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3 years ago

What is the quotient (6x4 − 15x3 + 10x2 − 10x + 4) ÷ (3x2 + 2)?

Mathematics

1 answer:

Marrrta [24]3 years ago

8 0

Answer:

The quotient is $2x^2-5x+2$

Step-by-step explanation:

We want to simplify:

$\frac{6x^4-15x^3+10x^2-10x+4}{3x^2+2}$

We factor the numerator to get:

$\frac{(x-2)(2x-1)(3x^2+2)}{3x^2+2}$

We cancel out the common factors to get:

$(x-2)(2x-1)$

Therefore the quotient is $2x^2-5x+2$

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Which function in vertex form is equivalent to f(x) = x² + x +1?

mylen [45]

Answer:

$\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}$

Step-by-step explanation:

NOTE :

$x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}$

………………………………………

f(x) = x² + x +1

$=x^{2}+2\times \frac{x}{2} +1$

$=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1$

$=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1$

$=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}$

4 0

2 years ago

Part 1. Determine the molar mass of a 0.622-gram sample of gas having a volume of 2.4 L at 287 K and 0.850 atm. Show your work.

sdas [7]

If a sample of gas is a 0.622-gram, volume of 2.4 L at 287 K and 0.850 atm. Then the molar mass of the gas is 7.18.

<h3>What is an ideal gas equation?</h3>

The ideal gas equation is given below.

$PV = nRT$

The equation can be written as

$\rm PV = \dfrac{m}{M} \ RT\\\\\\MPV = mRT$

Where M is the molar mass, P is the pressure, V is the volume, R is the universal gas constant, T is the temperature, and m is the mass of the gas.

Then the molar mass of a 0.622-gram sample of gas has a volume of 2.4 L at 287 K and 0.850 atm.

V = 2.4 L = 0.0024

P = 0.85 atm = 86126.25 Pa

T = 287 K

m = 0.622

R = 8.314

Then we have

$\begin{aligned} \rm M \times 86126.25 \times 0.0024&= 0.622 \times 8.314 \times 287\\\\\rm M &= 7.18 \end{aligned}$

Then the molar mass of the gas is 7.18.

More about the ideal gas equation link is given below.

brainly.com/question/4147359

#SPJ1

6 0

2 years ago

Find the distance between the points (-5, -7) and (-4 -8)

Margarita [4]

It should be the square root of 2 (~1.141)

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3 years ago

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Romashka [77]

Answer:

Step-by-step explanation:

The answer should be A. If you rotate it around point A the rectangle would be up right on the x axis

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3 years ago

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grigory [225]

The 3 one hope this helps:)

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3 years ago

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