f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20

Three roots of this polynomial function are −1, 1, and 3 + i.

Which of the following describes the number and nature of all the roots of this function?


f (x) has two real roots and one imaginary root.

f (x) has three real roots.

f (x) has five real roots.

f (x) has three real roots and two imaginary roots.

The equation of the line is:

[tex]y=\frac{-1}{2}x-26[/tex]

The point-slope equation of a line is given as:

[tex]y-y_1=m(x-x_1)[/tex]

where m represents the slope, and is calculated as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For the line passing through the points (-32, - 10) and (-74, 11)

[tex]x_1=-32, y_1=-10, x_2=-74, y_2=11[/tex]

Substitute these points into the slope formula to get the slope of the line

[tex]m=\frac{11-(-10)}{-74-(-32)} \\\\m=\frac{11+10}{-74+32} \\\\m=\frac{21}{-42} \\\\m=\frac{-1}{2}[/tex]

Substitute [tex]m=\frac{-1}{2}, x_1=-32, y_1=-10[/tex] into the line equation

[tex]y-(-10)=\frac{-1}{2}(x-(-32))\\\\y+10=\frac{-1}{2}x-16\\\\y= \frac{-1}{2}x-16-10\\\\y=\frac{-1}{2}x-26[/tex]

The equation of the line is:

[tex]y=\frac{-1}{2}x-26[/tex]

Learn more on equation of a line here: https://brainly.com/question/13763238

Answer:

[tex]\boxed{\sf D)\:-24a^3b^7}[/tex]

Step-by-step explanation:

[tex]\sf (3a^2b^4)(-8ab^3)[/tex]

We'll use rule of exponents to simplify expression.

[tex]\sf 3^1a^2b^4(-8)^1a^1b^3[/tex]

Now, use the commutative property of multiplication.

[tex]\sf 3^1(-8)^1a^2a^2b^4b^4[/tex]

In order to multiply power of the same base, we add their exponents.

[tex]\sf 3^2(-8)^1a^{2+1}b^{4+3}[/tex]

→ Add exponents:

[tex]\sf 3^1(-8)^1a^3b^7[/tex]

→ Multiply 3* -8

[tex]\sf -24a^3b^7[/tex]

__________________________________________

Answer:

hello which grade question i

Answer:

f(-18) = -5

Step-by-step explanation:

Substitute−18forxiny=

1/3 x+1:

y= 1/3x+1

y= 1/3(−18)+1

y=−5(Simplify both sides of the equation)

Answer:

1.) Smith

2.) Johnson

Answer:

Step-by-step explanation:

The most no. of tickets sold is 60.

The pictorial representation of data in the form of vertical or horizontal rectangular bars, whose length is proportional to the data's measurement, is known as a bar graph. Data are typically grouped in this way. Bar charts are another name for them. In statistics, bar graphs are one way to handle data.

Given  the graph between total student and number of ticket sold,

where students shown in Y axis and tickets sold in X axis,

as Shown in graph maximum number of tickets sold are 51 to 60

Hence the maximum number of ticket sold is 60.

Learn more about bar graph;

https://brainly.com/question/13298277

#SPJ2

Answer:

7

Step-by-step explanation:

12-(-3)-2(4)

12-(-3)-8

15-8=7

======================================================

Explanation:

PDF = probability density function

The given joint PDF is

[tex]f(x,y) = \begin{cases}ax \ \ \ \text{ if } 1 \le x \le y \le 2\\0 \ \ \ \ \ \text{ otherwise}\end{cases}[/tex]

Let's focus on the [tex]1 \le x \le y \le 2[/tex]. Specifically the x term for now. Erasing out the y term, we have the inequality [tex]1 \le x \le 2[/tex] which says x is between 1 and 2, inclusive. We have almost the same story for y, but there's another condition attached to it: y must also be equal to or larger than x.

So let's say x = 1.5. This would mean [tex]1.5 \le y \le 2[/tex]. As another example, x = 1.7  leads to [tex]1.7 \le y \le 2[/tex]. In general, we would say [tex]x \le y \le 2[/tex] where x is between 1 and 2.

As x gets bigger, the range of possible y values gets smaller. If x = 2, then y has no choice but to be 2 as well.

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

Based on that, we'll have a double integral that looks like this:

[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\[/tex]

The outer integral handles the x terms that range from 1 to 2, describing [tex]1 \le x \le 2[/tex]. Note the dx on the outside. The order of the dy and dx matters.

On the inside, we have the integral for dy ranging from x to 2 to describe the interval [tex]x \le y \le 2[/tex]

To have f(x,y) be a PDF, the volume under the f(x,y) surface must be 1, where the volume is based on the bounds set up. So we must have V = 1. We'll use this later.

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

Let's simplify the double integral.

We'll start by computing the inner integral with respect to y.

[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\\displaystyle V = \int_{1}^{2}\int_{x}^{2}\left(ax\right)dydx\\\\\displaystyle V = \int_{1}^{2}\left(axy\Bigg|_{x}^{2}\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(ax(2) - ax(x)\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\[/tex]

Then we'll finish it off by integrating with respect to x.

[tex]\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\\displaystyle V = \left(ax^2 - \frac{1}{3}ax^3\right)\Bigg|_{1}^{2}\\\\\displaystyle V = \left(a(2)^2 - \frac{1}{3}a(2)^3\right) - \left(a(1)^2 - \frac{1}{3}a(1)^3\right)\\\\\displaystyle V = \left(4a - \frac{8}{3}a\right)-\left(a - \frac{1}{3}a\right)\\\\[/tex]

[tex]\displaystyle V = 4a - \frac{8}{3}a-a + \frac{1}{3}a\\\\\displaystyle V = 3a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9}{3}a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9-8+1}{3}a\\\\\displaystyle V = \frac{2}{3}a\\\\[/tex]

Side note: We don't have to worry about the "plus C" integration constant when working with definite integrals.

Recall that V = 1. So,

[tex]\displaystyle V = \frac{2}{3}a\\\\\displaystyle \frac{2}{3}a = 1\\\\\displaystyle a = \frac{3}{2} = 1.5\\\\[/tex]

a = 3/2 is the final answer.

The volume of the storage room is the amount of space in the storage room, and it is 720 cubic feet

The dimensions are given as:

[tex]Width = 6ft[/tex]

[tex]Depth = 10ft[/tex]

[tex]Height = 12ft[/tex]

The volume of the storage room is the product of the dimensions.

So, we have:

[tex]Volume= Width \times Depth \times Height[/tex]

Substitute values for Width, Depth and Height

[tex]Volume= 6ft \times 10ft \times 12ft[/tex]

Multiply the dimensions

[tex]Volume= 720ft^3[/tex]

Hence, the volume of the storage room is 720 cubic feet

Read more about volumes at:

https://brainly.in/question/2593668

100 mph per hour

Step-by-step explanation:

solution

speed of auto mobile=50mph

distance already traveled when the airplane took out in pursuit=200miles

time taken to overtake the car=4 hours

Now,

let the speed of airplane be X

X=50×4+200

or,X=200+200

or,X=400

or, X=400÷4

Therefore, X=100

Answer:

The answer is y= 100 +15x

Step-by-step explanation:

You start with a service fee of $100

$15 per hour

x because the amount of hours can vary

y which is the total cost

y= 100+ 15x

Answer:

113

Step-by-step explanation:

The supplement of angle 3 is congruent to 67, because they are corresponding angles. After you subtract the supplement from 180, you should get angle 3

180-67=113

Answer:

∠3 measures 113°

Step-by-step explanation:

These are consecutive interior angles. It's difficult to explain in words because none of the lines are marked in any way, but I marked the angles in the attached image. Because both downward facing lines are parallel, both sets of corresponding red and blue angles are congruent.

∠3 corresponds to the angle supplementary to the 67° angle. Supplementary angles add up to 180°, so ∠3 and 67° also have to add up to 180°. Hopefully my image makes that a little more clear.

[tex]x+67=180\\x=113[/tex]

∠3 measures 113°

Answer:

so you just use the equation to get the formula and extract the common denominator

Step-by-step explanation:

because i said so

Answer:W= B-3 or 3=B-W

Step-by-step explanation:

Answer:

A. (A) Yes

B. (A) Yes

C. (B) No

Step-by-step explanation:

A is Categorical because it is not based on numbers.

B is Categorical because it is not based on numbers.

C is Not Categorical because it is based on numbers.

Answer:

AOB forms must be collected every time a beneficiary fills a Medicare part b prescription

Answer:

12

Step-by-step explanation:

You do 6+6, or 2+2+2+2+2+2=12

Step-by-step explanation:

several possibilities to solve this.

let's start with subtracting the second equation from the first

-x + 2y - z = 0

- -x - y +2z = 0

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

0 3y - 3z = 0

y - z = 0

y = z

now we use this in e.g. the first equation :

-x + 2z - z = 0

-x + z = 0

z = x (therefore, also x = y)

now we use this in the third equation :

2x - x = 8

x = 8 = y = z

Answer:

-1/2 + i/10 sqrt(55)  , -1/2 - i/10 sqrt(55)

Step-by-step explanation:

5x^2+5x+4=0

a=5  b= 5  c=4

Using the quadratic formula

-b ± sqrt( b^2 -4ac)

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

  2a

-5 ± sqrt( 5^2 - 4(5)(4))

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

2(5)

-5±sqrt( 25 - 80)

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

10

-5± sqrt(-55)

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

10

-5/10  ± 1/10  i sqrt(55)

-1/2 + i/10 sqrt(55)  and -1/2 - i/10 sqrt(55)

Answer:

x= -5 ± i√55 / 10

Step-by-step explanation:

hope i helped

Using fractions, it is found that of the students that went camping, [tex]\mathbf{\frac{23}{84}}[/tex] were at Lake Camp.

The students who went camping are divided according to the following fractions:

The sum of all these fractions is 100% = 1, hence:

[tex]\frac{1}{7} + \frac{1}{3} + \frac{1}{4} + x = 1[/tex]

[tex]\frac{12 + 28 + 21 + 84x}{84} = 1[/tex]

[tex]84x + 61 = 84[/tex]

[tex]84x = 23[/tex]

[tex]x = \frac{23}{84}[/tex]

Of the students that went camping, [tex]\mathbf{\frac{23}{84}}[/tex] were at Lake Camp.

A similar problem is given at https://brainly.com/question/24372153

Answer:

half-class

Step-by-step explanation:

Answer:

42.86%

Step-by-step explanation:

Event = Girl

Therare 6 girls and 8 boys, which are thus 6+8 =14 students in total and thus there are 14 possible out comes.

# of possible outcomes = 14

There are 6 girls in the class and thus there are 6 favorable outcomes.

# of favorable outcomes = 6

The probability is the number of favorable outcomes divided by the number of possible outcomes.

P(Girl) = # of favorable outcomes

            # of possible outcomes

= [tex]\frac{6}{14}[/tex]

= [tex]\frac{3}{7}[/tex]

≈ 0.4286

= 42.86%

Result

[tex]\frac{3}{7}[/tex] ≈ 0.4286 = 42.86%

Answer:

Down, Down, Right, Right, diagonal left, up, right

Step-by-step explanation:

Not gonna do every equation here tho lol

Answer:

18/100 or 9/50

Step-by-step explanation:

First, put 0.18 over 100 because there are 2 digits in the decimal, so you convert it to 18/100. Then, simplify it, and because the GCF is 2, divide the numerator and denominator. The final fraction ins 9/50.

Answer:

i guess it's will be C

Step-by-step explanation:

Answer:

Step-by-step explanation:

An example of one fraction that does NOT terminate is 2/3.

2/3 = 0.666666666666666 ....  That's the easy way to tackle the problem. Pick out the ones that don't terminate.

5/7 is the other one. It does not terminate either. It has 6 digits in a block that keeps on repeating itself forever.

5/7 = .571428 571428 which goes on forever.

So the two that do terminate are

3/2 which = 1.5

3/4 which = 0.75

Answer:

The first recipe - 3/4 tsp of salt in 1 cup of water

Step-by-step explanation:

1st recipe Salt per cup = 3/4 tsp / 1 cup = 3/4 tsp salt

2nd recipe Salt per cup = 1 tsp / 2 cups = 1/2 tsp salt

3/4 tsp > 1/2 tsp, hence the first recipe is saltier

If my calculations are correct, the percentage decrease faced here is roughly 38.2%. Based on the calculations, the bicycle costs 199$ and when the cost is subtracted from 520, you would create the percentage of 38.2%.