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3 years ago

How many no real complex roots does the polynomial f (x) = x^4 - x^2- 12 have?

Mathematics

1 answer:

asambeis [7]3 years ago

6 0

<h3>Answer:</h3>

2 real roots
2 complex roots

<h3>Step-by-step explanation:</h3>

f(x) factors as ...

... f(x) = (x² -4)(x² +3) = (x -2)(x +2)(x² +3)

The real roots are x = ±2.

The complex roots are x = ±i√3.

___

We don't know what "no real complex roots" means. We suspect your answer may be C. 2.

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the ratio of boys to girls in janices classroom is 3:5, and there are a total of 32 students in the class, help plss

svetoff [14.1K]

9514 1404 393

Answer:

12 boys
20 girls

Step-by-step explanation:

The total number of students (32) corresponds to the total number of ratio units (3+5 = 8), so each ratio unit represents 32/8 = 4 students.

The 3 ratio units representing boys will stand for 3×4 = 12 boys.

The 5 ratio units representing girls will stand for 5×4 = 20 girls.

There are 12 boys and 20 girls in Janice's classroom.

_____

<em>Additional comment</em>

I find the above solution to be the easiest.

You can also write a system of equations. Let b and g represent the numbers of boys and girls, respectively.

b/g = 3/5

b +g = 32

Multiplying the first equation by g gives an expression for b that can be substituted into the second equation:

b = (3/5)g

(3/5)g +g = 32

8/5g = 32 . . . . . . . . . . . . . . . . . collect terms

g = (5/8)(32) = 5·4 = 20 . . . . . . multiply by 5/8

b = (3/5)(20) = 3·4 = 12 . . . . . . . find b using the value of g

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2 years ago

A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation

Rzqust [24]

Answer: 0.6065

Step-by-step explanation:

Given : The machine's output is normally distributed with

$\mu=27\text{ ounces per cup}$

$\sigma=3\text{ ounces per cup}$

Let x be the random variable that represents the output of machine .

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 21 ounces

$z=\dfrac{21-27}{3}\approx-2$

For x= 28 ounces

$z=\dfrac{28-27}{3}\approx0.33$

Using the standard normal distribution table , we have

The p-value : $P(21$

$P(z$

Hence, the probability of filling a cup between 21 and 28 ounces= 0.6065

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3 years ago

Find the distance between the pair of coordinates: (-4, -3) and (-8, 7). A 10.77 B 3.74 C 04 D 12.65 Question

kenny6666 [7]

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8 - (-4)]^2 + [7 - (-3)]^2}\implies d=\sqrt{(-8+4)^2 + (7+3)^2} \\\\\\ d=\sqrt{(-4)^2 + 10^2}\implies d=\sqrt{116}\implies d\approx 10.77$

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2 years ago

A function g(x) is defined as shown.

FromTheMoon [43]

Answer:

g(4) = 12

Step-by-step explanation:

We need to find the value the function g(x) when x = 4, that is;

g(4)

In the first definition of the function, the value of x is strictly less than 4. Consequently, we shall use the second definition of the function to evaluate g(4)

In the second definition, g(x) is given as;

Q(x) = 0.5x + 10

plug in x = 4 and simplify;

Q(4) = 0.5(4) + 10

Q(4) = 12

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3 years ago

High Points!!!

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

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3 years ago