5 less than two times a number is equal to 4 less than the same number.

Mathematics

2 answers:

kati45 [8]3 years ago

3 0

Answer:

x=1

Step-by-step explanation:

2x-5=x-4

x=1

Montano1993 [528]3 years ago

3 0

Answer:

The number is 1

Step-by-step explanation:

Let the number be x

2(x) - 5 = x - 4

2x - 5 = x - 4

2x - x = -4 + 5

x = 1

Therefore the number is 1

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Juli2301 [7.4K]

I. xy + 2y=3 Not linear equation because is grade 2 equation (xy).

II. x-2y = y Are linear equations in two unknowns (x and y).

III. 3x + 2y = 5 Are linear equations in two unknowns (x and y).

<h2>Corect ansver: C) II and III only</h2><h2></h2>

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4 years ago

10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.

Gre4nikov [31]

Answer:

$\large\boxed{x\in(-2,\ 2)}$

Step-by-step explanation:

$f(x)=12x-x^3$

Calculate the derivative of the function:

$f'(x)=\left(12x-x^3\right)'=(12x)'-\left(x^3\right)'=12-3x^2$

Calculate the zeros of the derivative:

$f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2$

Let's check the derivative sign:

$f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2$