Answers
Given:
• Degree of polynomial = 3
,• Zeros of the polynomial: 2, 3 - 2i
Let's find the polynomial.
Since the polynomail is of degree 3, it's highest exponent will be 3.
Equate the zeros to zero:
x = 2
Subtract 2 from both sides:
x - 2 = 2 - 2
x - 2 = 0
x = (3 - 2i)
Since this root is a complex conjugate, we have the other complex root: (3 + 2i)
Hence, we have:
(x - (3 - 2i)) and (x - (3 + 2i)).
Therefore, to write the function, we have:
[tex]f(x)=(x-2)(x-(3-2i))(x-(3+2i))[/tex]Now, simplify the expression:
[tex]\begin{gathered} f(x)=(x-2)(x-3+2i)(x-3-2i) \\ \\ f(x)=x(x-3+2i)-2(x-3+2i)(x-3-2i) \\ \\ f(x)=x^2-3x+2ix-2x+6-4i(x-3-2i) \\ \\ f(x)=x^2-5x+2ix-4i+6(x-3-2i) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} f(x)=x(x^2-5x+2ix-4i+6)-3(x^2-5x+2ix-4i+6)-2i(x^2-5x+2ix-4i+6) \\ \\ f(x)=x^3-5x^2+2ix^2-4ix+6x-3x^2+15x-6ix+12i-18-2ix^2+10ix-4i^2x-8-12i^{} \end{gathered}[/tex]Combine like terms:
[tex]\begin{gathered} f(x)=x^3-5x^2-3x^2-4ix-6ix+10ix+2ix^2-2ix^2+6x+15x+12i-12i-8-16 \\ \\ f(x)=x^3-8x^2+25x-26 \end{gathered}[/tex]ANSWER:
[tex]f(x)=x^3-8x^2+25x-26[/tex]Related Questions
what is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters? round to the nearest hundred
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Right triangular pyramid
base = 5 meters
altitude = 4 meters
Volume = ?
Step 02:
The volume of a right triangular pyramid
V = 1/3 B * h
B = 1/2 b * h
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\cdot5m\cdot4m \\ B=\text{ }10m^2 \end{gathered}[/tex][tex]V\text{ = }\frac{1}{3}\cdot10m^2\cdot4m=\text{ }13.3333m^3[/tex]The answer is:
The volume of the pyramid is 13.33 m³.
There is one male snake, and the rest are female. She needs one vitamin pill for every female snake. How many vitamin pills does she need if the number of snakes is: a. 10b. 6C. X
Answers
We are told that there is one male snake, and the rest are female.
She needs one vitamin pill for every female snake.
1. If there are 10 snakes, this means that if one is male, the number of female snakes are:
[tex]10-1=9\text{ females}[/tex]Sine one vitamin pill is needed for each female snake, she would need 9 vitamin pills.
2. If there are 6 snakes, this means that if one is male, the number of female snakes are:
[tex]6-1=5\text{ females}[/tex]Sine one vitamin pill is needed for each female snake, she would need 5 vitamin pills.
3. If there are X snakes, this means that if one is male, the number of female snakes are:
[tex]X-1=(X-1)\text{ females}[/tex]Sine one vitamin pill is needed for each female snake, she would need (X-1) vitamin pills.
Explain how you found the diagonal length of the package.
Answers
First find diagonal of base D =√( 10^2 + 10^2)= √200
Then find diagonal lenght L = √ (D^2 + 10^2) = √ (200 + 100) =√300
L= √300 = √3•√100 = √3• 10
L= √3•10 = 10•√3 (by conmutative property)
#24Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.
Answers
We have the function:
g(x) = x/(x - 2)
Notice that if x = 2 the denominator equals zero and then we have a vertical asymptote at x = 2. Furthermore, if x = 0, g(0) = 0.
The graph of g(x) is shown below:
As you can notice, there is no a discontinuity at x = 0.
when taking a 19 question multiple choice test ,where each question has 3 possible answers ,it would be unusual to get or more questions correct by guessing alone consider "unusual " to be more than two standard deviations away from expected.
Answers
we have that
You have 1 in 3 probability of guessing the correct answer for a single question
you have 19 opportunities to guess
so
19*(1/3)=19/3=18/3+1/3=6 1/3
therefore
would be unusual to get 7 or more questions correct by guessing alone
A line passes through the point −6, 3 and has a slope of 32 .Write an equation in slope-intercept form for this line.
Answers
The equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195.
What is the slope - intercept form of the equation of a straight line?
The slope - intercept form of the equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that passes through the point (−6, 3) and has a slope of 32.
We know that the slope - intercept form can be written as -
y = mx + c
Now, the slope of the line = [m] = 32
Since, the line passes through the point (-6, 3), we can write -
3 = 32 x -6 + c
3 = -192 + c
c = 3 + 192
c = 195
So, the equation of the straight line that passes through the point (-6, 3) will be -
y = 32x + 195
Therefore, the equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195
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How do I graph a line with a equation in slope intercept form?An example is y=-3x+3, how do I graph this?
Answers
we have
y=-3x+3
to graph a line we need at least two points
so
Find out the intercepts
y-intercept (value of y when the value of x is zero)
For x=0
y=-3(0)+3
y=3
y-intercept is (0,3)
x-intercept (value of x when the value of y is zero)
For y=0
0=-3x+3
3x=3
x=1
x-intercept is (1,0)
therefore
Plot the points (0,3) and (1,0)
and join them to graph the line
see the attached figure to better understand the problem
32. Challenging. Read this one very carefully. Carla runs a small business where she makes artificial flower arrangements. A customer has placed a large order for 100 identical arrangements. Carla has made a list of supplies that she needs to make the entire order. Each arrangement needs a plastic molding. It will cost Carla $3.25 for each plastic molding. She also needs 4 packages of colored netting, which sell for $15.00 each. However, the company she orders from has a special on the netting packages. If you buy 3 packages of netting, you get a package for free. Polyester fabric is another item she will need. She needs 180 square feet of polyester fabric that sells for $5.20 per square yard. Lastly she needs artificial stems. She will need 6 stems per arrangement and they are sold in packs of 10. The cost for one pack of artificial stems is $2.50. if Carla sells each arrangement for $20.00,How much money will Carla make off the order once she subtracts her expenses for the supplies.
Answers
Substract expenses
Carlas expenses are
1. 100 Arrangements
2. Plastic molding PM = 3.25
3. Colored netting CN = 15
4. Four packages netting = 3 packages
5. 180 feet2 ,. 1 yard2=5.20
6. 10 stems = 2.5x10 = $25
7. Arrangement price AP = 20.00
Then substract
20 minus 3.25 = 16.75
16.75 x100= $1675
4. 4 packages nettingx 15 = $60 - $15 = $45
5. Now
In 180 feet2 ,there are 60 yards2
then polyester price is 60x5.2= $312
6. She needs 100x6= 600 stems
600/10 = 60 packs
60 packs x 2.50= $150
Then answer is
Carla's money = 1675 - 45 - 312 - 150 = $1168 dollars
Determine the midpoint between A(2,13) and O (-4,3)
Answers
The midpoint between two points can be found by averaging their coordinates. This is done below:
[tex]\begin{gathered} x_m\text{ = }\frac{x_1+x_2}{2} \\ y_m\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Using the above expressions we can apply the coordinates of the points we want to find, A(2,13) and O(-4,3).
[tex]\begin{gathered} x_m\text{ = }\frac{2\text{ -4}}{2} \\ x_m\text{ = }\frac{-2}{2} \\ x_m\text{ = -1} \end{gathered}[/tex][tex]\begin{gathered} y_m\text{ = }\frac{3+13}{2} \\ y_m\text{ = }\frac{16}{2} \\ y_m\text{ = 8} \end{gathered}[/tex]The coordinates of the midpoint are (-1,8).
what is the value of x of the perimeter of the following figure is 30 miles?
Answers
The Solution:
Given:
We are required to find the value of x if the perimeter is 30 miles.
[tex]Perimeter=2(3x-8)+2(6x+5)=6x-16+12x+10=30[/tex][tex]\begin{gathered} 6x+12x-6=30 \\ \\ 18x=30+6 \\ \\ 18x=36 \end{gathered}[/tex]Divide both sides by 18.
[tex]\begin{gathered} x=\frac{36}{18}=2 \\ \\ x=2 \end{gathered}[/tex]Therefore, the correct answer is 2.
Consider the following system of equations.ſ x - 4y = -34x - 2y = -12Step 2 of 2: Determine if the point (3, 1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Answers
Given:
x - 4y = -3
4x - 2y = -12
To determine if the point (3, 1) lies on both of the lines in the system of equations:
Substitute (3, 1) in the first equation, we get
3 - 4(1) = -3
3 - 4 =-3
-1 = -3
But,
[tex]-1\ne-3[/tex]Substitute (3, 1) in the second equation, we get
4(3) - 2(1) = -12
12 - 2 = -12
10 = -12
But,
[tex]10\ne-12[/tex]Hence, the answer is, No.
The point (3, 1) does not lie on both of the lines in the system of equations.
The population of Canada, as estimated every five years since 1960, is shown in the table. 1. . Calculate the finite differences for the data set.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data set
STEP 2: Find the finite difference
We first find the differences in the output values which is the population as seen below
[tex]\begin{gathered} 19.68-17.91=1.77 \\ 21.32-19.68=1.64 \\ 23.21-21.32=1.89 \\ 24.59-23.21=1.38 \\ 25.94-24.59=1.35 \\ 27.79-25.94=1.85 \\ 29.35-27.79=1.56 \\ 30.77-29.35=1.42 \\ 32.31-30.77=1.54 \\ 34.01-32.31=1.70 \\ 35.75-34.01=1.74 \end{gathered}[/tex]STEP 3: Find the second order difference
[tex]\begin{gathered} 1.64-1.77=-0.13 \\ 1.89-1.64=0.25 \\ 1.38-1.89=-0.51 \\ 1.35-1.38=-0.03 \\ 1.85-1.38=0.47 \\ 1.56-1.85=-0.29 \\ 1.42-1.56=-0.14 \\ 1.54-1.42=0.12 \\ 1.70-1.54=0.16 \\ 1.74-1.70=0.04 \end{gathered}[/tex]STEP 4: Find the third order difference
[tex]undefined[/tex]Solve the given quadratic inequality. Write the answer in interval notation.
Answers
Which angles are adjacent to each other? Select all that apply.
Answers
Answer:
I think it's all the options but I cant confirm.
Step-by-step explanation:
adjacent angles are angles that:
- have the same vertex
- share one side
What is the value of the trig ratio sin A?
Answers
The sine relation is given by the length of the opposite leg to the angle over the length of the hypotenuse.
So, for the given triangle, we have:
[tex]\begin{gathered} \sin A=\frac{BC}{AC}\\ \\ \sin A=\frac{20}{29} \end{gathered}[/tex]Therefore the value of sin A is 20/29.
What is the x-intercept of the line y=-2x+6? (3,0) -6,0) (0,3) (-3,3)
Answers
The given equation is expressed as
y = - 2x + 6
The x intercept of a line is the point at which y = 0
By applying this concept, it means that
0 = - 2x + 6
Adding 2x to both sides of the equation, it becomes
0 + 2x = - 2x + 2x + 6
2x = 6
Dividing both sides by 2, it becomes
2x/2 = 6/2
x = 3
Therefore, the correct option is (3, 0)
Complete the equation, and tell which property you used.7. (3 X 10) X 8 = X (10 X 8)8. 16 + 31 = 31 +9. 0 +__= 9110. 21 x__= 9 X 21Problem Solving(RealWorld11. The Metro Theater has 20 rows of seats with 18seats in each row. Tickets cost $5. The theater'sincome in dollars if all seats are sold is (20 X 18)X 5. Use properties to find the total income.12. The numbers of students in the foursixth-grade classes at Northside School are 26,19, 34, and 21. Use properties to find the totalnumber of students in the four classes.
Answers
7. (3 X 10) X 8 = 3 X (10 X 8)
In this case, we use the associative property of the multiplication (you can group the factors in any way).
8. 16 + 31 = 31 + 16
Commutative property.
9. 0 + 91 = 91
Identity property
10. 21 x 9 = 9 X 21
Commutative property
11. The income is (20 * 18) * 5.
We can multiply the three numbers together, using the associative property.
20 * 18 * 5 = 1800
12. In this case, we have to add each of the groups:
26 + 19 + 34 + 21 = 100
We don't need to apply any properrty in particular. We can add them in any order taking into account the commutative property.
A manufacturing company currently uses 15 workers to load and unload trucks. Each worker can move an average of 15 boxes per minute. A robotics firm has built a robot that can load and unload boxes at the rate of 21 boxes per minute. How many robots will it take to do the same job as the 15 humans?
Answers
It will take 11 robots to do the same job as the 15 humans
Explanation:Given:
Workers in use = 15
Each worker can move an average of 15 boxes per minute.
A robot has been built that can move an average of 21 boxes per minute
15 worker would move:
15 * 15 boxes = 225 boxes per minute.
The number of robots it will take to move 225 boxes is:
225/21 = 10.7
It will take 11 robots to do the same job as the 15 humans
What is an
equation of the line that passes through the points (5, 7) and (-5, -1)?
Answers
Answer:
y - 7 = 0.8(x - 5) ory = 0.8x + 3Step-by-step explanation:
Given2 points (5, 7) and (- 5, - 1)To findEquation of the line passing through the given pointsSolutionFind the slope of the line using slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\dfrac{-1-7}{-5-5}=\dfrac{-8}{-10}=0.8[/tex]Use one of the points and the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex][tex]y-7=0.8(x-5)[/tex]This can be converted to slope-intercept form:
[tex]y = mx + b[/tex][tex]y -7=0.8(x-5)[/tex][tex]y -7=0.8x-0.8*5[/tex][tex]y -7=0.8x-4[/tex][tex]y =0.8x-4+7[/tex][tex]y=0.8x+3[/tex]Bao is mixing flour and water to make dough the graph shows how much water he uses for different amounts of flour .How many liters of water does Bao use per liter or flour?------ liters for this one your answer should be a simplified proper fraction like 3/5.How many liters of flour does Bao use per liter of water?------ liters.
Answers
To know how many liters of water Bao use per liter of flour we have to divide the liters or flour so:
[tex]\frac{1}{3}=0.33[/tex]So Bao uses 0.33 or 1/3 of water per liter or flour
and to know hoy manu liters of flour Bao use per liter of water we have to made the oposite division so:
[tex]\frac{3}{1}=3[/tex]She use 3 liters of flour per liter of water
the bakers want to sell their house for 145,500.After 2 months,the bakers decided to mark down the price of their house 8% to sell more quickly. How much are the bakers selling their house for now?
Answers
Answer:
133,860
Step-by-step explanation:
The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".
* No we have our key elements:
- Starting amount = 145,500
- Rate of change = 8%
* We will get the "8%" of the number 145,500
- Firstly, "8%" means 8/100
- So, 0.08 will be our new rate of change.
* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.
- 145,500 × 0.08 = 133,860 ; the same as
145,500 × 8/100 = 133,860
An elliptical-shaped path surrounds a garden, modeled by quantity x minus 20 end quantity squared over 169 plus quantity y minus 18 end quantity squared over 289 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?
Answers
In general, the equation of an ellipse centered at (h,k) and axis equal to a and b, and parallel to the y-axis is
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1,a>b[/tex]And the maximum distance between two points on the ellipse is equal to the length of the major axis; in our case,
[tex]\begin{gathered} a^2=289,b^2=169 \\ \Rightarrow a=17,b=13 \end{gathered}[/tex]Therefore, the answer is 17 feet, the major axis.
Exact value of tan 2pi/3
Answers
Given:
[tex]\tan\frac{2\pi}{3}[/tex]Find-:
Exact value
Explanation -
So, the value is:
[tex]=\tan\frac{2\pi}{3}[/tex][tex]\begin{gathered} =\tan\frac{2\pi}{3} \\ \\ \pi=180\text{ then,} \\ \\ =\tan(\frac{2\times180}{3}) \\ \\ =\tan(120) \end{gathered}[/tex]So value is:
[tex]\tan(120)=-\sqrt{3}[/tex]What is the slope of (-8, -3) and (-7, -6)
Answers
To find the slope, we use the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the given points.
[tex]m=\frac{-6-(-3)}{-7-(-8)}=\frac{-6+3}{-7+8}=\frac{-3}{1}=-3[/tex]Hence, the slope is -3.For the equation 5x+36=x, Which value could be a solution
Answers
Solution;
[tex]\begin{gathered} 5x+36=x \\ 5x-x+36=x-x \\ 4x+36=0 \\ \end{gathered}[/tex][tex]\begin{gathered} 4x+36-36=0-36 \\ 4x=-36 \end{gathered}[/tex][tex]x=-\frac{36}{4}=-9[/tex]x=-9
4+4x=2x+8+2x-5 help please
Answers
Simplify the expression.
[tex]\begin{gathered} 4+4x=2x+8+2x-5 \\ 4x-2x-2x=8-5-4 \\ 0=-1 \end{gathered}[/tex]Thus, the equation is solved.
NO LINKS!! Show all work where necessary to get full credit Part 2
Answers
21. Circle R
A circle is named using its center.22. RV
A radius connects the center to a point on the circle.23. ZV
A chord connects two points on the circle.24. TX
A diameter passes through the center of the circle and connects two points on the circle.25. RV
See 22 and 24.26. 4 feet
The diameter is twice the radius, 2(2)=4.Answer:
21. R
22. RU
23. VZ
24. BE
25. RU
26. 4 feet
Step-by-step explanation:
Question 21
A circle is named by its center.
Therefore the name of the given circle is R.
Question 22
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
RZ, RT, RU, RV, RW and RX.Question 23
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
WZ, TX and VZ.Question 24
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameters of the given circle are:
TX and WZ.Question 25
As the diameters are TX and WZ, they contain the radii RZ, RT, RW and RX.
Therefore, the radii that are not contained in the diameter is:
RU and RV.Question 26
The diameter is twice the length of the radius.
Therefore, if the radius of the circle is 2 feet:
⇒ Diameter = 2 × 2 = 4 feet.
How is the input force different from the output force?
Responses
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is applied to the problem, and the output force is the movement that results.
The input force is applied to the problem, and the output force is the movement that results.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
Answers
The input force different from the output force is D. The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
What is a simple machine?A simple machine is a mechanical device that alters the magnitude or direction of a force. In general, they are the most basic systems that exploit mechanical advantage to multiply force.
A simple machine is a mechanical device that adjusts the direction or amplitude of a force. According to Newton's third law, if object A exerts a force on object B, object B will exert a force of same size and opposite direction on object A.
In that situation, the input force is done by object A, and the output force is done by object B as a reaction.
With this in mind, we can see that the proper answer is: "The input force is applied to the simple machine, and the output force is the force applied to an item."
Learn more about force on:
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Find the missing side of this righttriangle.x816x= V[?]=Enter the number that belongs in the green box.Enter
Answers
As gien by the question
There are given that the right angle triangle.
Now,
To find the value of x, use Pythagoras theorem:
So,
From the Pythagoras theorem;
[tex]\begin{gathered} x^2+8^2=16^2 \\ x^2+64=256 \\ x^2=256-64 \\ x=\sqrt[]{192} \end{gathered}[/tex]Hence, the value of x is shown below:
[tex]x=\sqrt[]{192}[/tex]At Joe's Café 1 cup of coffee and 3 doughnuts cost $7.54, and 2 cups of coffee and 2 doughnuts cost $8.32. What is thecost of 1 cup of coffee?
Answers
To answer this question, we can proceed as follows:
1. Let x be the cost of a cup of coffee.
2. Let y be the cost of a doughnut.
Then, we can express the question, algebraically, as follows:
[tex]\begin{cases}x+3y=7.54 \\ 2x+2y=8.32\end{cases}[/tex]Now, we can solve this linear equation system by