The function f(x) is a cubic function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.
Answers
The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
What is a polynomial function?
Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.
By using the given table, we can plot the points on the graph and we can draw a graph
• Fitted coefficients:
a = 9
b = -9
c = -1
d = 1
Then we can prepare the polynomial as
y = 9 - 9x - x² + x³
Now write down in the standard form, we get
f(x) = x³ - x² -9x + 9
Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
To learn more about polynomials, visit:
https://brainly.com/question/2833285
#SPJ1
Related Questions
Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
Answers
The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:
By the cross product property, \(AC^2 = BC \cdot AD\).
To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
\($\frac{AB}{BC} = \frac{AD}{AB}$\)
Cross-multiplying, we get:
\($AB^2 = BC \cdot AD$\)
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
\($\frac{AC}{BC} = \frac{AD}{AC}$\)
Cross-multiplying, we have:
\($AC^2 = BC \cdot AD$\)
Now, we can substitute the derived expressions into the original equation:
\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)
It was made possible by cross-product property.
Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:
By the cross product property, \(AC^2 = BC \cdot AD\).
For more questions on cross-product property:
https://brainly.com/question/14542172
#SPJ8
Which of the following are not trigonometry identities? Check all that apply
Answers
That’s the answer bro trust xx
Answer:A
Step-by-step explanation:
Good luck on the exam!
. Write an expression equivalent to 3w - 3w + 3w with just one term. - What property or properties applies?
Answers
Answer:
w(3-3+3)
Step-by-step explanation:
distibutitve property
what is 3 1/2 times 2 2/3?
Answers
Answer:
The answer is 9 1/3.
Need help solving this.
Answers
The option that needs revision is option 3. This is because you cannot place point A anywhere on PQ. A is created by the construction of Circle A. A is the center of circle A.
What is the process of constructing a line tangent to another circle ? Identify the circle to which the tangent line will be drawn.Draw the radius of the circle from its center to the point where the tangent line is desired.Construct a perpendicular line to the radius at the point where the tangent line is desired. This can be done using a compass or by drawing a line perpendicular to the radius.Use a compass to draw an arc from the center of the circle that intersects the perpendicular line at two points.Connect the center of the circle to one of the points of intersection on the perpendicular line. The line drawn in stes p 5 is the tangent line to the circle at the desired points.Learn more about Circle at:
https://brainly.com/question/24375372
#SPJ1
Example: Divide 3 loaves between 5 people First, divide two of the loaves into thirds... each person gets one third each, with one third left over Then divide the left-over third from the second loaf into fifths So, each person gets: 1/5 and the third loaf into fifths each person gets one fifth each each person gets a slice (one fifteenth) 1/15 3/5 The Egyptians used the approximated process to work on the area of a circle as shown in the picture. 1.4 Show the representation of the fractions on the second row. (2) 1.5 Show the algorithm/abstract strategy to justify the 3/5 found as the answer. (3)
Answers
The algorithm justifies the answer of 3/5 as the fraction each person gets.
Representation of the fractions on the second row:
From what you described, two of the loaves were divided into thirds.
This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.
Therefore, each person receives one fifth from this remaining third.
So, the representation of the fractions on the second row would be:
Each person receives 1/3 (one third) from the two loaves.
Each person receives 1/5 (one fifth) from the remaining third.
Algorithm/Abstract strategy to justify the 3/5 found as the answer:
To find the final answer of 3/5, we can follow the steps you provided:
Divide two loaves into thirds, giving each person 1/3.
Divide the remaining third from the second loaf into fifths, giving each person 1/5.
Combining the fractions, each person has 1/3 + 1/5.
To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:
1/3 = 5/15 (multiplying numerator and denominator by 5)
1/5 = 3/15 (multiplying numerator and denominator by 3)
Now, we can add the fractions:
5/15 + 3/15 = 8/15
Therefore, each person receives 8/15 of a loaf.
Simplifying this fraction, we get 3/5.
Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.
Learn more about Algorithm/Abstract strategy click;
https://brainly.com/question/29438718
#SPJ1
Solve equation
176 =-4(4 + 6m)
Answers
to solve for m
distribute into parentheses
176 = -16 - 24m
get m on one side
176 + 16 = -24m
192 = -24m
divide by -24
-8 = m
m = -8
Write an equation of a line that passes through (0 -5) and (2, -5)
Answers
Solution:
Step-1: Find the slope of the line.
Slope = Rise/Run = y₂ - y₁/x₂ - x₁=> -5 - (-5)/2 - 0=> -5 + 5/2=> 0/2 = 0Step-2: Find the y-intercept.
When looking at point (0 -5), we can see that the x-coordinate is 0.
This means that:
The y-intercept must be -5.Step-3: Create the equation.
y = (m)x + (b)=> y = 0x + (-5)=> y = -5Evaluate the variable expression when a = -2, b = 5, C = -5, and d = 3.
-4b + 1 (ac + bd)
5
5
Answers
Answer:
-4(5)+1(-2*-5+5*3)
Step-by-step explanation:
-20+1(10+15)
-19(25)
-475
Answer:
5
Step-by-step explanation:
Given :- a = -2 , b = 5 , c = -5 & d = 3
Solution :-
- 4 b + 1 ( ac + bd )- 4 ( 5 ) + 1 ( (-2)(-5) + (5)(3))-20 + -2 × -5 + 3 × 5-20 + 10 + 15- 20 + 255Active dry yeast and bread machine yeast were not available in stores during the coronavirus pandemic. Fleischmann’s attempted to staff two shifts to produce enough active dry yeast to put some yeast back on the market. If the first shift produced 1½ times as many yeast packets as the second shift, and 5,600 packets of yeast were produced during the month, how many packets of yeast were produced on each shift
Answers
Based on the rate of the production of yeast packets by the two shifts of Fleischmann’s, the packets produced in each shift were:
First shift - 3,360 packets Second shift - 2,240 packets What number of yeast packets were produced?Assuming that the number of yeast packets produced in the second shift is x, the number produced in the first shift would be:
= 1½ × x
= 1.5x
The number of yeast packets in the second shift is:
x + 1.5x = 5,600
2.5x = 5,600
x = 5,600 / 2.5
= 2,240 packets
The number of yeast packets in the first shift is:
= 2,240 x 1.5
= 3,360 packets
Find out more on solving for missing values at https://brainly.com/question/11897331.
#SPJ1
The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 8 dollars.
If a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 37.4 dollars? Round your answer to four decimal places.
Answers
Answer:
The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:
standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7
To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:
z = (37.4 - 40) / (8 / 7) = -1.225
Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.
give thanks, your welcome <3
Step-by-step explanation:
Please help it’s due today!!!!
Answers
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
Read more on isosceles triangle here: brainly.com/question/19238666
#SPJ1
Laura is creating the following design out of wood for it to be light enough she needs it’s area to be less than 80 square inches will Laura’s design be light enough justify you’re answer.
11inches 9inches 5Inches 5inches
Sorry I can’t show a pic
Answers
The area of a shape is the amount of space it can occupy.
Laura's design will be light enough
The shape is given as a trapezium (see attachment).
First, calculate the height (h) of the trapezium using the following Pythagoras theorem
\(5^2 = h^2 + x^2\)
Where:
\(x = \frac{11 - 9}{2} = 1\)
So, we have:
\(5^2 = h^2 + x^2\)
\(5^2 = h^2 + 1^2\)
\(25 = h^2 + 1\)
Collect like terms
\(h^2 = 25 -1\)
\(h^2 = 24\)
Take square roots
\(h = 4.90\)
The area of the shape is then calculated as follows:
\(Area = \frac{1}{2}(11 + 9) \times h\)
\(Area = \frac{1}{2}(11 + 9) \times 4.90\)
\(Area = \frac{1}{2} \times 20 \times 4.90\)
\(Area = 10 \times 4.90\)
\(Area = 49\)
The area of the shape is 49 square inches.
Hence, the shape will be light enough (because 49 is less than 80)
Read more about areas at:
https://brainly.com/question/16418397
36 x 1/15
Show your work
Answers
Answer:
2.4
Step-by-step explanation:
explanation is in the image above
Match each graph to its equation. 1. y = 2x - 3 2. y = -2x + 3 3. y = 2x + 3 4. y = -2x - 3
Answers
Answer:
There you are, hope this helps.
The required graph of the equation has been shown,
To draw the graph of the given equaiton,
1. y = 2x - 3 2. y = -2x + 3 3. y = 2x + 3 4. y = -2x - 3
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
1. y = 2x - 3
The slope is m = 2 and has a negative y-intercept of -3
2. y = -2x + 3
The slope is m = -2 and has a y-intercept of 3
3. y = 2x + 3
The slope is m = 2 and has a y-intercept of 3
4. y = -2x - 3
The slope is m = -2 and has a y-intercept of -3
Thus, the required graph of the equation has been shown,
Learn more about graphs here:
brainly.com/question/16608196
#SPJ2
Two students, Joseph and Madelyn, line up one behind the other. How many different ways can they stand in line?
Answers
Answer:
2 ways
Step-by-step explanation:
One with Joseph in front and Madelyn in back.
And the other with Madelyn in front and Joseph in back.
Find the distance between the two points in simplest radical form
(6,-4) and (1,-6)
Answers
Answer
\(\sqrt29\)
Step-by-step explanation:
1. Write the distance formula:
\(\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)
2. Substitute
Substitue (6, -4) and (1, -6) into
\(\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)
\(\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}\)
3. Calculate
\(\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}\)
\(\sqrt(-5) ^{2} + (-2)^{2}\)
\(\sqrt5 ^{2} + 2^{2}\)
\(\sqrt25 + 4\)
\(\sqrt29\)
Based on the information below what are the values of x and y of the solution to the system of equations used to create the information ?
Answers
Answer:
(D). x = 2 , y = - 5
Step-by-step explanation:
A = - 8 + 48 = 40
\(A_{x}\) = -76 + 156 = 80
\(A_{y}\) = 104 - 304 = - 200
x = \(\frac{A_{x} }{A}\) = 2
y = \(\frac{A_{y} }{A}\) = - 5
( 2, - 5 )
Answer:
D is the answer
Step-by-step explanation:
I need help I haven’t been here a week and I don’t understand my homework
Solve either
Answers
Answer: you need to add
Step-by-step explanation: I would ask your teacher to help you understand the lesson.
Twelve of the 28 students in a class have a dog. What is the ratio of students who have a dog to students who do not?
Answers
Answer:
28/12
Step-by-step explanation:
URGENT!!! due in 20 minutes GRAPH TRANSLATIONS 2 questions. Will mark brainliest!!!!
Answers
Answer:
Function f is translated to the right 2 units, and then up 1 unit to obtain function g.
To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:
Function f is translated to the right 2 units.
Function f is translated up 1 unit.
Function f is translated to the right 2 units, and then up 1 unit to obtain function g.
To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:
Function f is translated to the right 2 units.
Function f is translated up 1 unit.
Step-by-step explanation:
Select the correct answer.
(-1,1)
(0,-1)
(5,-11)
(10,-21)
What is the domain of the set of ordered pairs above?
A.
{-1, 1}
B.
{-1, 0, 5, 10}
C.
{-1, 10}
D.
{1, -1, -11, -21}
Answers
Amadi is three times as old as Chima. The sum of their ages is 24
Answers
Answer:
Amadi: 20 years old
Chima : 4 years old
569,820 divide by 4
569,820 divide by 5
569,820 divide by 10
569,820 divide by 6
569,820 divide by 9
569,820 divide by 3
569,820 divide by 2
and when your done just tell me which one has no remainders (If u tell me the remainders, u get 1 bonus point and that equals........18 POINTS!!)
Answers
Answer:
569820/4=142455
569820/5=113964
569820/10=56982
569820/6=94970
569820/9=63313.33333333333333 (remainder)
569820/3=189940
569820/2=284910
Step-by-step explanation:
PLZ PLZ PLZ HELPPPP
Answers
Answer:
LCD is 6
first choice
Step-by-step explanation:
least common denominator of 2 and 3 is 6
The terms central location or central tendency relate to the way quantitative data tend to cluster around some middle or central value.
a. True
b. False
Answers
Answer:
A: True
Step-by-step explanation:
It's true because central tendency is defined as a branch of descriptive statistics that shows the centre of the data distribution.
This central tendency could be mean, median or mode.
in a village the bell rings every 30 minutes at the junior school and every 45 minutes at the high school both schools start lessons at 8 a.m. if the high school bell ring 45 minutes how many times during the day with this bell ring at the same time as the Junior
Answers
12:00
SolutionConcept
we know that, the bell will rings again at the same time will be LCM of their individual time.Sum
LCM = 2 * 2 * 2 * 3 * 5 = 120 minutes.
Therefore
we can conclude that, both bells will ring again together after 120 minutes or 2 hours. 10AM + 2 hours = 12:00 noon.
art teacher has 450 sheets of construction paper on first day of school. students used 18 sheets during each school day. how many school days did the construction paper last?
Answers
Answer:
25
Step-by-step explanation:
025
18 |450
- 36
090
- 90
00
Answer for brainliest asap
Answers
Step-by-step explanation:
Draw a line to each similar vertex
2.72981366 rounded to nearest hundredth
Answers
Answer:
I would say 2.73 or 2.72 l can never remember which it is
Step-by-step explanation:
Sorry if it’s wrong!!!
Answer:
2.73
Step-by-step explanation: