find a polynomial f(x) of degree 3 with real coefficients and the following zeros -1, 3-i
The least polynomial that contains the roots - 1 and 3 - i is x³ - 5 · x² + 4 · x + 10.
What is the least polynomial that contains a given set?
In this case we need to find a polynomial that contains a set of roots, a real root and a complex root. In accordace to the quadratic formula, the root 3 - i must be accompanied by its conjugate, that is, 3 + i to guarantee that all coefficients of the polynomial are real.
Then, the factor form of the cubic equation is:
f(x) = (x + 1) · (x - 3 + i) · (x - 3 - i)
f(x) = (x + 1) · [x² - (3 - i) · x - (3 + i) · x + (3 - i) · (3 + i)
f(x) = (x + 1) · (x² - 3 · x + i x - 3 · x - i x + 9 - i²)
f(x) = (x +1) · (x² - 6 · x + 10)
f(x) = x³ - 6 · x² + 10 · x + x² - 6 · x + 10
f(x) = x³ - 5 · x² + 4 · x + 10
The least polynomial is x³ - 5 · x² + 4 · x + 10.
To learn more on least polynomials: https://brainly.com/question/25667747
#SPJ1
in the diagram below the lager angle is 4 times bigger than the smaller angle.find larger angle
Let the smaller angle be
[tex]=x[/tex]The larger angle is 4 times bigger than the smaller angle means
[tex]\begin{gathered} \text{larger angle =y} \\ \text{Therefore,} \\ y=4\times x \\ y=4x \end{gathered}[/tex]Concept:
The sum of two or more angles on a straight line is always 180°
Therefore,
[tex]x+y=180^0[/tex]By substituting the value of y=4x in the equation above, we will have
[tex]\begin{gathered} x+4x=180^0 \\ 5x=180^0 \\ \text{divide both sides by 5} \\ \frac{5x}{5}=\frac{180^0}{5} \\ x=36^0 \end{gathered}[/tex]substitute the value of x= 36° in y=4x to find the value of the bigger angle
[tex]\begin{gathered} y=4x \\ \text{when x=36} \\ y=4\times36 \\ y=144^0 \end{gathered}[/tex]Hence,
The larger angle is =144 °
OPTION D IS THE CORRECT ANSWER
3(x+3)= x +13 ansewr!
Answer: x=2
Step-by-step explanation:
1. Distribute
2. Subtract 9 from both sides
3. Simplify
4. Subtract x from both sides
5. Simplify
6. Divide both sides by the same factor
7. Simplify
Find the area of 2x-9 + x+5
Answer: 3x-4
Step-by-step explanation: First Simplify, add the numbers 2x-9+x+5=2x-4+x Then combine like terms, 2x-4+x= 3x-4
What sets does -√3,1 and 0 belong to
√2 and -√3 belong to the set of Irrational Numbers.
1 belong to the following sets:
• Rational
,• Whole
,• Natural
,• Integers
0 belongs to the following sets:
• Rational
,• Whole
,• Integers
Mai runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4 laps of the track? Write your answer as an improper fraction
The minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken.
Speed = distance /time
Also, Time = distance/ speed
In this case, the distance is 4 laps of 400 meters, so;
4 x 400=1600 meters
Speed = 250 per minute
Now,
Time =1600 meters /250 meter per minute
= 6,40 minutes is the same 6 minutes 24 seconds
Hence, the minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.
Learn more about speed here;
https://brainly.com/question/7359669
#SPJ1
Select the correct answer from each drop-down menu. a cash card has a starting value of $25. if the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month. the relationship between the number of months after the first year and the amount remaining on the card is . the independent variable is the . the dependent variable is the .
The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)
a) the independent variable is the: Number of month after the first year
b) the dependent variable is the: Amount remaining on the card
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Starting value= $25Decrease= $2.50 per monthWriting the equation according to the information gave, we have:
y = 25 - (2.50x)
Where:
Amount remaining on the card = yNumber of month after the first year = xThe relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Learn more about equation at: brainly.com/question/2972832 and brainly.com/question/27815607
#SPJ4
Find the distance between C & D. C = (8, -3) and D = (-9, -6) CD= [?] Round to the nearest tenth. Hint: Use the distance formula.
The distance between C and D is 17.26 units
What is meant by distance?
Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.
Distance CD = √{(-9-8)² + (-6+3)²}
= √{(-17)² + (-3)²}
= √{289 + 9}
= √298
= 17.26 units
Hence, the distance between C and D is 17.26 units
To know more about distance, click on the link
https://brainly.com/question/12356021
#SPJ9
Answer: 17.3
Step-by-step explanation:
How many solutions does this equation have?
-7k 2k= -9k
no solution
one solution
infinitely many solutions
Submit
Answer:
1 answer
Step-by-step explanation:
when the terms are collected
[tex]4k = 0[/tex]
[tex]k = 0[/tex]
Simplify using the properties of exponents: (x^4 y^-3)^4/x^0y^2
Answer:
Rewrite using the commutative property of multiplication.
2
(
2
x
0
y
2
)
−
3
y
x
3
Anything raised to
0
is
1
.
2
(
2
⋅
1
y
2
)
−
3
y
x
3
Multiply
2
by
1
.
2
(
2
y
2
)
−
3
y
x
3
Rewrite the expression using the negative exponent rule
b
−
n
=
1
b
n
.
2
1
(
2
y
2
)
3
y
x
3
Simplify the denominator.
Tap for more steps...
2
1
8
y
6
y
x
3
Simplify terms.
x
3
4
y
5
Consider the sequence 9, 16, 25, 36, 49, ...
(1) Write down the next two terms of
the sequence.
i) Find, in terms of n, a formula for the n term
of the sequence.
i) Hence, find the 25th term.
Answer:
1) 64 and 81
2) a(n) = (n + 2)^2, where n = 1, 2, 3, ...
3) a(25) = (25 + 2)^2 = 27^2 = 729
Evelyn is 2.5 years younger than James. Two times the sum of their age is 57. Write and solve an equation to find Evelyn age.
The age of Evelyn is 10.5 years finding by the properties of linear equation.
What is linear equation?
A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Let the age of James is x years.
The age of Evelyn is x - 2.5 years
Sum of age of Evelyn and James are x + x - 2.5 = 2x - 2.5
According to question,
2 x (2x - 2.5) = 57
=> 4x - 5 = 57
=> 4x = 57 - 5
=> 4x = 52
=> x = 52/4
=> x = 13
Age of James is 13 years and the age of Evelyn is 13 - 2.5 = 10.5 years.
To learn more about linear equation from the given link
https://brainly.com/question/26310043
#SPJ9
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars? if segment ad ≅ segment cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad ≅ segment cd, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if m∠acd = 90° then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if m∠acd = 90° then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.
To learn more about Perpendicular bisector theorem refer to:
https://brainly.com/question/4137998
#SPJ4
Find length between AC-3,8) and B(5,-4) in simplest radical form:
The Points are in the form (x,y), and they are A(-3,8) and B(5,-4).
The length between two points is:
[tex]\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]In this case:
[tex]\text{length = }\sqrt[]{(-3-5)^2+(8-(-4))^2}=\sqrt[]{(-8)^2+(12)^2}=\sqrt[]{64+144}[/tex][tex]\text{length =}\sqrt[]{208}\text{ = }\sqrt[]{16\cdot13}=4\sqrt[]{13}[/tex]The correct anser is:
[tex]\text{length = 4}\sqrt[]{13}[/tex]3potniIn a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments of equal lengths 8 cm and 2 cm. What is the length of the altitude?O 10 cm
Answer:
[tex]\text{The altitude is 4cm.}[/tex]Step-by-step explanation:
Let's illustrate the situation in a diagram to understand.
In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.
Therefore,
[tex]\begin{gathered} \frac{8}{a}=\frac{a}{2} \\ 2\cdot8=a^2 \\ 16=a^2 \\ a=\sqrt[]{16} \\ a=4\text{ cm} \end{gathered}[/tex]The vertical distance is
. The horizontal distance is
. So the slope can be represented by the ratio
. The ordered pair for the red point on the line is
. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal
please help ill give brainly
.
Answer:
. The horizontal distance
Step-by-step explanation:
The vertical distance is
. The horizontal distance is
. So the slope can be represented by the ratio
. The ordered pair for the red point on the line is
. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal
please help ill give brainly
.
Below is the change received by Julia after buying a magazine.She paid for the magazine using a £10 note. Work out the price of the magazine.
pls provide the picture below, because of that its an incomplete answer
Which equation has the solution x = 5? Select each correct answer. Responses
A) 11 + 6x = 22
B) 3x + 1 = 9
C) 18−2x=9
D) 25/x+4=9
E) x/5 + 5 = 6
F) 32−4x=12
The equation that has the same solution as x = 5 are as follows:
25 / x + 4 = 9x / 5 + 5 = 6 32 - 4x = 12 How to solve equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
In other words, an equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation can be solved as follows:
The equation will have the same solution as x = 5.
Therefore,
25 / x + 4 = 9
subtract 4 from both sides of the equation
25 / x + 4 = 9
25 / x + 4 - 4 = 9 - 4
25 / x = 5
cross multiply
5x = 25
divide both sides by 5
x = 25 / 5
x = 5
x / 5 + 5 = 6
x / 5 = 6 - 5
x / 5 = 1
cross multiply
x = 5
32 - 4x = 12
- 4x = 12 - 32
- 4x = - 20
divide both sides of the equations by - 4
x = -20 / - 4
x = 5
Therefore, the equation with same solution are 25 / x + 4 = 9, x / 5 + 5 = 6 and 32 - 4x = 12
learn more on equation here: https://brainly.com/question/14410653
#SPJ1
what is an equation of the line that passes through the points (5,-6) and (-5,-2)
The equation of line is 11y + 3x + 37 = 0
What is Equation of Line ?
The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
The given points are, (5, -6) and (-5, -2)
To find slope we have formula ,
m = (y2 - y1 ) / (x2 - x1)
where,
(x1, x2) = (5, -6) and,
(y1, y2) = (-5, -2)
Put the values in given formula of slope,
m = (-2 - (-5) ) / (-6 - 5)
m = (-2 + 5) / (-11)
m = - (3/11)
we get the slope, now to find the equation of line.
We know, the equation of the line with slope intercept is
y = mx + b
Now, for x and y value take any point and put it into this equation and find 'b'
let's take (-5, -2)
-2 = -(3/11) * -5 + b
-2 = 15/11 + b
-2 = (15 + 11b) / 11
-22 = 15 + 11b
-22 - 15 = 11b
-37 = 11b
b = -37/11
We got m = - 3/11 and b = -37/11
Now put these value in equation of line and form the equation
y = mx + b
y = -3/11 x - 37/11
11y = -3x - 37
3x + 11y + 37 = 0
Hence, the equation of line is 11y + 3x + 37 = 0
To read more about the Equation of Line.
https://brainly.com/question/18831322
#SPJ13
The Beta club is selling chocolate to raise money for Beta convention. Chocolate bars sell for $1.25 each and chocolate covered almonds sell for $2.00 each. The Beta club needs to raise more than $375 for all members to attend the convention. The students can sell up to 500 bars and covered almonds altogether.
1. Write a system of inequalities that can be used to represent this situation.
2. The club sells 100 chocolate bars. What is the least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention? Justify your answer.
(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
In the question ,
Part(1)
let the number of chocolates be "x" .
let the number of chocolates with covered almonds be "y"
price of each chocolate bar = $1.25
price of each chocolate covered almonds = $2
Beta club needs more than $375
So , according to the question
1.25x + 2y > 375
and also the students can sell up to 500 bars and covered almonds altogether.
So , x+y ≤ 500 .
Part(2)
Given , the club sells 100 chocolate bars.
substituting x= 100 in the inequality 1.25x + 2y > 375 , we get
1.25(100) + 2y > 375
125 + 2y > 375
2y > 375-125
2y > 250
y > 125
least number of chocolate covered almonds to be sold is 126 .
Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
Learn more about Inequality here
https://brainly.com/question/21857626
#SPJ1
9. The density of an
object can be found by taking its mass and dividing by its volume.
equation to represent the relationship between
the three quantities
Write an (density, mass, and volume) in each situation. Let the density, D, be measured in
grams/cubic centimeters (or g/cm'3).
a. The mass is 500 grams
and the volume is 40 cubic centimeters.
b.
The mass is 125 grams and the volume is u cubic centimeters.
C.
The volume is 1.4 cubic centimeters and the density is 80 grams per cubic
centimeter.
d bnt
d. The mass is m grams and the volume is v cubic centimeters.
(From Unit 2, Lesson 2
When the mass is 500 grams and the volume is 40 cubic centimeters then density is 12.5 gm per cc.
When the mass is 125 grams and the volume is 1.4 cubic centimeters then density is 89.28 gm per cc.
What is a simple definition of density?The amount per unit of length, area, or volume as. a: a substance's mass per unit volume. b: the distribution of an amount (such as mass, electricity, or energy) per unit, typically of space.
D = M/V
a) M = 500 gms
V = 40 cubic cm
D = 500/40
D = 12.5 gm per cc
b) M = 125 gms
V = 1.4 cubic cm
D = 125/1.4
D =89.28 gm per cc
To know more about density visit:
https://brainly.com/question/952755
#SPJ13
Complete the equation so that it has no solution 9(x-4)-5x=
Answer:
9(x-4)-5x=
open brackets
9x-36-5x=0
relate with similar expressions
note,when negative crosses the equal sign,it becomes positive
9x-5x=36
4x=36
x=9
Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home. What does the X axis represent. What does the y-axis represent?
Based on the information provided about Arthur, we have the following:
The x-axis of the graph would represent the amount of time that Arthur spends on his way home.The y-axis of the graph would represent the distance covered by Arthur from a reference position (home).What is a graph?In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate).
What is distance?Distance simply refers to the amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of the physical object's direction, starting point, or ending point.
In conclusion, the distance covered by a physical object (body) over a particular period of time can be plotted by using a position-time graph as shown in the image attached below.
Read more on distance here: https://brainly.com/question/19384814
#SPJ1
A rental car company charges $76.50 per day to rent a car and $0.06 for every mile driven. Hunter wants to rent a car, knowing that:
He plans to drive 400 miles.
He has at most $330 to spend.
Use the drop-down menu below to write an inequality representing d, the total number of days Hunter can rent the car while staying within his budget.
The inequality representing d, the total number of days is 76.5d + 24 ≤ 330
How to determine the inequality that represents the scenario?From the question, the given parameters are:
Charges per day = $76.50
Charges per mile = $0.06
This means that the equation that represents the total charges for d days is
Total = Charges per day x Number of days + Charges per mile x Number of miles
So, we have
Total = 76.5 x d + 0.06 x m
Where m represents the number of miles
From the question, we have
He plans to drive 400 miles.He has at most $330 to spend.This means that
m = 400 and Total ≤ 330
So, we have
76.5 x d + 0.06 x 400 ≤ 330
Solve
76.5 x d + 24 ≤ 330
This gives
76.5d + 24 ≤ 330
Hence, the inequality that represents the scenario is 76.5d + 24 ≤ 330
Read more about inequality at
https://brainly.com/question/25275758
#SPJ1
Please be quick!
Clare has been working to save money and wants to have an equation to model the amount of money in
her bank account.
She has been depositing $175 a month consistently. She doesn't remember how much money she
deposited initially; however, on her last statement she saw that her account has been open for 10 months
and currently has $2475 in it.
Write an equation for the amount of money in Clare's bank account after x months. Which equation form
did you choose?
The initial amount that was deposited by Clare is $725.
The equation for the amount of money in Clare's bank account after x months will be 725 + 175x
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let the amount deposited initially be x.
Based on the information, this will be illustrated as:
x + 175(10) = 2475
x + 1750 = 2475
Collect like terms
x = 2475 - 1750
x = 725
The initial amount is $725.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Which problem could be solved with the expression 3 (5 – 2) - 1?Choose 1 answer:Stephanie had 3 apples. She then found 5 more but immediately ate 2 of them. Several minuteslater, she ate 1 more. How many apples does she still have?Orlando had 5 action figures but decided to give 2 of them to his younger brother. His parents wereso impressed with his kindness that they tripled the action figures he had left. Since he got so manynew action figures, he then gave 1 more to his brother. How many action figures does he now have?Of Ralph's 5 toy cars, he gave 2 to his sister. After that, he found 1 more toy car. Then, he decidedto go to the store and triple his number of cars. How many toy cars does Ralph have now?Stuck? Review related articles/videos or use a hint.Report a problem
The given expression is 3 x (5-2)-1
From the options
If Orlando has 5 actions figures.
He decides to give 2 of them to his younger brother, then he will have (5-2) action figures left
His parents were happy with him and tripled what he had left
3 x ( 5 -2 ) action figures.
If he had so many actions figures after that and he gave his brother 1 more action figure then he will have
3 x ( 5-2) - 1 action figures left.
The right answer is therefore option B
I REALLLY would like to ACTUALLY understand how to solve this. Please tell me how you got the steps. So far, this was my thinking:
[tex]\frac{4x+2}{x^{2} -9+8} = \frac{2(x+1)}{(x-1)(x-8)}[/tex]
Please let me know what comes next?????
The empty boxes of the numerators for the given rational expression is to be filled with 4x and 2 respectively.
What is a rational expression?Rational expression is a division of two polynomials. Which implies that the numerator and denominator of the fraction consists of polynomials.
To solve this, we will first factorise the expression of the denominator as follows;
x² - 9x + 8 = x² - 8x - x + 8
x² - 9x + 8 = x(x - 8) -1(x - 8)
x² - 9x + 8 = (x - 1)(x - 8)
Hence, we can rewrite the rational expression as:
(4x + 2)/[(x - 1)(x - 8)]
we can break the expression further by dividing each term of the numerator with the expression (x - 1)(x - 8) as follows;
(4x + 2)/[(x - 1)(x - 8] = [4x/(x - 1)(x - 8)] + [2/(x - 1)(x - 8)]
Therefore, 4x and 2 will be the appropriate values to be filled in the empty boxes equated to the rational expression.
Learn more about rational expression here: https://brainly.com/question/12375170
#SPJ1
Consider the density curve plotted below:1.63.24.86.480.050.10.150.20.25XPDF(X)Density CurveFind P(X<1.6) : Find P(X>4.8) :
Given:
There is a density curve given in the question
Required:
We need to find for
[tex]\begin{gathered} P(X<1.6) \\ P(X>4.8) \end{gathered}[/tex]Explanation:
Part a
We want to find P(X<1.6)
For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:
[tex]P(X<1.6)=\frac{1}{2}*1.6*0.05=0.04[/tex]Part b
For this case we want to find this probability:
P(X>4.8)
and we can complement rule and we got
[tex]P(X>4.8)=1-P(X<4.8)=1-\frac{1}{2}*4.8*0.15=0.64[/tex]Final answer:
0.04
0.64
17. What are the roots of the equation s² - 7 = 74?
18. One of the roots of x² - 8x = 0 is 8. What is the other root?
paanswer po ngaun
w solution if meron po sana
Answer:
17. s = 9
18. x = 8x^(½)
Step-by-step explanation:
s² - 7 = 74?
s² = 74 + 7
s² = 81
√(s²) = √(81)
s = 9
x² - 8x = 0
x² = 0 + 8x
x² = 8x
√(x²) = √(8x)
x = 8x^(½)
OR by factoring
x²−8x=0
x(x−8)=0
x=0 or x−8=0
x=0 or x=8
Problem
Grandma baked 96\ cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.
How many cookies did Cindy receive?
Write your answer as an expression.
I Need a VERY clear answer please
The expression to show the number of cookies that Cindy receive is 96/8 - c.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, 96 cookies were shared among 8 people and Cindy has c fewer cookies. This will be:
= 96/8 - c
This illustrates the concept of expression.
Learn more about expressions on
brainly.com/question/723406
#SPJ1