Answers
The quartic equation behind the graph is y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8.
How to derive the expression for a quartic function
Quartic functions are fourth grade polynomials and according to the fundamental theorem of algebra, such kind of expressions have at least two real roots and at most four real roots. The graph of the picture shows a polynomial with two roots of multiplicity 2: x₁ = - 1, x₂ = 2.
y = a · (x + 1)² · (x - 2)² (1)
Where a is the leading coefficient.
If we know that (x, y) = (0, 4), then the leading coefficient of the polynomial is:
4 = a · (0 + 1) · (0 - 2)
4 = - 2 · a
a = - 2
Then, the quartic equation is equal to:
y = - 2 · (x + 1)² · (x - 2)²
y = - 2 · (x² + 2 · x + 1) · (x² - 4 · x + 4)
y = - 2 · [(x² + 2 · x + 1) · x² + (x² + 2 · x + 1) · (- 4 · x) + (x² + 2 · x + 1) · 4]
y = - 2 · (x⁴ + 2 · x³ + x² - 4 · x³ - 8 · x² - 4 · x + 4 · x² + 8 · x + 4)
y = - 2 · (x⁴ - 2 · x³ - 3 · x² + 4 · x + 4)
y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8
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Related Questions
how to find h’(3)
base on the graph
Answers
By the quotient rule for differentiation,
[tex]\displaystyle h'(x) = \dfrac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]
According to the plots of [tex]f[/tex] and [tex]g[/tex], we have [tex]f(3)=2[/tex] and [tex]g(3)=3[/tex].
On the interval [2, 4], [tex]f[/tex] is a line through the points (2, 5) and (4, -1), and hence has slope (-1 - 5)/(4 - 2) = -3, so [tex]f'(3)=-3[/tex]. We can similarly find [tex]g'(3)=2[/tex].
Then
[tex]h'(3) = \dfrac{3\cdot(-3)-2\cdot2}{3^2} = \boxed{-\dfrac{13}9}[/tex]
there were 3 ponies. rodrick rode each pony 6 times. how many pony rides did sarah take?
Answers
Answer: 0
Step-by-step explanation: I am going by the words , there WERE 3 ponies. So Sarah couldn’t take any rides.
Find the area of the kite. 9 2 3
Answers
Answer:
33 units²
Refer to the attached page
I've shown the complete calculation over there.
Answer: 33
Step-by-step explanation:
one easy way to do it is by finding the area of the 4 triangles.
because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.
3 plus 3 plus 13.5 plus 13.5
to get 33
A strain of bacterial cells doubles inpopulation every 2 days. A single cell is placed in a dish with sufficient nutrients to sustain a colony. Which equation will
calculate d, the number of days after which there will be 256 bacterial cells in
the dish?
Answers
The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
How to determine the equation of the number of days?The given parameters are:
Rate, r = doubles every two days
Initial number of strain, a = 1
This means that the function is an exponential function.
An exponential function is represented as:
A(d) = a * r^d
Since the strain doubles every two days, we have:
A(d) = a * r^(d/2)
Substitute the known values in the above equation
A(d) = 1 * 2^(d/2)
Evaluate the product
A(d) = 2^(d/2)
When there are 256 bacterial cells, the equation becomes
2^(d/2) = 256
Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
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The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013. What was the cost of hiring a car for 2 days in 2013?
Answers
The cost of hiring a car for 2 days in 2013 is Rs. 316.8
How to find the cost of hiring in 2013 ?The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013.
Therefore,
cost of hiring for 2018 = Rs. 264
Therefore,
let
cost of hiring in 2013 = 20%(264) + 264
cost of hiring in 2013 = 20 / 100 × 264 + 264
cost of hiring in 2013 = 1 / 5 × 264 + 264
cost of hiring in 2013 = 264 / 5 + 264
cost of hiring in 2013 = 52.8 + 264
cost of hiring in 2013 = 316.8
Therefore, the cost of hiring a car for 2 days in 2013 is Rs. 316.8.
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in mongolia the temperature can dip down to -45C in January. The temperature in July may reach 40C. What is the temperature range in Mongolia?
Answers
Answer:
85 C
Step-by-step explanation:
Temperature range means the difference between the maximum and minimum in temperature for an area. 40C-(-45C)=85 C
If X and Y are distinct digits such that the eight-digit number 7448X24Y is divisible by both 8 and 9, then find X - Y.
Answers
The value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7
How to determine the distinct digits X and Y?The eight-digit number is given as:
7448X24Y
Also, from the question
The number is divisible by 8 and 9
When a number is divisible by 8, then the last three digits of that number would be divisible by 8.
When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.
So, we have:
24Y is divisible by 8
The possible value of Y from the above statement is 0
This is so because 240 is divisible by 8
The sum of the digits of the number would be divisible by 9.
This means that:
7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y
Substitute 0 for Y
29 + X + Y = 29 + X + 0
Evaluate the sum
29 + X + Y = 29 + X
36 is divided by 9
So, we have
29 + X = 36
Subtract 29 from both sides of the equation
X = 7
So, we have
X = 7 and Y = 0
X - Y is calculated as:
X - Y = 7 - 0
Evaluate the difference in the above equation
X - Y = 7
Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7
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Assume that a sample is used to estimate a population proportion p. Find the 95% confidence for a sample of size 246 with 52% successes. Enter your answer as an open -interval using decimals
Answers
Using the z-distribution, the 95% confidence interval for the proportion is given as follows:
(0.4576, 0.5824).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The other parameters for the interval are given as follows:
[tex]n = 246, \pi = 0.52[/tex].
The lower and upper bound of the interval, respectively, are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]
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0
100
200
300
400 500 600 700
Quantity Supplied
nstructions: Refer to the graph and answer the questions below.
Suppose the price is $6. What is the Quantity Supplied?
Suppose the Quantity Supplied is 200. What must the price be?
Suppose the price is $5 resulting in a Quantity Supplied of 300. Then the pric
Answers
Answer:
a. 400
b. 4$
Step-by-step explanation:
2$ equals 0 Quantity
3$ equals 100 Quantity
4$ equals 200 Quantity
We can see that starting from 2$, a dollar will increase the Quantity by 100
If x= -2 and y=√12 then 2(3x³+ 2y²)=
Answers
Answer:
Step-by-step explanation:
Begin by filling in x as -2 and y as √12 in the given expression:
[tex]2(3(-2)^3+2(\sqrt{12})^2)[/tex]. Work inside the parenthesis first and deal with those exponents:
(-2)³ is the same as (-2)(-2)(-2) which is -8;
(√12)² is the same as (√12)(√12) which is √144 which is 12.
Filling those simplifications in:
[tex]2(3(-8)+2(12))=2(-24+24)=2(0)=0[/tex]
The area of a rectangular cocktail table is x^2-18x+32 If the width is x-16 what is its length?
Answers
Answer: (x-2)
Step-by-step explanation:
This problem is a middle-term factorization, or factoring by splitting the middle term.
We have the equation
x^2 - 18x + 32
This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.
x^2 - 18x + 32
= x^2 - 16x - 2x + 32
= x(x-16) - 2(x - 16)
= (x-16) (x-2) -------> we get this through taking (x-16) common
We could also pretend that the length is x - y, where y is the number we need to finish the equation.
x^2 - 18x + 32
= (x-16) (x-y)
= x^2 -16x - xy + 16y
-16 minus 2 is -18, which is our middle term.
Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.
Our answer is that the length is (x-2).
Kelsey is looking for a job cutting hair. One option is self-employment at The Oakland Salon, where she would pay $400 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Kelsey pay?
Answers
she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.
How to find the amount paid to either salon that is equal?she would pay $400 per month to rent a station and keep all of her earnings.
Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut.
Therefore,
let
x = number of haircut
Hence,
4x = 400
divide both sides by 4
4x / 4 = 400 / 4
x = 100
Therefore, she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.
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FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
A) IF P(A OR B) = 0.6, P(B) = 0.3, AND P(A AND B) = 0.1, FIND P(A).
Answers
The value of the probability P(A) is 0.40
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.6
P(B) = 0.3
P(A and B) = 0.1
To calculate the probability P(A), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
0.1 = 0.3 + P(A) - 0.6
Collect the like terms
P(A)= 0.1 - 0.3 + 0.6
Evaluate the expression
P(A)= 0.4
Hence, the value of the probability P(A) is 0.40
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Answer the following.
(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation.
(b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
Answers
Answer:
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a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.
b. 1.1105 pounds is written in standard notation as 1.1105 pounds.
We have,
(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one
non-zero digit to the left of the decimal point.
The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.
So,
= 0.00000896
= 896/100000000
= 896 x 100/100 x [tex]10^{-8}[/tex]
= 896/100 x [tex]10^{-8 + 2}[/tex]
= 8.96 × [tex]10^{-6}[/tex]
(b)
To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.
1.1105 pounds is written in standard notation as 1.1105 pounds.
Thus,
a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.
b. 1.1105 pounds is written in standard notation as 1.1105 pounds.
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Find the perimeter of the rectangle 2A+ 4
a
Answers
L = length
W = Width
posite
A rectangle, a triangle, and a hexagon are drawn on the
same plane, as shown. How many points of
intersection are there between the rectangle and
hexagon?
Answers
The number of points of intersection between the rectangle and hexagon is = 4
What is point of intersection?The point of intersection between two or more lines is where the lines met at a particular plane. The point of intersection an equally be referred to as the vertex.
A rectangle is a quadrilateral because it's made up of four sides of which the two sides which are opposite, are equal and parallel.
A triangle is a polygon that is made up of three lines that meet to form edges and angles.
A hexagon is a polygon that is made up of six sides and six angles.
From the attached image, the rectangle which has four sides, made an intersection with the hexagon at four points which are marked with an asterisk.
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Answer:
2
Step-by-step explanation:
B
Given: ∠1=∠2
If AC3, BC = 5, and AB=7, find AD.
020
04
040
2/3
Answers
Answer:
Option 3
Step-by-step explanation:
[tex]\frac{5}{3}=\frac{AD}{7-AD} \\ \\ 35-5AD=3AD \\ \\ 35=8AD \\ \\ AD=4 \frac{3}{8}[/tex]
A new outlet is being planned with an allocated budget of $50,000 per month for advertising and planned average price of $10.00 per pizza. Estimate the monthly sales (number of pizzas) of this outlet.
Answers
Answer:
5,000
[tex]50000 \div 10 = 5000[/tex]
Jason wants to receive monthly payments of $3,250 for 15 years. How much does he have to invest now in an annuity that has an annual interest rate of 3.6% to achieve his goal? Round your answer to the nearest hundred.
Answer: $451,500
Answers
The amount she should invest today in the annuity is $455,450.40.
How much should be invested today?The first step is to determine the future value of the monthly annuity.
Future value = monthly payment x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 3.6/12 = 0.3%n = number of periods : 15 x 12 = 180Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92
The second step is to determine the present value of this future annuity:
774, 171.92 / (1.036^15) = $455,450.40
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a fisherman travels 9mi downstream with the current in the same time he travels 3 mi upstream against the current. if the speed of the current is 5mph what is the speed at which the fisherman travels in still water
Answers
Answer:
10 mph
Step-by-step explanation:
speed of boat in still water = x
speed of current = 5
speed of boat with current (downstream) = x + 5
speed of boat against current (upstream) = x - 5
distance downstream = 9
distance upstream = 3
time = t
speed = distance/time
distance = speed × time
downstream:
9 = (x + 5)t
upstream:
3 = (x - 5)t
9 = xt + 5t
3 = xt - 5t
9 = xt + 5t
-3 = -xt + 5t
-----------------
6 = 10t
t = 0.6
9 = (x + 5)0.6
15 = x + 5
x = 10
evaluate the logarithm e^in4
Answers
The value of the evaluation of logarithm e^in4 is 4
How to determine the logarithmGiven the expression as;
e^in4
To put in logarithmic form, equate to the power of the "Lin,ln value"
Now, let's equate it to the value of the exponential
e^in4 = 4
We have that'
[tex]loge x = loge 4[/tex]; this is the logarithmic form of the expression but we need to find the value of 'x'
To find the value, let's cancel out the like variables, we have
[tex]x = 4[/tex]
Then we have the value to be
x = 4
Thus, the value of the evaluation of logarithm e^in4 is 4
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22. Kim earns x dollars per hour for the first 40 hour she works in a week
and 1-
1¹/1/12 times as much for each hour over 40. If she worked 52 hours
last week, how much, in dollars, did she earn?
(A) 52X
0+1=1/x
(C) 52x+1-¹-x
(B) 40+1
(D) 52x-1-x
(E) 58x
Answers
40+1 in dollars per hour
Solve for the value of w.
(4W-8)°
(3w+6)°
Answers
Step-by-step explanation:
4W-8=3W+6
4W-3W=6+8
W=14°
lets find the value of W in this straight line
4W-8°=180°(angle on a straight line)
collect like terms
4W=180°+8°
4W=188°
divide both sides by the coefficient of W which is 4
W=47°
if i am correct pls rate it
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the Empirical Rule to estimate the proportion.
Answers
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
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Live fund are selling their holdings at $5000 per share. How much would live fun receive if they sold half their holdings in Marx brothers?
Answers
Answer:
2500
Step-by-step explanation:
5000 ÷ 2 = 2500
A cone has one-third times the volume of a cylinder with the same base and
altitude.
A. True
B. False
Answers
Answer:
A cone has one -third times the volume of a cylinder with the same base and altitude. True
The answer is A. True.
Assuming the cylinder and cone have same base and altitude, the formulas are :
Cylinder = πr²hCone = 1/3πr²hBased on this, we can understand that :
A cone has one-third times the volume of a cylinder with the same base and altitude.
Find the square.
(7m-3) 2
49m²-21m-9
Answers
Step-by-step explanation:
(7m - 3)² = 49m² - 42m + 9
play it through and do the actual multiplication behind the square :
(7m - 3)² = (7m - 3)(7m - 3) =
= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =
= 49m² - 2×21m + 9 = 49m² - 42m + 9
Coach Kirby is forming dodgeball teams from students in her physical education class.
She wants teams that each have 6 students. There are fewer than 48 students in the class,
so Coach Kirby can't form as many full teams as she wants.
1)) Let x represent how many full teams Coach Kirby can form. Which inequality describes
the problem?
6x < 48
6x > 48
Solve the inequality. Then, complete the sentence to describe the solution.
1) Coach Kirby can form fewer than 8|
full teams.
Please hurry
Answers
Answer:
6x<48
Step-by-step explanation:
ik its this one because theres 48 players and 6 teams both are even numbers so if you did 48÷6x you would get 8 but theres fewer than 48 kids
What’s an Inequality?
Answers
Answer:
mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Answer:
The quality of being unequal or uneven is known as the inequality.Janet plans to save $22.50 each week until she has enough to buy a $180 bicycle. After how many weeks will she have enough money for a bicycle.
Answers
Answer:
Step-by-step explanation:
8weeeks bc 22.50*8=180
