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3 years ago

Is (x +1) a factor of f(x) = x3 + 2x2 −5x − 6 ? Yes No

Mathematics

2 answers:

sertanlavr [38]3 years ago

5 0

Answer:

Yes.

Step-by-step explanation:

You can find it out by factoring but ill do it easier way.

(x + 1 ) = 0 put the first and second equation to 0

x = -1

x³ + 2x² - 5x - 6 = 0 Now plug in the x in the equation

(-1)³ + 2(-1)² - 5(-1) - 6 = 0

0 = 0

so (x + 1) is a factor.

Firlakuza [10]3 years ago

5 0

Answer:

Yes

Step-by-step explanation:

If x + 1 is a factor

x = -1 should be a root

Check for the remainder:

(-1)³ + 2(-1)² −5(-1) − 6

Therefore it's a root, hence x+1 is a factor

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The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and

Firdavs [7]

Answer:

$P(39 < X < 48 ) = 0.8767$

95% of all sample means will fall between $40.1 < \mu < 49.9$

$\= x = 41. 795$

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * 2.5$

=> $E =4.9$

Generally the 95% of all sample means will fall between

$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

=> $P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90$

=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

Generally from the z-table the critical value of 0.90 is

$z = -1.282$

$\frac{\= x -45 }{ 2.5} = -1.282$

=> $\= x = 41. 795$

Considering question 2

Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

$s = \frac{1}{5} \sigma$

Generally the standard deviation of the sample mean is mathematically represented as

$s = \frac{\sigma }{ \sqrt{n} }$

=> $\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }$

=> $n = 5^2$

=> $n = 25$

5 0

3 years ago

8 less than 2 times a number is greater than the sum of the same number and 9

lyudmila [28]

step-by-step explanation:

every time we see "a number" or "the same number," we can add a variable (we'll use x here). rewriting the problem, we get: 8 less than 2 times x is gr8er than the sum of x and 9.

next, we can work backwards to write an inequality. we know from the word problem above that the number on the left side of the equation is 8 less than 2x, so we can rewrite that part like this: 2x-8.

for the right side of the equation, all we have to do is simplify "the sum of x and 9" to x + 9. so now the inequality should look like this: 2x - 8 > x + 9.

now we'll solve the inequality just like an equation: subtract x from both sides of the inequality, so now we have: x - 8 > 9.

then, we can add 8 to both sides to get the x by itself, and we get the answer: x > 15

hope this helps! <em>:)</em>

4 0

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Which is the correct fair share for the

Fantom [35]

It is 1/3
Bc there is 3 c

7 0

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