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2 years ago

Use the Factor Theorem to determine whether x + 1 is a factor of P(x) = 2x³+4x²–2x−8.

Mathematics

1 answer:

Harman [31]2 years ago

5 0

Answer: $2x^2+2x-4-\frac{4}{x+1}$

Not a factor because there is a remainder.

Step-by-step explanation:

Let's use synthetic division to solve this..

-1 ║ 2 | 4 | -2 | -8

║ | -2| -2 | 4

║ 2 | 2| -4 | -4

$2x^2+2x-4-\frac{4}{x+1}$

PS: if anyone knows a better way to do a synthetic division chart please let me know.

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Which of the following functions illustrates a change in amplitude?

OLEGan [10]

Answer:

Correct option is A.

Step-by-step explanation:

Given the following functions we have to choose the option which illustrates a change in amplitude.

Multiplying a sine or cosine function by a constant changes the graph of the parent function i.e results in change in the amplitude of function. Amplitude is the measure of distance from the sinusoidal axis to the maximum or the minimum.

Option A: y = 3cos4x

The parent function is f(x) = cos x.

The amplitude of function changes from 1 to 3.

Option B: y = 1+sinx

The parent function is f(x) = sin x

The amplitude remains same i.e 1

Option C: y = -2-cos(x - pi)

Here also remains same.

Option D: y = tan 2x

The tangent function does not have an amplitude because it has no maximum or minimum value.

Hence, correct option is A.

7 0

4 years ago

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A container holds 4800 cubic inches of waste. The dimensions of the container are tripled. How many cubic feet

Ray Of Light [21]

This is a 3-D container and the dimensional factor is F=3. The volume increases by a factor of 33 = 27.

The answer is 4608 x 27 / 123 = 72

4 0

2 years ago

What is the missing length???

Kaylis [27]

Answer:

Step-by-step explanation:

144/60 = 2.4

60/2.4 = x

x = 25

8 0

3 years ago

Plzz help will mark brainliest don't do it for the points plzz!!!!

Maru [420]

Answer:

Your answer will be A. positive correlation

Step-by-step explanation:

hope this helps :)

7 0

3 years ago

The heights of women in the USA are normally distributed with a mean of 64 inches and a standard deviation of 3 inches.

Rainbow [258]

Answer:

(a) 0.2061

(b) 0.2514

Step-by-step explanation:

Let <em>X</em> denote the heights of women in the USA.

It is provided that <em>X</em> follows a normal distribution with a mean of 64 inches and a standard deviation of 3 inches.

(a)

Compute the probability that the sample mean is greater than 63 inches as follows:

$P(\bar X>63)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}>\frac{63-64}{3/\sqrt{6}})\\\\=P(Z>-0.82)\\\\=P(Z$

Thus, the probability that the sample mean is greater than 63 inches is 0.2061.

(b)

Compute the probability that a randomly selected woman is taller than 66 inches as follows:

$P(X>66)=P(\frac{X-\mu}{\sigma}>\frac{66-64}{3})\\\\=P(Z>0.67)\\\\=1-P(Z$

Thus, the probability that a randomly selected woman is taller than 66 inches is 0.2514.

(c)

Compute the probability that the mean height of a random sample of 100 women is greater than 66 inches as follows:

$P(\bar X>66)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}>\frac{66-64}{3/\sqrt{100}})\\\\=P(Z>6.67)\\\\\ =0$

Thus, the probability that the mean height of a random sample of 100 women is greater than 66 inches is 0.

8 0

3 years ago