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3 years ago

The graph of f(x)=2x^3+x^2-4x-2 is shown. How many of the roots of f(x) are rational

Mathematics

2 answers:

Alexeev081 [22]3 years ago

7 0

We can one theorem to help us find rational roots of this polynomial.

2x^3 + x^2 - 4x - 2

We'll use Descartes' rule of signs.

Because there is 1 sign change, 1 of the 3 roots will be positive.

Now we can make the value of x -1 to see how many negative roots there will be.

-2 + 1 + 4 - 2

There are 2 sign changes, so we know there will be 2 negative roots.

Because of this, we should have 3 real, rational roots.

ohaa [14]3 years ago

6 0

Answer:

The answer is 1

I don't know the step-by-step explanation

Step-by-step explanation:

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Which of these statements is true for f(x) = (1/2)^x

Ann [662]

<h3>Answer: D) The y intercept is (0,1)</h3>

This can be confirmed by plugging x = 0 into the function to find that...

y = (1/2)^x

y = (1/2)^0

y = 1

Recall that any nonzero value to the 0th power leads to 1. So we can say x^0 = 1 as long as x is not zero.

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Extra info (optional section):

We can rule out choice A because negative x values work in the domain. For instance, if x = -1, then it leads to y = (1/2)^x = (1/2)^(-1) = 2. The negative exponent will apply the reciprocal operation to the base fraction.
Choice B can also be ruled out because the range is y > 0. Or you could note that it is possible to get positive y values smaller than 1/2. Try x = 2 and you'll see it leads to y = 1/4 which is not greater than 1/2.
Choice C is false as well. The function f(x) = (1/2)^x is decreasing throughout the domain. A graph visually would show this due to it going downhill when moving from left to right. A table of values is a non-visual way to see we have a decreasing function. The table would show that y decreases when x increases.

6 0

3 years ago

Read 2 more answers

Each time Cali babysits, she gives 35% of

MrRissso [65]

The answer is X-(.35)x

6 0

2 years ago

Someone, please do all my answers I really do not get anything!

Marianna [84]

I can’t see anything but a black paper

3 0

3 years ago

Please help i will give brainliest !!!!

Alex

Answer:

2 dress shirts

5 plain shirts

Step-by-step explanation:

2 dress shirts = 28x2=56

5 plain shirts =15x5=75

56+75=131

2+5=7

4 0

3 years ago

In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear pow

leva [86]

Answer:

The test statistic z = z = 2.368 >1.97 (at 5% level of significance)

we rejected null hypothesis at 5% level of significance

There is significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Step-by-step explanation:

Given data In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents

The first sample proportion $p₁ = \frac{63}{100} =0.63$

The construction of 59 of 125 suburban residents are in favor

The second sample proportion $p_{2} = \frac{59}{125} = 0.472$

Given the sample sizes are n₁ = 100 and n₂ =125

Null hypothesis(H₀):-there is no significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Alternative hypothesis: H₁

There is significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Level of significance:-

∝ =0.05

Tabulated value z=1.96

Test statistic

$z = \frac{p_{1}-p_{2} }{\sqrt{pq(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }$

where $p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1} +n_{2} }$ q = 1- p

Substitute all values in above equation

$p = \frac{100X0.63+0.472X125}{100+125} = 0.542$

q = 1-p = 1 - 0.542 = 0.458

The test statistic

$z = \frac{0.63-0.472}{\sqrt{0.542X0.458}(\frac{1}{100}+\frac{1}{125} )}$

on simplification , we get

z = 2.368 >1.97 (at 5% level of significance)

we rejected null hypothesis at 5% level of significance

Conclusion:-

There is significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

8 0

3 years ago