Is the binomial a factor of the polynomial function? f(x) = x³ + 3x² -16x- 48 Select Yes or No for each binomial.
Answers
The binomial are factors of the given polynomial function f(x) = x³ + 3x² -16x- 48.
Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.
We can check whether the given binomials are factors of a given polynomial or not by factorizing the given polynomial.
[tex]f(x) = x^3 + 3x^2 -16x- 48[/tex]
Factoring out x² and 16, we get
[tex]f(x) = x^2(x + 3) -16(x+3)[/tex]
Now, factoring out (x+3), we get
[tex]f(x) = (x + 3)(x^2-16)[/tex]
Using Algebraic identity [tex]a^2-b^2=(a+b)(a-b)[/tex], we get
[tex]f(x) = (x + 3)(x+4)(x-4)[/tex]
So, it is clear that only the (x-4) binomial is a factor of the given polynomial and (x-3) and (x+2) are not.
Therefore, (x-4) is a factor of the given polynomial and (x-3) and (x+2) are not.
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Related Questions
Write an equation in slope-intercept form for the line with slope 5 and y-intercept -5 . Then graph the line.
Answers
Answer:
Step-by-step explanation: The equation for slope-intercept is y=mx+b
m= slope of the equation, b= y-intercept(what y is when x is zero)
there for the equation is y=5x-5
80% of what number is 280
Answers
Using the percentages formula, we know that 80% of 350 is 280.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, let the number be x:
Then, 80% of x is 280:Now, calculate as follows:
x/100 × 80 = 28080x = 280 × 10080x = 28000x = 28000/80x = 2800/8x = 350Therefore, using the percentages formula, we know that 80% of 350 is 280.
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Please I need some help understanding this
Answers
The values are given below,
Left Hand Limit i.e. lim x -> 1- f(x) = 3 ,
Right Hand Limit i.e. lim x -> 1+ f(x) = 1 ,
Function value at x = 1 i.e. f(1) = 1 ,
Left Hand Derivative lim x -> 1- f'(x)= -6 and
Right Hand Derivative lim -> 1+ f'(x) = -6.
So, the function f(x) is neither continuous nor differentiable at x = 1.
Given, a piecewise function
3㏑(3 - 2x) + 3 for x < 1
f(x) =
-3x² + 4 for x ≥ 1
Now, for lim x -> 1- f(x) we will consider the function 3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.
lim x -> 1 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3
= 3 ㏑(1) + 3
= 0 + 3
= 3
Now, for lim x -> 1+ f(x) we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.
lim x -> 1 -3x² + 4 = -3(1)² + 4
= -3 + 4
= 1
Now, for f( 1 ) we will consider the function -3x² + 4,
f(1) = -3(1)² + 4
= -3 + 4
= 1
Now, for lim x -> 1- f'(x) we will consider the derivative of the function
3㏑(3 - 2x) + 3,
lim x -> 1 -6/(3 - 2x) = -6/(3 - 2(1))
= -6
Now, for lim -> 1+ f'(x) we will consider the derivative of the function
-3x² + 4,
lim x -> 1 -6x = -6(1)
= -6
So, the function f(x) is neither continuous nor differentiable at x = 1.
Hence, lim x -> 1- f(x) = 3 , lim x -> 1+ f(x) = 1 , f( 1 ) = 1 , lim x -> 1- f'(x) = -6 and lim -> 1+ f'(x) = -6.
The function is neither continuous nor differentiable at x = 1.
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A bag contains 10 red balls, 8 green balls, and 6 blue balls. 2 balls are drawn at random at the bag. What is the probability that both balls are red?
Answers
Answer:
Assuming every single ball has an equal chance of being drawn, then if B is the probability of drawing a blue ball and R is the probability of drawing a red ball:
B + R = 1,
since either a red or blue ball will be drawn. Since each ball has an equal chance of being drawn:
16 p = 1, or
p = 1/16
where p is the chance to draw a single ball. Since there are 10 red balls, there are ten independent and different ways to draw a red ball, which means that
R = 10 p = 10/16 = 5/8.
You can either apply the first equation to find that
B = 1 - R = 3/8
or state directly that
B = 6 p = 6/16 = 3/8
since there are six independent and different ways to draw a blue ball from the bag.
Answer:
41.67%
Step-by-step explanation:
10+8+6= 24
10/24
First, you need to calculate your grade in percentages. The total answers count 24 - it's 100%, so we to get a 1% value, divide 24 by 100 to get 0.24. Next, calculate the percentage of 10: divide 10 by 1% value (0.24), and you get 41.67% - it's your percentage grade
For her party can Nina fill fewer than 10 bags with treats between 10 and 20 bags between 20 and 30 bags or more than 30 bags explain
Answers
The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:
Between 20 and 30 bags.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.
In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:
Number of bags = Number of treats / Treats per bag.
The values of these parameters are given as follows:
Number of treats: 78.Number of treats per bag: 3.Hence the numeric value of the expression is:
Number of bags = 78/3 = 26.
Which is a number between 20 and 30.
Missing InformationThe problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.
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The figure below is rotated 180° counterclockwise. What are the coordinates of the image of point W after this transformation?
Answers
The coordinates of the image of point W after a rotation of 180° counterclockwise are W'(-2,-5).
What is graph transformation?The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
The coordinates of the given point W are W(2,5).
The coordinate rule for a 180°counterclockwise rotation is:
(x,y)→(-x,-y)
Substitute (x,y) = (2,5) into the above coordinate rule:
(2,5) → (-2,-5)
Hence, the coordinates of the image of point W after a rotation of 180° counterclockwise are W'(-2,-5).
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Please help! Very hard! I will mark brainliest!
Answers
4. Definition of complementary
5. Substitution
6. Subtraction property
7. Definition of Congruence
What are corresponding angles?
According to the equivalent angle postulate, if a transversal meets two parallel lines, the corresponding angles must be congruent. In other words, the corresponding angles will always be identical if a transversal intersects two parallel lines.The angles that use the same relative location at each intersection of two parallel lines with a third line are known as corresponding angles to one another.The matching angles are similar to one another in nature.The two lines are parallel in nature if the corresponding angles in the two regions of intersection are congruent.Based on their sum, corresponding angles can be:Supplementary Corresponding Angles (if their sum is 180 degree)Complementary Corresponding angles (if their sum is 90 degrees)To know more about Corresponding Angles check the below link:
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Ahmad and Daryl had an equal amount of money at first. Ahmad's father gave him another $180, and Daryl spent $255. Ahmad then had 4 times as much money as Daryl. How much money did each of them have at first?
Answers
Answer:
$400
Step-by-step explanation:
Suppose Ahmad and Daryl both started with the same x amount of dollars.
Ahmad gains another 180 from his father, so he now has x+180 dollars.
Daryl spends 255, so he now has x-255 dollars.
After these events, Ahmad has 4 times as much money as Daryl, so
x+180=4(x-255)
Now we can solve for x to get the original amount of money.
x+180=4(x-255)
x+180=4x-1020
1200=3x
x=400
Both Ahmad and Daryl started with $400.
Which of the following is false?
O 7.401 < 7.411
O 6.881 > 6.429
O 3.391 < 3.42
1.224 1.242
Answers
Answer:
A-C are all true, What is option D?
Step-by-step explanation:
If D is 1.224 > 1.242 then that is the false statement
If D is 1.224 < 1.242 then there are no false statements.
The Data: Statistics about smoking and lung cancer for adults (age 18 and older) in the U.S:
⦁ Researchers estimate that 21.5% of men and 17% of women smoke cigarettes.1
⦁ The rate of new cases in 2008 showed that men develop lung cancer more often than women (70.2 and 50.5 cases per 100,000 persons, respectively).2
⦁ Smoking, a main cause of small cell and non-small cell lung cancer, correlates to 90% and 80% of lung cancer deaths in men and women, respectively.3 That is, 90% of men who are diagnosed with lung cancer are active smokers, and 80% of women who are diagnosed with lung cancer are active smokers.
Analyze the Conjecture:
1. What answer do you predict? Why? (2 points)
I predict 90% All the probabilities are given for the three different scenarios in men and women: people who smoke, people who develop lung cancer, and people who develop lung cancer who are also smokers. Then, these are even classified in terms of gender.
2. Given what you know about probability, how can you determine if smoking and lung cancer are related? (2 points)
Analyze the Data:
3. What is the probability that a randomly chosen man is a smoker? (1 point)
4. What is the probability that a randomly chosen man will be diagnosed with lung cancer? (1 point)
5. Given that a man has lung cancer, what is the probability that he is a smoker? Write this event with the correct conditional notation. (2 points)
6. What is the probability that a randomly selected man will be a smoker and be diagnosed with lung cancer? (2 points)
7. For a randomly selected man, are the events diagnosed with lung cancer and smoker independent events? Support your answer with probabilities. (2 points)
Consider the Case for Women:
8. For a randomly selected woman, are the events diagnosed with lung cancer and smoker independent or conditional? Support your answer with probabilities. (4 points)
Making a Decision:
9. What can you conclude about smoking and lung cancer? Are they conditional or independent events? (2 point)
10. Some people who have never smoked develop lung cancer. Does this disprove the evidence? (1 point)
Answers
All the probabilities are provided for the three situations involving men and women: smoking, developing lung cancer, and developing lung cancer while simultaneously smoking. Then, these are even divided into gender categories.
However, the last query is limited to males who smoke who develop lung cancer. Therefore, I believe that all of the other information is merely a red herring. You just need to search through the other options to locate the answer, which is already there. You should first disregard any possibilities involving ladies because we are only interested in men. The likelihood that males with lung cancer smoke is the next statistic you discover. The solution is 90%.
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0.5 divided by 516.3
Answers
The value of division when 0.5 divided by 516.3 is 0.000968
In this question, we have been given two decimal numbers 0.5 and 516.3
We need to find the value of division when 0.5 divided by 516.3
The division of decimal numbers is:
0.5/516.3 = 0.0009684292
0.5/516.3 ≈ 0.001
Therefore, the value of division when 0.5 divided by 516.3 is 0.000968
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Which decimal is equivalent to 201%?
210
2.01
2.10
0.201
Answers
Answer: 2.01
Step-by-step explanation:
A percentage is equal to x/100.
For example, 5% would be equal to 5/100.
5/100 = 0.05
So 201% = 201/100.
201/100 = 2.01
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8
Answers
Answer:
Step-by-step explanation:
find GH thank you sm nd will mark brainlist
Answers
Answer:
[tex]\text{GH} = 47[/tex]
Step-by-step explanation:
GH is one of the midsegments of triangle DEF. It divides both DE and EF to two equal segments (EH = HF, BG = GD).
A midsegment of a triangle has 3 characteristics:
- It splits the two sides it bisects into 2 equal segments.
- It is parallel to the side it doesn't bisect.
- It is equal to half the length of the side it doesn't bisect.
Applying the logic of the third characteristic, we can claim that GH = 1/2 * DF.
[tex]\text{GH} = \frac12\text{DF}\\\to 3x - 4 = \frac12 \times (9x - 59)\\\to 6x - 8 = 9x - 59\\\to 51 = 3x\\\to x = 17\\ \\\to \text{GH} = 3x - 4 = 3 \times 17 - 4 = 51 - 4 = 47[/tex]
1) A local fast food restaurant takes in $9000 in a 4 hour
period. Estimate how many hours it would take the same
restaurant to earn $20,250.
Answers
Answer: 9 hours
Step-by-step explanation:
Assuming they keep earning money at the same rate, we will set up a proportion to help us solve.
[tex]\displaystyle \frac{\$9,000}{4\;\text{hours}} =\frac{\$20,250}{x\;\text{hours}}[/tex]
Next, we will cross-multiply.
$9,000 * x = $20,250 * 4
$9,000x = $81,000
x = 9 hours
It will take the same restaurant about 9 hours to earn $20,250.
A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
Answers
The rocket reaches its maximum height at 2.25 second(s) after launch
The maximum height reached by the object is 88 feet.
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 72t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 72
Set to 0
-32t + 72 = 0
So, we have
32t = 72
Divide by 32
t = 2.25
Hence, the time is 2.25 seconds
The maximum heightIn (a), we have
t = 2.25
Substitute t = 2.25 in h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
Evaluate
h(2.25) = 88
Hence, the maximum height is 88 feet
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0000000036 * 000000716
Answers
Answer:
your answer is 25776
Step-by-step explanation:
Answer: 25776 is your answer
A salesman earns 40% commission on all the merchandise that he sells. Last month he sold $800 worth of merchandise. How much commission (in dollars) did he earn last month?
Answers
The commission when the salesman earns 40% commission on all the merchandise that he sells is $320.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the salesman earns 40% commission on all the merchandise that he sells and last month he sold $800 worth of merchandise.
The amount in commission will be:
= Commission percentage × Sales
= 40% × $800
= $320
The commission is $320.
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Write as a unit rate 44 point in 4 quarters
Answers
Answer: 11 points per quarter
Step-by-step explanation:
To find the Unit rate of 44 points in 4 quarters.
It is given that in 4 quarters there are 44 points
so we will divide 44 points by 4 quarters to get how many points are there in 1 quarter.
the unit rate = 44/4 = 11 points
There are 11 points in 1 quarter.
Question 1 (1 point) A small company wants to set up a server that is accessible from the company network as well as the Internet. Which of the following is MOST important to determine before allowing employees to access the server remotely The quality of the computer used to connect A security method of allowing connections The employees' home ISP speeds The geographical location of the employees
Answers
The most important to determine before allowing employees to access the server remotely is B. security method of allowing connections.
What is a computer network?Computer networking refers to the interconnection of computing devices that can exchange data and share resources. These networked devices use a set of rules known as communications protocols to transmit data over physical or wireless networks.
A computer network is a collection of computers that share resources that are located on or provided by network nodes. To communicate with one another, the computers use common communication protocols over digital interconnections.
Local-area networks (LANs) and wide-area networks (WANs) are the two basic network types (WANs). LANs connect computers and peripheral devices in a constrained physical area, such as a business office, laboratory, or college campus, using data-transmitting links (wires, Ethernet cables, fiber optics, Wi-Fi).
In this case, it should be noted that the security method that's used for allowing the connection is important. Based on the information illustrated, the correct option is B.
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PLEASE HELP! WILL GIVE BRAINLIEST IF IT IS CORRECT
Answers
The polynomial function of least degree with leading coefficient 1 and having zero at the given points is, [tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex].
What is polynomial?
A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 + 4x + 7 is an illustration of one with a single indeterminate x.
From the given polynomial, the least degree polynomials are,
f(x) = x^3 -5x^2 + 3x - x
[tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex]
These polynomial having leading coefficient 1.
Now to check x = 0, 1, (2 [tex]-\sqrt{5}[/tex]) are zeros of which polynomial.
Consider, the first polynomial
f(x) = x^3 -5x^2 + 3x - x
plug x = 0
f(0) = 0 - 5(0) + 3(0) - 0
f(0) = 0
plug x = 1
f(1) = 1^3 - 5(1)^2 +3(1) - 1
f(1) = 1 - 5 + 3 - 1
f(1) = -2
f(1) ≠ 0
Therefore, 1 is not the zero of this polynomial.
Now consider, the next polynomial
[tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex]
Plug x = 0
f(0) = 0
f(1) = 0
[tex]f(2-\sqrt{5} )=0[/tex]
Therefore, the polynomial [tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex] having given zeros.
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Answer:
[tex]f(x)=x^3-3x^2+\sqrt{5}x^2+2x-\sqrt{5}x[/tex]
Step-by-step explanation:
Given information:
Leading coefficient of 1.Zeros at x = 0, 1, 2-√5.Factor Theorem
If f(x) is a polynomial, and f(c) = 0, then (x – c) is a factor of f(x).
Therefore, the function in factored form is:
[tex]\implies f(x)=1 \cdot x(x-1)(x-(2-\sqrt{5}))[/tex]
[tex]\implies f(x)=x(x-1)(x-2+\sqrt{5})[/tex]
Expand the factored function:
[tex]\implies f(x)=x(x^2-2x+\sqrt{5}x-x+2-\sqrt{5})[/tex]
[tex]\implies f(x)=x(x^2-3x+\sqrt{5}x+2-\sqrt{5})[/tex]
[tex]\implies f(x)=x^3-3x^2+\sqrt{5}x^2+2x-\sqrt{5}x[/tex]
A library had 32 shelves of books. The books were placed either on the right or left side of the shelves. Each shelf had 21 books. There were 301 books on the left, how many books were there on the right?
Answers
Answer:
371
Step-by-step explanation:
hope it helped :)
Answer:
there are books on the right
371
Step-by-step explanation:
each shelves is 21
there are 32
books on the left 301
so the rest are on the right
21*32-301=371
so find how many are there and minus it by the books on the left side
[tex]21 \times 32 - 301[/tex]
how to calculate p-value in one-way anova table
Answers
The p-value in one-way anova table can be calculated using the following parameters
The numerator degrees of freedomThe denominator degrees of freedomThe F valueHow to determine the p-value in one-way anova table?The anova table represents the analysis of variance.
To calculate the p value from the anove table, the following parameters are needed
df Treatment, df Error and F value
The representation of the above parameters are:
The numerator degrees of freedom (df Treatment)The denominator degrees of freedom (df Error)When these values are known, we look up to the df Treatment, df Error and F values on the anova table, and write out the corresponding p value
Take for instance:
F-value = 2.358, df Treatment = 2df Error = 27The p-value for the above parameters is 0.1138
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Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (-9,3) (-5,7)
Line 2: (-11, 6) (-7, 2)
The slope of line 1 is
.
The slope of line 2 is
.
Answers
Answer:
Line 1: slope is 1
Line 2: slope is -1
Lines are perpendicular
Write a unit rate for the situation.
$12.50 for 5 ounces
Answers
A division is a process of splitting a specific amount into equal parts. The unit rate for $12.50 for 5 ounces is $2.5
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
$12.50 for 5 ounces
We need to find for a unit rate.
For this we need to use division. We have to split $12.50 among 5 ounces.
12.50 as Divisor and 5 as dividend.
Twelve point five zero divided by five
$12.50/5
2.5
Hence the unit rate for $12.50 for 5 ounces is $2.5
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A pizza restaurant used 1/2 of a liter of pizza sauce to make some pizzas. They put 1/8 of a liter of sauce on each pizza. How many pizzas did they make?
Answers
Answer:
4
Step-by-step explanation:
you can convert 1 half to 20/40 and 1/8 to 5/40 5,10,15,20 you can make 4 pizzas
IXL Please Help Fast!, Thank you guys for the help!
Answers
Answer:
FROM YOUR IXL I GOT IT FOR YOU
Step-by-step explanation:
find dy/dx of the following
1) y = tan^-1(3x-x³/1-3x²) where -1/√3 < x < 1/√3
Answers
[tex]{ \boxed{ \purple{ \sf{ \frac{dy}{dx} = \frac{3}{1 + {x}^{2}}}}}} [/tex]
Step-by-step explanation:
Given question is, [tex]{ \red{ \sf{y = {tan}^{ - 1}( \frac{3x - {x}^{3} }{1 - 3 {x}^{2} })}}}[/tex]
Put [tex]{ \tt{x = \tan \theta }}[/tex] then,
[tex]{ \tt{ \theta = { \tan}^{ - 1} x}}[/tex]
[tex]{ \red{ \sf{y = { \tan}^{ - 1}( \frac{3 \: tan \theta - { \tan}^{3} \theta}{1 - 3 { \tan}^{2} \theta})}}}[/tex]
But [tex]{ \green{ \sf{ \tan3 \theta = \frac{3 \: \tan \theta - { \tan}^{3} \theta }{1 - 3 \: { \tan}^{2} \theta}}}} [/tex]
[tex]{ \red{ \sf{y = { \tan}^{ - 1} ( \tan3 \theta)}}}[/tex]
[tex]{ \red{ \sf{y = 3 \theta}}}[/tex]
[tex]{ \red{ \sf{y = 3}}}{ \tt{ { \tan}^{ - 1} x}}[/tex]
[tex]{ \red{ \sf{ \frac{dy}{dx} = 3 \times }}}{ \tt{ \frac{1}{ {1 + x}^{2}}}} [/tex]
•°•[tex]{ \green{ \boxed{ \red{ \sf{ \frac{dy}{dx} = \frac{3}{1 + {x}^{2}}}}}}} [/tex]
A drone flying over a field of corn identifies a dry area. The coordinates of the vertices of the area are shown. To what coordinates should the portable irrigation system be sent to water the dry area? Explain your reasoning.
Answers
The coordinates to which the portable irrigation system should be sent to water the area are:
(495.75, 672).
Where to send the portable irrigation system?The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.
Hence the coordinates are given as follows:
x-coordinate: Mean of the x-coordinates of x = 56, x = 144, x = 888, x = 895.y-coordinate: Mean of the y-coordinates of y = 289, y = 332, y = 1012, y = 1055.Hence the x-coordinate of the point to which the system should be sent is:
x = (56 + 144 + 888 + 895)/4 = 495.75.
(the mean is given by the sum of the observations divided by the number of observations).
The y-coordinate of the point to which the system should be sent is:
y = (289 + 332 + 1012 + 1055)/4 = 672.
Missing InformationThe area is given by the image at the end of the answer.
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Arrange the following polynomials in order of their degree from least to greatest.
Answers
The polynomials in order of their degree from least to greatest are x, -3x² - 1, 4c² + c - 3, -8y³ + 5y - 2, y¹⁰
How to order the polynomials?The list of options represents the given parameters
The degree of a polynomial is the highest power of the polynomial
Take for instance, a polynomial ax^n has a degree of n
This means that the degrees of the given polynomials are:
Degree of x = 1Degree of -3x² - 1 = 2Degree of 4c² + c - 3 = 2Degree of -8y³ + 5y - 2 = 3Degree of y¹⁰ = 10The above represents the order of the polynomials
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