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1 year ago

Find all factors of 2x^3-3x^2-2x

Mathematics

1 answer:

Nesterboy [21]1 year ago

7 0

ANSWER:

x, 2x + 1, x -2

STEP-BY-STEP EXPLANATION:

We have the following expression:

$2x^3-3x^2-2x$

We simplify as follows to determine the factors:

$\begin{gathered} \text{ We factor the common term:} \\ \\ x\left(2x^2-3x-2\right) \\ \\ \text{ Now we factor the following term} \\ \\ 2x^2-3x-2 \\ \\ -3x=x-4x \\ \\ 2x^2+x-4x-2 \\ \\ \left(2x^2+x\right)+\left(-4x-2\right) \\ \\ x\left(2x+1\right)-2\left(2x+1\right) \\ \\ \left(2x+1\right)\left(x-2\right) \\ \\ \text{ Therefore:} \\ \\ 2x^3-3x^2-2x=x\left(2x+1\right)\left(x-2\right) \end{gathered}$

The factors would be x, 2x + 1, x -2

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artcher [175]

The system of linear inequalities are:

$a + b \geq 20\\\\2.50a + 7b\leq 80$

Solution:

Let "a" be the number of small candles bought

Let "b" be the number of large candles bought

He needs to buy at least 20 candles

Therefore, number of small candles and number of large candles bought must be at least 20

Thus, we frame a inequality as:

$a + b \geq 20$

"at least" means greater than or equal to

Here, we used "greater or equal to" symbol because, he can buy 20 candles or more than 20 candles also

From given,

Cost of 1 small candle = $ 2.50

Cost of 1 large candle = $ 7

He can spend no more than 80 dollars

Which means, he spend maximum 80 dollars or less than 80 dollars also

So we have to use "less than or equal to" symbol

Thus, we frame a inequality as:

Number of small candles bought x Cost of 1 small candle + number of large candles bought x Cost of 1 large candle $\leq$ 80

$a \times 2.50 + b \times 7 \leq 80\\\\2.50a + 7b\leq 80$

Thus the system of linear inequalities are:

$a + b \geq 20\\\\2.50a + 7b\leq 80$

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3 years ago

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18π meters.

Whitepunk [10]

Answer:

$A=81\pi\ m^{2}$

Step-by-step explanation:

Step 1

Find the radius of the circular cross section

we know that

The circumference is equal to

$C=2\pi r$

we have

$C=18\pi\ m$

substitute and solve for r

$18\pi=2\pi r$

simplify

$18=2 r$

$r=9\ m$

Step 2

Find the area of the circular cross section

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=9\ m$

substitute

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$A=81\pi\ m^{2}$

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3 years ago

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MissTica

Answer:

50.24 yards²

Step-by-step explanation:

The equation for area of circle is πr². So the calculation is 4² × 3.14.

16 × 3.14 = 50.24

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3 years ago

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rusak2 [61]

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Step-by-step explanation:

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Ronch [10]

Answer:

Step-by-step explanation:

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