Which is the completely factored form of 4x3 10x2 – 6x? 2(x 3)(2x – 1) 2x(x 3)(2x – 1) 2x(x – 3)(2x – 1) 2(x – 3)(2x 1).

Mathematics

1 answer:

Natalija [7]2 years ago

6 0

The equation 4x^3+10x^2 – 6x is factorized as 2x(x+3)(2x – 1).

Option B represents the correct factors of the equation.

<h3>What is a Factor of the number?</h3>

A factor of the number can be defined as a divisor of the number that divides it completely without leaving any remainder.

Given equation is 4x^3+10x^2 – 6x. This can be factorized as given below.

$4x^3+10x^2-6x = 0$

We take the common term 2x, then,

$2x ( 2x^2 + 5x -3)=0$

$2x ( 2x^2 +6x -x -3)=0$

$2x (2x (x+3) -1(x+3))=0$

$2x (2x-1)(x+3)=0$

Hence we can conclude that the factors of the given equation are 2x(x+3)(2x – 1). Option B shows the correct factors.

To know more about the factors, follow the link given below.

brainly.com/question/3423184.

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A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

$y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76$

The number of bacteria after 1 hour would approximate be <u>27,569 bacteria</u>

<u></u>

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

$y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103$