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3 years ago

which of the following correctly describes the end behavior of the polynomial function, f(x)=2x^4-3x^2+2x

Mathematics

2 answers:

Gnom [1K]3 years ago

8 0

Answer:

The end-behavior of the given function is: "Both ends upward".

Step-by-step explanation:

Given polynomial function is: $f(x)=2x^4-3x^2+2x$

For determining the end-behavior of a polynomial function, first we need to identify the degree and leading coefficient.

Degree means the highest exponent to the variable in the function. So, here degree is 4.

Leading coefficient is the coefficient of the first term in the function. So, here the leading coefficient is 2.

Now the rule is: If the degree of the polynomial function is even and the leading coefficient is positive, then both ends of the graph of function will be in upward direction.

So, the end-behavior of the given function is: "Both ends upward".

inna [77]3 years ago

4 0

Answer:

Both ends go up.

Step-by-step explanation:

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If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2 Express answer as a common fraction. Thanks!!

timama [110]

$x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0$

By the quadratic formula,

$x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2$

Then

$(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2$

$\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}$

Multiply numerator and denominator by the denominator's conjugate:

$\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15$

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3 years ago

Identify the outlier in the data set 6, 9, 3, 2, 10, 138, 13. Then, find the mean with and without the outlier. If necessary, ro

Andrews [41]

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With this upper outlier, the mean will be significantly higher. Without it, it will lower back down, so B is your answer

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3 years ago

Solve the following systems of inequalities and select the correct graph: 2x-y>4 x+y< -1

Serga [27]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% p

Stolb23 [73]

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

Then we know that the total amount of mixture will be:

$A + B = 80$

Then the total amount of pure fruit juice in the mixture will be:

$0.55A + 0.8B = 0.65 * 80$

$0.55A + 0.8B = 52$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

$-0.8A -0.8B = -0.8*80$