One zero of the polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers.
Given: f(x) = x^2 + 3x + 3 and zero: 3
Here's how to approach this problem:
The polynomial f(x) has a root of 3.
f(x) can be expressed as a product of two factors, where the first factor contains (x-3) as one of its roots, as follows:
f(x) = (x-3)(ax + b)
We can obtain the values of a and b by equating the coefficients of this equation to that of the given polynomial:
a + 3 = 1 (since coefficient of x in the given polynomial is 3)
-3a + b = 3 (since the constant term in the given polynomial is 3)
Solving these equations gives us a=-2 and b=9.
f(x) can thus be expressed as:
f(x) = (x-3)(-2x + 9)
Hence, the expression for the polynomial is f(x) = -(x-3)(2x-9).
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The manager of a store orders mystery games that cost $7.30 and sells them for $15.33. What is the mark-up as a percentage?
In order to find the price increase in percentage terms, we divide the price difference by the cost price.
The difference:
[tex]15.33-7.30=8.03[/tex]Rate:
[tex]\frac{8.03}{7.30}=\frac{x}{100}[/tex]
If we solve for [tex]x[/tex] in this equation, it will give us the price increase as a percentage.
The price increase should be [tex]110[/tex]%.
Henry is planning a party for his daughter, Rebecca. The party has a beach theme. Henry plans to fill a sandbox with fresh sand so the kids can build sandcastles. The sandbox is twelve feet long and two feet tall. The width of the sandbox is half of its length. What is the volume of sand needed to fill the sandbox?
Answer:144 ft³
Step-by-step explanation:
The width of the sandbox is half of its length, so we can start by finding the length:
Length = 12 feet
Width = 1/2 * Length = 1/2 * 12 feet = 6 feet
Height = 2 feet
The volume of sand needed to fill the sandbox is the product of its length, width, and height:
Volume = Length * Width * Height
Volume = 12 feet * 6 feet * 2 feet
Volume = 144 cubic feet
The cuboid below is made of silver and has a mass of 416 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p. Picture attached!
The density of the cuboid is 10.4 g/cm3 ( 1 d.p)
What is density?Density is the ratio of mass of a substance to its volume. It is measured in kg/m³ or g/cm³. It is a scalar quantity.
The density of a substance bis expressed as;
d = mass/volume
The mass = 416g
and the volume = l× w × h
length of the cuboid = 4cm
width of the cuboid = 2cm
and height = 5cm
Therefore the volume is calculated as :
V = 4× 2 × 5
V = 40cm³
the volume of the cuboid is 40cm³
The density can now be calculated as :
density = mass/volume
density = 416/40
= 10.4g/cm³
therefore the density of the cuboid is 10.4 g/cm³
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how do i solve 7/9 +8 1/4 fraction
Answer:
9 1/36
Step-by-step explanation:
set 7/9 and 1/4 to a common denominator
so lets do 36,
7 x 4 = 28
9 x 4 = 36
1 x 9 =9
4 x 9 =36
28/36 + 9/36 = 1 1/36
1+8 = 9
Write a quadratic equation with the given roots. Write the equation in the form ax2 + bx + c = 0 where a, b, and c are integers. 4/3 and -1
[tex]\begin{cases} x = \frac{4}{3} &\implies 3x=4\implies 3x -4=0\\ x = -1 &\implies x +1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( 3x -4 )( x +1 ) = 0} \hspace{5em}\stackrel{\textit{now assuming that}}{a=1}\hspace{3em}1( 3x -4 )( x +1 ) = 0 \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2-x-4=0 \end{array}}~\hfill[/tex]
151.8% of £613.71
Give your answer rounded to 2 DP.
Pls help me I only have 1 day lefhelp pls! ITS Prediction from line of best Fit
Answer:79
Step-by-step explanation:
y=12+91=79
a CD usually sells for $11.00. if the CD is 10% off and the sales tax is 7% what is the total price of the CD, including tax
0.90 x $11.00 = $9.90
This is the price of the CD before taxes are applied. To find the total price, including tax, we need to add the 7% sales tax to the discounted price:
Total price = discounted price + (sales tax x discounted price)
Total price = $9.90 + (0.07 x $9.90)
Total price = $9.90 + $0.69
Total price = $10.59
Therefore, the total price of the CD, including tax, is $10.59.
Please mark this answer as brainliest if possible.
The sun orbits the Milky Way galaxy at about 135 miles per second. Write your answers to the following in scientific notation.
A. How far does the sun travel in an hour?
B. How far does the sun travel in a week?
Expressing this in scientific notation, we get: Distance traveled in a week = 3.77 x [tex]10^7[/tex] miles/week
What is speed?Speed is a measure of how fast an object is moving, usually expressed in units of distance per unit time. It is defined as the distance traveled by an object divided by the time it takes to travel that distance.
According to question:The speed of the sun orbiting the Milky Way galaxy is 135 miles per second.
A. To find how far the sun travels in an hour, we need to multiply its speed by the number of seconds in an hour:
Distance traveled in an hour = 135 miles/second x 60 seconds/minute x 60 minutes/hour
Distance traveled in an hour = 486,000 miles/hour
Expressing this in scientific notation, we get:
Distance traveled in an hour = 4.86 x [tex]10^5[/tex] miles/hour
B. To find how far the sun travels in a week, we need to multiply its speed by the number of seconds in a week:
Distance traveled in a week = 135 miles/second x 60 seconds/minute x 60 minutes/hour x 24 hours/day x 7 days/week
Distance traveled in a week = 37,656,000 miles/week
Expressing this in scientific notation, we get:
Distance traveled in a week = 3.77 x [tex]10^7[/tex] miles/week
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How many days can the baby drink the juice if no one else drinks more
The baby will drink 45 liters of milk in 30 days when baby drink 3 liters of milk in 2 days.
To solve this problem, we can set up a proportion using the fact that the amount of milk the baby drinks is directly proportional to the number of days:
milk consumed / number of days = constant
Let's call the constant of proportionality k. Then we can write:
3 liters / 2 days = k
To find the value of k, we can solve for it:
k = 3 liters / 2 days = 1.5 liters/day
Now we can use this value of k to find how much milk the baby will drink in 30 days:
milk consumed / 30 days = 1.5 liters/day
Multiplying both sides by 30, we get:
milk consumed = 1.5 liters/day x 30 days = 45 liters
Therefore, the baby will drink 45 liters of milk in 30 days.
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The complete question is :
A baby drink 3 liters of milk in 2 days . How much milk will baby drink in 30 days.
A coffee pot holds 2 quarts of coffee. How much is this in cups?
A coffee pot that holds 2 quarts is equal to 8 cups. To determine the number of cups in a coffee pot that holds 2 quarts, multiply 2 quarts by 4 cups.
A quart is a unit of measurement that is equal to 4 cups of liquid. This means that a coffee pot that holds 2 quarts is equal to 8 cups. To figure out how many cups are in a quart, use the following equation: 1 quart = 4 cups. To determine the number of cups in a coffee pot that holds 2 quarts, multiply 2 quarts by 4 cups. The result is 8 cups. In other words, a coffee pot that holds 2 quarts is equal to 8 cups of liquid.
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Does the following set of ordered pairs represent a function?
(2,3) (3,4) (2,5) (5,8)
Answer:
No
Step-by-step explanation:
In order for a set of ordered pair to be a function all the x values need to be different. In this case we have two of the same x values so this set won't be a function.
write 3/4 5/7 19/25 11/5 smallest to largest
Answer:[tex]\frac{5}{7} \\\\ \\\\\frac{3}{4} \\\\\frac{19}{25} \\\\\frac{11}{5}[/tex]
Step-by-step explanation:
Majka company was started on january 1, year 1. During year 1, the company experienced the following accounting events: (1) issued 50,000 worth of common stock (2) earned cash revenues of $33,700, (3) paid cash expenses of $14,900, and (4) paid a $3,200 cash dividend to its stockholders. These were the only events that affected the company during year 1
(1) In General Ledger, Cash Account is $ 13900 , In revenue account The balance is $ $28600, in expense account the balance is $ $13200 and Trial balance is $28600.
(2) The income statement is $ 15400.
(3) Statement of Changes in Stockholders' Equity is $13900.
(4) Balance sheet is $ 13900.
Record the effects of each accounting event under the appropriate general ledger account headings.
Using the accounting equation, we have:
Asset = Shareholder's equity + Liabilities
Cash = Retained earning + Common stock
Cash = $28,600 - $13,200 - $1,500 = $13,900 = Assets
Retained earning = $28,600 - $13,200 - $1,500 = $13,900
Common stock = 0
Retained earning + Common stock = $13,900 + 0 = Shareholder's equity
Liabilities = 0
Therefore, we have:
(1) Majka Company
Accounting Equation for Year 1
Asset ($) = Shareholder's equity + Liabilities
13,900 = 13,900 + 0
(2) Prepare an income statement
Details Amount ($)
Revenue 28,600
Expenses (13,200)
Net Profit 15,400
Dividend (1,500)
Retained earning 13,900
(3) Statement of changes in stockholders’ equity
Details Amount ($)
Common stock 0
Beginning retained earning 0
Retained earning for the year 13,900
Stockholders’ equity 13,900
(4) Mijka Company, Balance sheet as at December 31, Year 1,
Details Amount ($)
Assets:
Cash 13,900
Liabilities:
Current and Long terms 0
Net total assets 13,900
Stockholders’ equity:
Common stock 0
Retained earning 13,900
Stockholders’ equity 13,900
Complete Question:
Majka Company was started on January 1, Year 1. During Year 1, the company experienced the following three accounting events: (1) earned cash revenues of $28,600, (2) paid cash expenses of $13,200, and (3) paid a $1,500 cash dividend to its stockholders. These were the only events that affected the company during Year 1. Required Record the effects of each accounting event under the appropriate general ledger account headings. Prepare an income statement, statement of changes in stockholders’ equity, and a balance sheet dated December 31, Year 1, for Mijka Company.
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In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Suppose the demand and supply of tea are modeled by the two following functions: Q = 34P + 53 Q = -25P + 177 What is the equilibrium price of tea? Round your answer to two places after the decimal point (0.01).
According to the question the equilibrium price of tea is 2.10.
What is equilibrium?Equilibrium is a state of balance in which all forces acting on an object are equal and opposite, so no net force is acting on the object. This state of balance is also known as a "steady state". Equilibrium is an important concept in many areas of science, such as physics and chemistry, because it allows us to analyze how objects interact in a stable environment. Equilibrium can also be used to describe a state of financial balance, where all parties involved in a transaction are satisfied with the outcome.
The equilibrium price can be found by setting the two equations equal to one another and solving for P.
34P + 53 = -25P + 177
59P = 124
P = 124/59
P = 2.10
Therefore, the equilibrium price of tea is 2.10.
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I’m so confused pls help me <3
Answer:16.7%
Step-by-step explanation: He has a 33% chance of losing in chess and 50% of losing in pool. So when you convert the two percentages to decimals and multiply them the result is 0.167. Convert the number back into a percentage, it's 16.7%.
rewrite the following into the stnadard from of a quadratic equation
[tex]2x^{2} -1[/tex]
Answer:
[tex]2x^{2} +0x+-1=0[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is:
[tex]ax^{2} +bx+c=0[/tex]The expression provided ([tex]2x^{2} -1[/tex]), can be rewritten in standard form by setting it to equal zero:
[tex]2x^{2} -1 = 0[/tex]In this case, a would be equal to 2, b equal to 0, and c equal to -1.
The length of Anna's square pencil case is 6 in and the width is 4 1/2 in what is the area of the pencil case?
If the length of Anna's square pencil case is 6 in and the width is 4 1/2 in, then the area of the pencil case is 27 square inches
The area of a rectangle can be calculated by multiplying its length by its width.
In this case, Anna's pencil case is a square, which means that its length and width are equal. The length of the pencil case is given as 6 inches, so its width is also 6 inches.
Therefore, the area of the pencil case is:
Area = length x width
Substitute the values in the equation
Area = 6 in x 4.5 in
Area = 27 square inches
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Find the surface area of the sphere. Round your answer to the nearest hundredth.
Rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.
What is surface area ?Surface area is the measure οf the tοtal area that the surface οf an οbject οccupies. It is a twο-dimensiοnal measurement, typically expressed in square units, such as square meters (m²) οr square feet (ft²).
Tο find the surface area (A) οf a sphere with a given circumference (C), we first need tο find the diameter (d) οf the sphere.
The fοrmula fοr the circumference (C) οf a sphere is:
C = 2πr
where r is the radius οf the sphere.
Given that the circumference is 4π ft, we have:
4π = 2πr
Sοlving fοr r, we get:
r = 2 ft
Nοw we can use the fοrmula fοr the surface area οf a sphere with diameter d:
A = 4π(d/2)²
Substituting d = 4 ft (since diameter = 2r), we get:
A = 4π(4/2)²
A = 4π(2)²
A = 4π(4)
A = 16π
A ≈ 50.27
Therefοre, rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.
A ≈ 50.27
Therefοre, rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.
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the amount of time tim spends answering work e-mails in a given day has a mean of one hour and a standard deviation of ten minutes. what would best describe the total amount of time, measured in hours, tim would spend answering e-mails over the course of 100 days
The best estimate for the total amount of time Tim would spend answering e-mails over the course of 100 days is 100 hours with a standard deviation of 0.53 hours.
To find the total amount of time Tim would spend answering emails over the course of 100 days, we need to use the concept of the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approaches a normal distribution regardless of the underlying distribution.
To calculate the standard deviation of the total amount of time Tim spends answering emails over 100 days, we can use the formula:
standard deviation = square root of (n * variance)
where n is the number of days and variance is the variance of the amount of time Tim spends in a day answering emails.
Substituting the values, we get:
standard deviation = square root of (100 * 0.0028) = 0.53 hours
Therefore, Tim would spend an average of 100 hours over the span of 100 days responding to emails, with a standard deviation of 0.53 hours, according to the best estimate.
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The perimeter of a rectangle is 72, and the width is 4 less
han 3 times the length. What is the length?
12
O 10
O 16
O 14
Answer:
Answer: 10
Step-by-step explanation:
Let L be the length of the rectangle, and W be the width.
From the problem, we know that:
The perimeter of the rectangle is 72, which means that:
2(L + W) = 72
L + W = 36
The width is 4 less than 3 times the length:
W = 3L - 4
Substituting W = 3L - 4 into the first equation, we get:
L + 3L - 4 = 36
4L = 40
L = 10
Therefore, the length of the rectangle is 10. Answer: 10
Write down the domain and range of: y = 2*
The domain is (-∝, ∝) and the range is y > 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
y = 2^x
The domain of the function is the set of all real numbers
This is so because there is no restriction on the input values
The range of the function is the set of positive real numbers
Since any positive number can be obtained by raising 2 to a power, and the function is never negative or zero.
We can write the range as y > 0.
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17. Which graphic organizer correctly groups the following numbers? (1 point) 4.1,-9,3,-2.2
A graphic organizer that correctly groups the following numbers 4.1, -9, 3, -2.2 is; B. graphic organizer B.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 4.1, -2.2 12, 1/2, 0.5, √16, -29, etc.
What is an integer?In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).
Based on the given data set 4.1, -9, 3, -2.2, the numbers should be correctly grouped as follows;
Rational number = 4.1 and -2.2.
Integer = -9.
Whole number = 3.
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A game show has a contestant pick one of five doors to reveal the prize the contestant wins. A photo of a new boat is behind one of the doors, and joke prizes are behind the others. Which BEST describes the probability of winning the new boat?
*
impossible
likely
unlikely
certain
Answer:
Step-by-step explanation:
The probability of winning the new boat is unlikely, since there is only one boat behind one of the five doors, while the other four doors have joke prizes. Assuming that each door has an equal chance of being selected by the contestant, the probability of choosing the door with the boat is 1/5 or 20%. However, the probability of not winning the boat is 4/5 or 80%. Therefore, it is unlikely that the contestant will win the boat.
This question has two parts. First, answer Part A. Then, answer
Part A
Find the Error A student was finding the value of x.
Which of the following explains the student's error?
The student's error is adding two non-adjacent angles and then solving for x.
What are the opposite angles?
Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles.
The student's error is that they incorrectly added the two given angles together.
The angles 2x+6 and 60 are not adjacent angles and therefore cannot be added together to find the sum of the two angles.
In the figure, if the angle formed by the intersection of the lines is labeled as angle A, then we know that angle A is equal to 2x+6 and angle B is equal to 60.
These two angles are opposite angles and not adjacent angles, so they do not add up to 180 degrees.
Therefore, the student's error is adding two non-adjacent angles and then solving for x.
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Challenging y’all a little
Answer:
identify a relationship among Tn,Sn and Sn-1 where n>1
Type your answer in to the boxes. The three points marked on the graph are the vertices (corners) of a parallelogram Y 10 q 8 5 B 3 2 2 3 5 6 7 8 9 10 X What are the coordinates of the fourth vertex?
The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
What is cοοrdinate?A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.
First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:
Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]
Distance Yq = [tex]\sqrt{8 + 25 }[/tex]
Distance Yq =[tex]\sqrt{ 33}[/tex]
Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]
Distance 5B = [tex]\sqrt{2}[/tex]
Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:
x = (33/2)
Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,
Slοpe Yq = (10-5)/(8-10) = -5/2Slοpe B-missing vertex = -5/2
write the equatiοn οf the line passing thrοugh B and the missing vertex:
y - 2 = (-5/2)(x - 3)
Simplifying, we get:
y = (-5/2)x + (19/2)
Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.
Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).
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three brothers shared a sum in the ratio of 3:4:5 . If the highest got 37500 how much did they share
The amount of they share altogether is 90000
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
For example if two boys are to share 10 mangoes with ratio 1:4. The first boy will get 1/5 × 10 = 2 mangoes and the other boy will get 4/5 × 10 = 4×2 = 8 mangoes.
Three brothers are to share in ratio 3:4:5. The highest ratio is 5. And the the highest ratio gets 37500. The total ratio is 12 i.e 3+4+5 = 12
Represent the total money by x
Then, 5/12 × x = 37500
5x = 37500 × 12
5x = 450000
divide both sides by 5
x = 450000/5
x = 90000
therefore the amount they shared is 90000.
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help pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
yea
Step-by-step explanation:
u need more details