly because because it creates more interest

4 0

2 years ago