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seropon [69]
3 years ago
5

The polynomial x^2+3x-1 is a factor of x^4+3x^3-2x^2-3x+1 true or false?

Mathematics
1 answer:
pashok25 [27]3 years ago
7 0

Answer:

Yes, it is true that x^2+3x-1  is a factor of x^4+3x^3-2x^2-3x+1.

Step-by-step explanation:

Let us try to factorize x^4+3x^3-2x^2-3x+1

x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3

Let us try to make a whole square of the given terms:

\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\

--------------

Formula used above:

a^{2} -2 \times a \times b +b^{2}  = (a-b)^2

In the above equation, we had a = x, b = 1.

--------------

Further solving the above equation, taking 3x common out of 3x^3-3x

\Rightarrow (x^2-1)^2+3x(x^2-1)\\

Taking (x^{2} -1) common out of the above term:

\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)

So, the two factors are (x^2-1)\ and\ (x^2+3x-1).

\therefore The statement that x^2+3x-1  is a factor of x^4+3x^3-2x^2-3x+1 is <em>True.</em>

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Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level. The
sattari [20]

Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) \sqrt{\frac{pq}{n} }

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as  proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the  proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value  ± 1.28.

We have alpha equal to 0.2  for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) \sqrt{\frac{pq}{n} }

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 \sqrt{\frac{0.8*0.2}{200} }

0.8 ± 0.03620

0.8362, 0.7638

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8 0
3 years ago
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Sergio039 [100]

Answer:

The area of ∆DEF = 4.5in²

Step-by-step explanation:

From the above diagram,

∆BAC ~∆DEF

It is important to note that if two triangles are similar, the ratio of their areas is equal or equivalent to the ratio of the areas of their sides

This means for the above question, that

We have the bigger triangle = ∆BAC has a side of 4 in and Area = 8 in²

The small triangle has a side of 3in

Finding the scale factor k = ratio of the sides of both Triangles

k = 4/3

k² = (4/3)²

k² = 16/9

Hence,

Area of ∆BAC/ Area of ∆DEF = 16/9

8in²/Area of ∆DEF = 16/9

We cross Multiply

8 in² × 9 = Area of ∆DEF × 16

Divide both sides by 16

Area of ∆DEF = 72/16

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djverab [1.8K]

Answer:

a) f(2) = 4

b) g(3) = 3

c) g(1/3) = -1

d) f(3) = 1/2

e) g(-2) = 2

f) f(π) = 3

Step-by-step explanation:

We are given:

f={(2,4),(-4,3),(3,1/2),(π,3)} and g={(3,3),(-2,2),(1/3,-1)}

We need to find the following values of f and g

a) f(2)

f(2) means when x=2, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =2 then y=4

So, f(2) = 4

b) g(3)

g(3) means when x=3, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =3 then y=3

So, g(3) = 3

c) g(1/3)

g(1/3) means when x=1/3, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =1/3 then y=-1

So, g(3) = -1

d) f(3)

f(3) means when x=3, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =3 then y=1/2

So, f(3) = 1/2

e) g(-2)

g(-2) means when x=-2, we need to find the value of y.

Looking at the given g={(3,3),(-2,2),(1/3,-1)}, when x =-2 then y=2

So, g(-2) = 2

f) f(π)

f(π) means when x=π, we need to find the value of y.

Looking at the given f={(2,4),(-4,3),(3,1/2),(π,3)} , when x =π then y=3

So, f(π) = 3

6 0
3 years ago
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