The least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².
What do we mean by polynomial function?A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.So, given zeroes are -1, 3+3i.
We got: x = -1Then, x + 1 = 0.Hence, one factor of the polynomial function is (x+1).Similarly,
We have: 3+3iRewrite as: x = 3 + √-9Square both the sides: x² = 9 - 9So, the other factor is x².So, the polynomial has the function: (x+1)x²
(x+1)x²x³ + x²f(x) = x³ + x²Therefore, the least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².
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A support pole for an ancient structure is found to have one-sixth of the carbon-14 of a modern, living tree. How long ago did the tree used to make the support pole die? Give your answer to the nearest whole number. (Assume that half-life of carbon-14 is 5770 years.)
14912 years ago, the tree that was used to kill the support pole died which is one-sixth of the carbon-14 of a modern, living tree.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
One-sixth of a modern, living tree's carbon-14 is present in an ancient structure.
Assume that the half-life of carbon-14 is 5770 years
As per the given condition, the expression would be
[tex]A(t) = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\\A(t) = (0.167)A_o}[/tex]
[tex](0.167)A_o} = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
[tex](0.167) = \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
Take the logarithms of both sides to get:
[tex]log(0.167) =log \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]
Using logₐ(xⁿ) = n logₐx.
⇒ log 0.167= (t/5770) log (0.5)
⇒ log 0.167/ log (0.5)= (t/5770)
⇒ 3 = (t/5770)
⇒ t = 3 × 5770
⇒ t = 14912
Hence, 14912 years ago, the tree that was used to kill the support pole died.
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The arcade charges 24 tokens to play 6 games.
How many tokens will 10 games cost?
Answer: 40
Step-by-step explanation:
if 6 games = 24 tokens
then 1 game = 24/6=4
so 10 games = 4*10=40
Answer:
40
Step-by-step explanation:
24/6 = 4 tokens per game
4*10 games = 40
find the value of x in 5/9 = x/54
Answer:
[tex] \large \sf \: x=30[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
5/9 = x/54
Step 1: Cross-multiply.
5/9 = x/54
(5)*(54)=x*(9)
270=9x
Step 2: Flip the equation.
9x=270
Step 3: Divide both sides by 9.
9x/9 = 270/9
x=30
Find the domain of f(x) and the interval.
f(x)=√x² - 2x +48
Answer:
Step-by-step explanation:
go pathways gives all the answers
Will mark u brainliest Question
Question
What is the turning point of the graph of f(x)=|x−2|+3?
(2, 3)
(−3, 2)
(3, 2)
(2, −3)
The turning point of the function f(x) = |x-2| + 3 will be (3, 2).
Here,
We have to find the turning point of the graph of function,
f(x) = |x−2|+3
What is an absolute function?
The non-negative value of real number without regard to its sign is known as its absolute value.
Now,
The absolute function is;
f(x) = |x+3| -2.
Since, When we plot the graph of the absolute function f(x) = |x+3| -2,
it will give two straight lines which is shown in the graph.
Clearly, The graph of the function changes its position at the coordinate
(3, 2).
Therefore, The absolute function having its turning point at the coordinate ( 3, 2).
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Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Learn with an example
Susan is going to ship some gifts to family members, and she is considering two shipping
companies. The first shipping company charges a fee of $20 to ship a medium box, plus an
additional $1 per pound. A second shipping company charges $5 for the same size of box,
plus an additional $4 per pound. At a certain weight, the two shipping methods will cost tre
same amount. How much will it cost? What is that weight?
The two shipping methods both cost $
Submit
at a weight of
pounds.
The first company shipping charge is 5 $
the second company shipping charge is 2 $
let the size of the box be 'x'
Given the first company charged as below
20$ for medium-sized and an extra 1$ for one pound
= 20x + 1
The second company charged as below
$5 for the same size of the box, plus an additional $4 per pound
= 5x + 4
The price of the two shipping options will be same.
20x + 1 = 5x + 4
20x - 5x = 4- 1
15x = 3
x= 3 / 15
x = 1/5
x = 0.2
∴ 20x+1 = 20 * 0.2 +1 = 5
5x + 4 = 5 * 0.2 + 1 = 2
Therefore, The first company's shipping fee is $5, whereas the second company's fee is $2.
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40 Members of arwick youth club go on a trip to a leisure centre they go in minibuses that can each seat up to 15 people. It costs £30 for each minibus and £150 for the group to have use of the leisure centre. How much will the trip cost per person
The trip cost per person is 6 pounds.
What is a unit rate?Unit rate is the ratio of two different units, with the denominator as 1.
It means a rate for one of something.
We have,
Total members = 40
Each minibus cost = 30 pounds
Leisure centre cost = 150 pounds
Each minibus can carry = 15 people
The number of minibusses needed to carry 40 members:
= 40 / 15
= 2.67
= 3 minibusses.
This means we need 3 minibusses to carry 40 members.
Now,
The total cost for the trip:
= 150 pounds + 3 x 30 pounds
= 150 + 90
= 240 pounds
The cost per person:
= 240 / 40
= 6 pounds
Thus the trip cost per person is 6 pounds.
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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
What is the numerical value of K?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
XZ is the perpendicular bisector of segment WYSegment WX = 3k + 17Segment XY = 7k - 7Value of k = ?Since XZ is a perpendicular bisector of segment WY,
Segment WX is equal to Segment XY
Segment WX = Segment XY
Plug in the given values and solve for k.
3k + 17 = 7k - 7
Collect like terms
3k - 7k = -7 - 17
-4k = -24
Divide both sides by the coefficient of k
-4k/-4 = -24/-4
k = 6
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
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Which number below is NOT equal to the others?
1/8
18/10
1.8
1 4/5
Answer:
1/8
Step-by-step explanation:
When worked out, all numbers are equal to 1.8 except 1/8. (1/8 is equal to .125)
1/8) 1 divided by 8 is .125
18/10) 18 divided by 10 is 1.8
1.8) 1.8=1.8
1 4/5) 4 divided by 5 is .8, and when you add the 1 it ends up as 1.8
translation: (x,y) →(x - 5, y + 1)
Z(−3, –4), K(−2, −1), (0, -1)
The translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).
We are given the translation as:
(x , y) → (x - 5 , y + 1)
Now we have some points:
Z (−3, –4)
K (−2, −1)
M (0, -1)
We need to translate these points.
For Z (−3, –4), we get the translation as:
Z (−3, –4) = Z' ( - 3 - 5 , - 4 + 1)
Z (−3, –4) = Z' ( - 8 , - 3 )
For K (−2, −1), we get the translation as:
K (−2, −1) = K' ( - 2 - 5 , - 1 + 1)
K (−2, −1) = K' ( - 7 , 0 )
For M (0, -1), we get the translation as:
M (0, -1) = K' ( 0 - 5 , - 1 + 1)
M (0, -1) = K' ( - 5 , 0 )
Therefore, we get the translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).
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(3x 3 +4x 2 )+(3x 3 −4x 2 −9x)
Answer:
9x
Step-by-step explanation:
=9x+8x+9x-8x-9x
=9x
How much colder was Tuesday then Saturday? if
+5 degree.
Formula for Length Change due to Thermal Expansion: The formula for calculating the change in length of a substance due to thermal expansion is ΔL=αLΔT Δ L = α L Δ T where L is the original length of the substance and ΔT is the change in temperature of the substance either in degrees Celsius or in Kelvin.
For comparision of temperature -
Subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C.
Given data
temperature of tuesday = 55 degree
temperature of saturday = 60 degree
Difference between temperature = 60 -55 = 5 degree.
Hence, 5 degree more colder was Tuesday then Saturday.
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Determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. X 0 1 2 P(X) 0 1/3 2/3 Select all that apply: The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is not a probability distribution, since at least one of the probabilities is greater than 1 or less than 0. The given distribution is a probability distribution, since the sum of probabilities is equal to 1. The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1.
The distribution is a probability distribution, and the reasons are
The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is a probability distribution, since the sum of probabilities is equal to 1. How to determine whether the distribution is a probability distribution?The probability distribution is given as:
X 0 1 2
P(X) 0 1/3 2/3
From the above table of probability distribution, we can see that each probability value is between 0 and 1 (inclusive)
Also, the sum of probabilities is 1
i.e. 0 + 1/3 + 2/3 = 1
Hence, the distribution is a probability distribution, and the reasons are
The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is a probability distribution, since the sum of probabilities is equal to 1.Read more about probability distribution at
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This week Andrei got a promotion at work that came with a 2 % pay increase. If now his monthly salary is $ 1683 , how much was he making before the raise?
Enter your answer as a decimal. If needed, round to the nearest penny. Do not use commas.
1683 доллара - 102% . Найдем 1 процент и умножим его на 100%, тем самым получив ответ:
1) 1683 / 102 = 16.5 доллара - 1 % от всей зарплаты
2) 16.5 * 100 = 1650 - изначальная сумма, которую получал Андрей до повышения.
Ответ : 1650 $
A 13 foot ladder is leaning on a wall. the bottom of the ladder has a diatance of 5 feet from the base of the wall.
What is the distance, in feet, between the ground and the top of the lafder?
Answer:
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On the weekdays a grocery store has 14301 customers and on the weekends the grocery store has 11856 customers . How many more customers does the grocery store have on weekdays than on weekends?
Answer:
2445
Step-by-step explanation:
it would have 2445 more costumers
Answer:
2445
Step-by-step explanation:
Subtract.
14301 - 11856 = 2445 more people on weekdays
Find the measure of the missing angles.
Answer:
x=26, y=90
Step-by-step explanation:
This is what I did,
I knew that y = 90 because it is a Right Angle. I subtracted 90 - 64 and that got me = y 26
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answer:
Step-by-step explanation:
it would be great if u had the image, but at least I can give some advice: use the method of rise over run to find the slope. use 2 points and count the number of squares "rising" and turn right and count the number of squares "running". left and down if it's going downward.
for the y intercept, find the x that equals 0. your coodinate should look like this: (0, *insert y*)
How to solve this problem? -2x + 4 < 16
Answer:
the answer is 7+1-7+0/xx{12
Step-by-step explanation:
the answer above stated is correctly corrected correct
One pizza will feed 5 people. How many pizzas are needed for 40 people?
Answer:
8 pizzas
Step-by-step explanation:
Point A appears on the number line as shown below:
Answer:
C) x² + y²Step-by-step explanation:
According to the graph, point A has a negative value, between - 1 and zero.
All the expressions could result in negative value apart from the sum of the squares, which is never negative.
Correct choice is C.
3=
X/
3
One step equations with positive whole number
-1.12345...
rational, irrational and or real number?
Answer: Irrational Number
Step-by-step explanation: It's Irrational because it cant be represented as a simple fraction.
6. A household spend 120 on purchase of a commodity when it price is 6 per unit. When the rises to 10 per unit his total expenditure on this commodity becomes 180.calculate price elasticity of demand by percentage change method.
Therefore, the price elasticity of demand by percentage change method is -0.025.
Given the price of a first commodity (p₁) = 6 rs
the price of a second commodity (p₂) = 10 rs
Expenditure on first commodity (s₁) = 120
Expenditure on second commodity (s₂) = 180
We need to find the quantity as
120 = 6 * Q₁. 180 = 10 * Q₂
Q₁ = 120 / 6 Q₂ = 180 / 10
Q₁ = 20 Q₂ = 18
price elasticity of demand by percentage change method as
Eₐ = P / Q * ΔQ /ΔP
ΔQ = Q₂ - Q₁ = 18 -20 = -2
ΔP = p₂ - p₁ = 10 - 6 = 4
Eₐ = 6 / 120 * -2 / 4
Eₐ = - 0.025
Therefore, the price elasticity of demand by percentage change method is -0.025.
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Question
Consider the following two loans for Po = $15,000.
• Loan A: 5 year loan, annual interest rate of 8%, monthly repayments of $304.15.
Loan B: 3 year loan, annual interest rate of 11%, monthly repayments of $491.08.
Calculate the absolute difference between the total interest paid on both loans. Give your answer to the nearest ten dollars.
Do not include the dollar sign in your answer
Answer:
570
Step-by-step explanation:
570
The absolute difference that is between the loans paid as 570
How to solve for the absolute differenceWe have the following details:
Po = $15000
loan a 5 year loan, interest = 8 percent and repayments = 304.15 dollars
Loan b
3 year loan, interest = 11 percent repayments = $491.08
Total number of repayments = 5 x 12 = 60
Total repayments = 304.15 dollars x 60
= $18249
The total interest that is paid for A would be
$18249 - $15000
= $3249
For the second loan
Total number of repayments = 3 x 12 months = 36
Total repayment = 36 x 491.08 = $17678.88
The total interest for the loan B would be: $17678.88 - $15,000
= $2678.88
Then the absolute difference between the paid loan would be
$3249 - $2678.88 = 570.12
Hence we would have the absolute difference that is between the loans paid as 570.
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What are the solutions to –24x – 24 = x3 + 8x2?
Answer:
–24x – 24 = x3 + 8x2
Step-by-step explanation:
-24x-24=x^3+8x^2
x^3+8x^2+24=-24x-24+24
x^3+8x^2+24=-24x
x^3+8x^2+24+24x=-24x+24x
x^3+8x^2+24x+24=0
Answer: x=-2
Step-by-step explanation:
[tex]-24x-24=x^3+8x^2\\-24x-24+24=x^3+8x^2+24\\-24x=x^3+8x^2+24\\-24x+24x=x^3+8x^2+24+24x\\0=x^3+8x^2+24x+24\\x^3+8x^2+24x+24=0\\x^3+8x^2+12x+12x+24=0\\(x)(x^2+8x+12)+(12)(x+2)=0\\(x)(x^2+2x+6x+12)+(12)(x+2)=0\\(x)((x)(x+2)+6(x+2))+(12)(x+2)=0\\(x+2)((x)(x+6)+12)=0\\ (x+2)(x^2+6x+12)=0\\x+2=0\\x+2-2=0+(-2)\\x=-2\\x^2+6x+12=0\\D=(-6)^2-(4)(1)(12)\\D=36-48\\D=-12\\Hence,\\The\ equation\ has\ no\ valid \ roots\\Thus,\\x=-2[/tex]
Helpp??
A playground has 2 slides,
3 swings, and monkey bars.
What's the probability that a kid
will decide to use a slide if they
pick at random?
Jack has 80 marbles.
He gives 1/5
of the marbles to his friends.
(c) Work out how many marbles Jack now has.
inq
Answer:
He now has 64 marbles.
Step-by-step explanation:
This is because 1/5 of 80 is 16.
Determine the point(s), if any, at which the graph of the function has a horizontal tangent line. Y= 1/2x^2 +7x (Give the answer as x,y coordinates)
Answer:
i don't know how to attach the file
PLS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
Answer: x=18 ==> C
Step-by-step explanation:
19+15+11=14+15+?
19+11=14+?
30=14+?
?=16
?+11+x=19+15+11
x+?=19+15
x+16=34
x=18 ==> C