Answer the following questions for
f(x) = -x^4 + x^3 - 7x^2 + 9x + 18
A.) How many total zeros does this function have? Explain how you know. (1 point)
B.) Using p/q, list all possible rational zeros. (3 points)
C.) Using Descartes' Rule of Signs, how many possible positive, negative, and complex (imaginary) zeros are possible... list all possibilities. It would be helpful to make a table (4 points)
D.) Describe the end behavior of this graph. (2 points)
Answers
All the possible values of the polynomial are given below, with the complete explanation.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
We have a function polynomial,
f(x) = -x⁴ + x³ - 7x² + 9x + 18.
A). The degree of the polynomial is 4.
That means, it has 4 zeros.
B). Using p/q:
The factor of constant term 18 are ±2, ±3, ±6, ±9, ±18.
The factor of leading coefficient -1 are ±1.
Now, by p/q,
all possible rational zeros = ±2, ±3, ±6, ±9, ±18.
C). Using Descartes' Rule of Signs,
There are 3 times the sign changes for the positive and negative both times.
So, the possible positive number of roots are 3 or 3-2 = 1.
The possible negative number of roots are 3 or 3-2 = 1.
And the complex roots comes in the pair.
So, there are 2 possible complex roots if there is only a negative and a positive roots.
D). From the attached graph,
the end behavior of the polynomial is negative infinity.
Therefore, all the required values are given above.
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Related Questions
if the variance of the population a is 10 and the variance of the population b is 15, does it mean that population a has less variability than population b?
Answers
Yes, the given statement is true if the variance of the population 'a' is smaller than the variance of population 'b' it represents that population 'b' is more variable than 'a'.
Population variance represents the measurement of spread of group data points.It shows the average squared deviation from the given mean.Whenever data points are very near to the mean then the variance has smaller value.And when data points are far away to the mean then it has larger value of variance.Here variance of population 'a' is 10 which is smaller than the variance of population 'b' .It represents population 'a' is less variable than population 'b'.Therefore, the given statement is true for the variance of population 'a' and 'b'.
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Write x^4 +5x^2-8 in quadratic form, if possible
Answers
Writing x^4 + 5x^2 - 8 in quadratic form will result to
y² + 5y - 8How to write the equation in quadratic formQuadratic equation involves having the variables to be in exponents of 2 as the maximum. That is making the equation degree 2
The equation x^4 + 5x^2 - 8 is rewritten by say
x² = y
then we have
y² + 5y - 8
The equation in quadratic form is y² + 5y - 8
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which function models the table? Help!!
Answers
if there are 250 members of the 8th grade class, then what percent prefer either tennis or football? (the tennis is 20 and the football is 14)
Answers
The percentage of preference of tennis or football is, 13.6%
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
The total number of students who prefer tennis is 20.
And the total number who prefer football is 14,
so the total number who prefer either tennis or football is
⇒ 20 + 14
⇒ 34
To find the percentage of students who prefer either tennis or football, we can divide the number of students who prefer either by the total number of students and multiply by 100:
(34 / 250) x 100 = 13.6%
So, approximately 13.6% of the 8th grade class prefer either tennis or football.
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the number of new cases of a disorder in a population that emerge in a particular time interval is called the:
Answers
The number of new cases of a disorder in a population that emerge in a particular time interval is called the incidence.
About incidenceIncidence refers to the rate at which a new event occurs in a population. Incidence takes into account the variable time period during which a disease-free individual becomes at risk of spreading the disease.
In incident calculations, the quantifier is the number of events that have occurred in a given time. Then the quantifier of the denominator is the population that is at risk of experiencing the event during this period.
Simply put, incidence refers to new cases and is used to determine the etiology of the disease. While prevalence is more widely used to refer to health status in certain populations.
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Which rectangular prism has the largest volume?
Answers
Answer:
The first one is largest volume: 27
Step-by-step explanation:
1) 3*3*3=27
2)4*4*1=16
3)2*4*2=16
4)1*6*2=12
Two boats were 400 miles apart at midnight and were both sailing to the same port on Honolulu. One boat was heading west and the other was heading east. If they both arrived at 8:00am, find the speed of each boat if one was 20MPH faster than the other.
Answers
The speed of the air or water increases and its pressure decreases as it circles the longer-path side of the sail or keel. The air or water will attempt to migrate from the side of high pressure to the side of low pressure as it moves along the sail or keel in response to the consequent pressure difference.
How is sailing speed determined?Theoretical displacement hull speed is determined by the following equation: velocity in knots = 1.35 x waterline length in feet squared.
Use x to symbolise the slower boat's speed.
Therefore, the faster boat's speed would be x + 20 mph.
They met for 8 hours, hence the distance they travelled overall during that period is depicted as
Distance: (x + 20) * 8 + x * 8
Thus, we have
Distance: 16x plus 160
At twilight, the two boats were separated by 400 kilometres.
The distance equation is as follows.
400 = 16x + 160
Analyze similar terms
16x = 240
multiply by 16
x = 15
Remember that
20 mph faster boat equals x.
Thus, we have
Speedier boat = 15 plus 20
Speedier boat = 35
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the dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. the data is divided into equal-sized subgroups with 25% of the adults in each subgroup. which measure of center can you most accurately estimate from this information?
Answers
which measure of center can you most accurately estimate from this information: Median
The median divides the data into equal-sized groups. So approximately 50% of the data is above the median and approximately 50% of the data is below the median.
Calculating the median
The median is the value in a data set, implying that half of data focuses have a value more modest or equivalent to the median and half of data focuses have a value higher or equivalent to the median.
For a little data set, you first count the quantity of data focuses (n) and organize the data focuses in expanding request. Assuming the quantity of data focuses is lopsided, you add 1 to the quantity of places and separation the outcomes by 2 to get the rank of the data point whose value is the median.
The rank is the place of the data point after the data set has been organized in expanding request: the smallest value is rank 1, the second-smallest value is rank 2, and so forth.
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the complete question is:
The dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. The data is divided into equal-sized subgroups with 25% of the adults in each subgroup.
Which measure of center can you most accurately estimate from this information?
1. mean
2. median
A coral reef is located near to a chemical plant. Scientists measure the number of colonies of coral over a period of 20 years. Each year, the
number of colonies is 5 times the previous year.
Which equation shows the number of colonies, c after t years?
c=5-25²
c=25-3²
c=25-5²
c=25+3t
c=25-20¹
SCALE:
0 - 1 - 2 - n
25-125-625-n
Find out which equation best suits N on the scale.
Answers
Answer:
c = 25 * 5^t
Step-by-step explanation:
c = 25 * 5^t
This equation best suits N on the scale as it follows the pattern of the number of colonies being 5 times the previous year.
Solve for x :
[tex] \it{ \large{2x - 6 = 2(3x + 5)}}[/tex]
Thank You!
Answers
2x-6x=6+10
-4x=16 (divide both sides with -4)
X=-4
Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 19, 13, 7,
Answers
An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 19 - 6(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 19
Second term, a₂ = 13
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = 13 - 19
Common difference, d = -6
Substituting the parameters into the mathematical expression, we have;
aₙ = 19 + (n - 1)(-6)
aₙ = 19 - 6(n - 1).
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Calculate the area of the figure below using the following information:
Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units
Image of irregular pentagon with vertices points A, B, C, D, and E starting at upper left moving clockwise. Two dotted diagonal lines, one connecting vertices A and C, and the second connecting vertices A and D.
Answers
The area of figure ABCDE is 26.5 square units.
What is a Triangle?Three angles, three sides, and three vertices make up the closed shape of a triangle. It is one of the most fundamental geometric shapes, and the symbol for it is.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape
Given:
Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units
To calculate the area of the figure we have to add the area of the individual triangles together.
So, Area of figure ABCDE
= Area of triangle ABC + Area of triangle ACD + Area of triangle AED
= 7.95 + 9.8 + 8.75
= 26.5 square units
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I need help on this problem
Answers
The distance of Main Street is given by the equation D = 319.25 feet
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the distance of Main Street be D
Now , let the triangle be represented as ΔABC
The base of the triangle BC = 300 feet
The hypotenuse of the triangle AC = distance between First avenue and Canal street
The measure of angle ∠BAC = 70°
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin 70° = 300 / D
Multiply by D on both sides of the equation , we get
D ( sin 70° ) = 300
Divide by sin 70° on both sides , we get
D = 300 / ( sin 70° )
On further simplification , we get
D = 300 / 0.939692
D = 319.2535
D = 319.25 feet
Hence , the distance is 319.25 feet
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the difference of two numbers is 52. the larger number is three less than six times the smaller number. find the numbers. (enter your answers as a comma-separated list.)
Answers
If the difference of two numbers is 52 and larger number is six times the smaller number , then the smaller number is 11 , larger number is 63 .
Let the smaller number be denoted by "x".
according to the information that, "larger number is three less than six times the smaller number" ;
So, the larger number can be represented as 6x - 3.
The difference between the two numbers is 52,
that means ; (6x - 3) - x = 52
On Solving for x ;
we get ;
⇒ 5x = 55
⇒ x = 11
Therefore , the smaller number is 11, and the larger number is 6×11-3 = 63.
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Year 9 students from a school were asked to choose one language to study. The table shows information about their choices. Students in maths class 9s1 were told to draw a pie chart to ultralight
Answers
Hexagon HEXAGZ has vertices H(3,0), E(1, -2), X(-1, -2), A(-3,0), G(-2,2), and Z(1,2). What are the coordinates of the image of HEXAGZ for a dilation with center (0,0) and a scale factor of 3.5?
Answers
Answer: ion know
Step-by-step explanation: 1 + 2 = 3
you can infer causality from a correlational result, but only when the r value is greater than
a.0
b.0.5
c.1
Answers
A correlational result can be used to infer causality, but only if the value of r is greater than 0.
What is infer causality?In statistics, a correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. A positive correlation coefficient implies that two variables are related (as one variable increases, so does the other), whereas a negative correlation value shows that two variables are inversely related (as one variable increases, the other decreases).A correlation value of zero shows that no relationship exists between two variables. However, a correlation coefficient greater than 0 does not imply causality, meaning that it cannot be concluded that one variable causes changes in the other variable. Establishing causality requires additional evidence and methods such as experimental designs or causal inference techniques.To learn more about infer causality refers to:
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Question 6 Mathematics
Answers
The predicted number of barrels of crude oil for October is given as follows:
19.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
y = -0.02x² + 0.14x + 19.6.
October is the 10th month, hence the prediction is obtained as follows:
y = -0.02(10)² + 0.14(10) + 19.6
y = 19.
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HELP THIS IS FOR EXTRA CREDIT AND ITS DUE TODAY
You spin a spinner that is equally divided into 11 parts. 3 parts are green, 3 parts are speckled, 2 parts are white, and 3 parts are yellow.
What is the probability of the spinner not stopping at a white section? Write your answer as a decimal rounded to the nearest hundredth.
Answers
Answer: The probability of the spinner stopping at a green section and then rolling a 3 is 1/22
Step-by-step explanation: A spinner stopping at a green section
B: rolling a 3
the spinner is divided into 11 parts, 3 of them are green, then:
P(A) = 3/11
the number cube has 6 numbers, then:
P(B) = 1/6
The two events are independent, then:
P(A∩B) = P(A)*P(B) = 3/11 * 1/6 = 1/22
Select the trigonometric equation that can be used to find x.
Answers
Answer:
tan(64)= x/11
Step-by-step explanation:
if we make 64 degrees are central angle then that means the side along the right angle is the adjacent and side x is the opposite
since tan∅ = opposite/adjacent
we know angle is 64 and adjacent is 11
thus,
tan 64 = x/11
An item is regularly priced at $30. Maria bought it on sale for 80% off the regular price. How much did Maria pay?
Answers
Answer:
$24
Step-by-step explanation:
30 times .80=24
10 m
55 m
60 m
90 m
20 m
15 m
Whats the perimeter
Answers
The perimeter of the polygon is 250m
What is polygon? what its perimeter?A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface. The polygon can be divided into two different types, such as regular polygons and irregular polygons, depending on its sides and angles.
The total of a polygon's sides is referred to as the polygon's perimeter. If a polygon has regular sides, its perimeter may be calculated using the formula Perimeter of Regular Polygon = (Number of Sides) x (Polygonal Side Length) units.
Given the sides of the polygon are 10 m, 55 m, 60 m, 90 m, 20 m and 15 m.
The perimeter of the polygon = sum of all sides
The perimeter of the polygon = 10m + 55m + 60m + 90m + 20m + 15 m.
The perimeter of the polygon = 250m
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lisle and linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and linda walks 2.8 kilometers every 30 minutes. how far apart are they after 1 hour?
Answers
The total distance between lisle and Linda will be 10.4 kilometers.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that lisle and Linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and Linda walks 2.8 kilometers every 30 minutes.
lisle's distance in an hour:-
0.8 x 6 = 4.8 Km
Linda's distance in an hour:-
2.8 x 2 = 5.6 Km
Total distance = 4.8 + 5.6 = 10.4 Km
Therefore, there will be 10.4 kilometers between Lisle and Linda overall.
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suppose that you are awarded prize money if you match at least three of the winning numbers. the probability that you will win some prize money is .
Answers
The frequency of winning numbers you can match, determines your chance of winning a prize.
The likelihood of earning some money is one if you can match three or more of the winning numbers (certain). However, the probability of winning any prizes is zero if you can only match two or fewer of the winning numbers (impossible).
Probability distribution: The probability that a random variable will take on a specific value or range of values is expressed mathematically as a probability distribution. It is often referred to as a probability mass function or a probability density function (PDF) (PMF). Each result of a random event, such as the roll of a dice, the toss of a coin, or a stock market return, is given a probability by the probability distribution.
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Solve for x on the diagram below
Answers
Answer:
x = 60°
Step-by-step explanation:
the 'x' angle and the adjacent 120° angle form a straight line
a straight line consists of 180°
Rule: 1, 2, 3, 5, 8,
Answers
Answer: 13, 21, 34...
Step-by-step explanation: 1+2 = 3, 2+3 = 5, 3+5 = 8, 5+8 = 13, 8=13 = 21, etc.
what is the probability that a standard normal random variable will be between .3 and 3.2?
Answers
0.3814 is the probability that a standard normal random variable .
What is the probability equation?
The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.
P(E) = positive outcomes/total outcomes is how it's expressed mathematically. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula. Mathematically speaking, it seems as follows: P(E) stands for positive outcomes/total outcomes.
P(0.3 < z < 3.2)
= P(z < 3.2) - P(z < 0.3)
= 0.9993 - 0.6179
= 0.3814
Probability = 0.3814
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
2(x-7) = 36
2x - 14 = 36
(add 14 to both sides)
2x = 50
(divide 2 by both sides)
x = 25
the average area of a bedroom in a home is 219 square feet with a standard deviation of 32.5 square feet. what is the largest a bedroom can be and be among the smallest 20% of bedrooms in a home?
Answers
The largest a bedroom can be and still be among the smallest 20% of bedrooms in a home is around 271 square feet.
To understand this answer, we have to use the concept of standard deviation, which is a measure of how spread out the data is from the mean. In this case, the average area of a bedroom is 219 square feet, with a standard deviation of 32.5 square feet. To calculate the 20th percentile, we need to find the value of X such that P(X < x) = 0.20, where P(X < x) is the cumulative distribution function of X.
We can use a standard normal table to find the Z-score corresponding to 0.20 and then convert it back to the original scale. The Z-score for 0.20 is -0.84. Therefore, x = 219 + 32.5 * (-0.84) = 271, which is the largest a bedroom can be and still be among the smallest 20% of bedrooms in a home.
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what is the unit of measurement for coding the length of lacerations? a. square inches b. inches c. square centimeters d. centimeters
Answers
The unit of measurement for coding the length of lacerations d)centimeters.
Centimeters are the most common unit of measurement used to code the length of lacerations. This is because they are a small enough unit of measurement that they can accurately describe even the smallest of lacerations.
Centimeters are also the most commonly used metric unit of length, making them the most useful when coding lacerations for medical records. In addition, centimeters are a more precise unit of measurement than inches and are accepted internationally as a unit of measurement, making them the best choice when coding lacerations.
Finally, centimeters are consistent units of measurement, making it easy to compare laceration lengths between different patients and different medical records.
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