Find a polynomial function with real coefficients that has the given zeros
1 -√3i, 2
Answers
Answer:
[tex]x^3-4x^2+8x-8[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(x-(1-\sqrt{3} i)(x-(1+\sqrt{3} i)(x-2)=\\\\(x^2-(1-\sqrt{3} i)x-(1+\sqrt{3} i)x+(1-\sqrt{3} i)(1+\sqrt{3} i))(x-2)=\\\\(x^2-x+\sqrt{3} i-x-\sqrt{3} i+1-(\sqrt{3} i)^2)(x-2)=\\\\(x^2-2x-3\cdot(-1))(x-2)=\\\\(x^2-2x+4)(x-2)=\\\\x^3-2x^2+4x-2x^2+4x-8=\\\\x^3-4x^2+8x-8[/tex]
Related Questions
Given the focus and directrix shown on the graph, what is the vertex form of the equation of the parabola?
[tex]x\ =\ \frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]x\ =\ 10(y\ +\ 3)^2\ +\ \frac{3}{2}[/tex]
[tex]x\ =\ \textrm{-}\frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]y\ =\ \frac{1}{10}(x\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
Answers
The vertex-form equation of the parabola is given as follows:
y = 1/10(y - 3)² - 3/2.
What is the equation of a horizontal parabola?An horizontal parabola of vertex (h,k) is modeled as follows:
x = (1/4p)(y - k)² + h.
In which:
The directrix is x = h - p.The focus is (h + p, k).In the context of this problem, we have that:
The directrix is x = -4.The focus is: (1,3), hence k = 3.A system of equations is built for h and p as follows:
h - p = -4.h + p = 1.Hence:
2h = -3
h = -3/2.
p = 1 + 3/2 = 2.5.
Then the equation is:
y = 1/10(y - 3)² - 3/2. (first option).
Missing informationThe graph is given by the image at the end of the answer.
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When you are on the 2nd step of factoring this trinomial,you should be listing the factors of?
Answers
Given:
The trinomial equation is given as,
[tex]3v^2-4v-7[/tex]The objective is to choose the correct value for which the factors are to be obtained for factorization.
Explanation:
From the step 1, to perform the factorization the values of a and c has to be multiplied.
Then in step 2, the factors need to be calculated for the product of a and c.
Product of a and c :
The product of a and c will be,
[tex]a\times c=3\times7=21[/tex]Thus, factors are to be listed for the number 21.
Hence, option (1) is the correct answer.
Not a timed or graded assignment. Quick answer = amazing review :)
Answers
The question is given to be:
[tex]\sqrt[]{\frac{64}{100}}[/tex]Recall the rule:
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]Therefore, the expression becomes:
[tex]\sqrt[]{\frac{64}{100}}=\frac{\sqrt[]{64}}{\sqrt[]{100}}[/tex]Recall that:
[tex]\begin{gathered} 8\times8=64,\therefore\sqrt[]{64}=8 \\ \text{and} \\ 10\times10=100,\therefore\sqrt[]{100}=10 \end{gathered}[/tex]Hence, the expression becomes:
[tex]\frac{\sqrt[]{64}}{\sqrt[]{100}}=\frac{8}{10}[/tex]Dividing through by 2, we have:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]Therefore, the answer is:
[tex]\sqrt[]{\frac{64}{100}}=\frac{4}{5}[/tex]good night I will send a picture of work
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In the form of the equation
S = m D + b
S represented on the y-axis
D represented on the x-axis
The independent is x
The dependent is y
Then D is the independent
S is the dependent
let us find the correct answer
Study the diagram, where AB and C'D are chords that intersect inside of the circle at point P, which is not the center.
Answers
Answer:
answer of the given question
A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?
5
36
35
36
cakes/week
cakes/week
1 cakes/week
35
01 cakes/week
Answers
The cake is divided into 12 equal slices. Jake had eaten 5 slices after 3 days. The weekly cake consumption rate is 11.6
What is algebraic expression?An algebraic expression is one that is composed of integer constants, variables, and algebraic operations. 3x2 2xy + c, for example, is an algebraic expression. Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an algebraic expression, for example. An algebraic expression is one that contains constants, variables, and algebraic operations. 3x2 2xy + d, for example, is an algebraic expression. Thus, an algebraic expression is composed of three types of fundamental elements: Coefficient (i.e. numbers) (i.e. numbers)Therefore,
The weekly cake consumption rate is 11.6
we have 7 days.
7days-3days =4
in 3 days he has eaten 5 slices
again 4-3 days=1
so in 6 days, he has eaten 10 slices
we have 1 day left.so if he eats 5 slices in 3 days, how many does he eat slices in 1 day?
5/3=1.6
10+1.6= 11.6
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A forest products company claims that the amount of usable lumber in its harvested trees averages142 cubic feet and has a standard deviation of 9 cubic feet. Assume that these amounts haveapproximately a normal distribution.1. What percent of the trees contain between 133 and 169 cubic feet of lumber? Round to twodecimal places.II. If 18,000 trees are usable, how many trees yield more than 151 cubic feet of lumber?
Answers
1) Considering that the amount of lumber in this Data Set has been normally distributed, then we can start by finding this Percentage (or probability in this interval, writing out the following expressions:
[tex]\begin{gathered} P(133Now we can replace it with the Z score formula, plugging into that the Mean, the Standard Deviation, and the given values:[tex]Z=\frac{X-\mu}{\sigma}[/tex]Then:
[tex]\begin{gathered} P(\frac{133-142}{9}<\frac{X-\mu}{\sigma}<\frac{169-142}{9}) \\ P(-1Checking a Z-score table we can state that the Percentage of the trees between 133 and 169 ft³ is:[tex]P(-12) Now, let's check for the second part, the number of trees. But before that, let's use the same process to get a percentage that fits into that:[tex]\begin{gathered} P(X>151)=\frac{151-142}{9}=1 \\ P(Z>1)=0.1587 \end{gathered}[/tex]Note that 0.1587 is the same as 15.87%. Multiplying that by the total number of trees we have:
[tex]18000\times0.1587=2856.6\approx2857[/tex]Rounding it off to the nearest whole.
3) Thus, The answers are:
i.84%
ii. 2857 trees
Isaiah is a plumber. One day he receives a house call from a potential customer in a differentcity. The distance on a map between his home and the customer's home is 8 inches. What isthe actual distance between Isaiah's home and the customer's home if the scale of the map is1 inch = 1 mile?
Answers
Given:
The distance on a map between his home and the customer's home, D=8 inches.
In the map, 1 inch=1 mile.
The actual distance between Isaiah's home and the customer's home is,
[tex]\begin{gathered} \text{Actual distance=8 inches}\times\frac{1\text{ mile}}{1\text{ inch}} \\ =8\text{ miles} \end{gathered}[/tex]Therefore, the actual distance between Isaiah's home and the customer's home is 8 miles.
9) The temperature outside feels like - 3°C on Thursday. When the temperature is taken, it is actually 16°C. Howmany degrees lower does the temperature feel?
Answers
The temperature feels
[tex]16-(-3)=19[/tex]degrees lower from the actual.
Reflected over the x-axis , horizontal shrink of 1/2, translated 7 down.
Answers
Given:
Reflected over the x-axis, horizontal shrink of 1/2, translated 7 down.
The parent function is y=|x|.
[tex]\begin{gathered} \text{reflected over x-axis=-f(x)} \\ \text{horizontal shrink=f(}\frac{x}{b}\text{)} \\ \text{translation to the down=f(x)-d} \end{gathered}[/tex]The function becomes,
[tex]y=-|2x|-7[/tex]Answer:
[tex]y=-|2x|-7[/tex]A park meadow is planted with wildflowers. The Parks Department plans to extend the length of the rectangular meadow by x meters. Which expressions represent the total area, in square meters, after the meadow's length is increased? Select all that apply. 15. A 310 + x B 15.5(20x) C 20x + 15.5 D 15.5x + 310 E 15.5(20 + x) F 35.5 + x Ilse the distributi
Answers
We have the following:
The area would be the length by the width, but since x amount was added to the length, it would be like this
[tex]\begin{gathered} A=w\cdot l \\ w=15.5 \\ l=20+x \end{gathered}[/tex]replacing
[tex]A=15.5\cdot(20+x)=310+15.5x[/tex]Therefore, the answer is E and D
For each level of confidence o below, determine the corresponding normal confidence interval. Assume each confidence interval is constructed for the same sample statistics.Drag each normal confidence interval given above to the level of confidence
Answers
Note that the width of the confidence interval increases as the confidence level increases.
Since the confidence intervals constructed are for the same sample statistic, the higher confidence interval will have a higher width.
The confidence levels have the following widths:
Therefore, the confidence intervals are matched such that the lowest interval has the smallest confidence level and the highest has the largest confidence level. This is shown below:
A triangular road sign has a base of 30 inches and a height of 40 inches. What is it’s area?
Answers
Answer:
600ft
Step-by-step explanation:
Because a triangle is half of a rectangle, the area can be found by taking the base times height and dividing by 2.
A = (b * h)/2
A = (40 * 30)/2
A = 1200/2
A = 600ft
How does basic algebra come to play in everyday life? Explain (or give examples) in at least two sentences
Answers
Explanation
1) Algebra can be used while cooking to estimate the amount of ingredients by solving some easy algebraic expressions of the head.
e.g 2 tea spoons of pepper out of a 1kg pack might be the right amount to spice a soup.
2) For example, a plumber may do some quick calculations to determine the number of pipes required for a house
e.g 5 pipes in the bathroom, two pipes in the toilet, three in the kitchen gives 10 pipes altogether.
Solve the following equations. (You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation.)
Answers
Given the equation:
[tex]200(1.06)^t=550[/tex]We divide each side by 200:
[tex]\begin{gathered} \frac{200}{200}(1.06)^t=\frac{550}{200} \\ 1.06^t=2.75 \end{gathered}[/tex]Now, we take the natural logarithm:
[tex]\begin{gathered} \ln (1.06^t)=\ln (2.75) \\ t\cdot\ln (1.06)=\ln (2.75) \\ \therefore t=\frac{\ln (2.75)}{\ln (1.06)} \end{gathered}[/tex]Are the answers to question six part a b c and d correct?
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Subway wants to know how their customers feel about their food quality and service. When each customer pays for their food, the Subway employee hands them their receipt and tells them that they have a chance to win $500 if they go on line and answer a few questions about the restaurant. a) Experimentb) Observational Studyc) None of thesed) Survey
Answers
From the question, we were told that a subway company decides to reward their customers if they go online and answer a few questions about the restaurant.
We are to determine what the process means.
The general view, examination, or description of something or someone in most cases for a reward is known as a survey.
So since subway wants its customers to go online and answer some question about the restaurant and get a reward, then it is a survey.
So, the process that was carried out is a survey.
Therefore, the correct option is D, which is survey.
What percent of 60 is 39?
Answers
Answer:
To find the percent of 60 is 39
Let x be the percent of 60 is 39,
we get,
[tex]\frac{x}{100}\times60=39[/tex]Solving this, we get
[tex]x=\frac{39\times10}{6}[/tex][tex]x=65[/tex]Hence 65 percent of 60 is 39.
Answer is: 65%
In circle D with the measure of minor aré CE = 162 degrees, find m of CFE
Answers
SOLUTION
Step 1: Make a more comprehensive sketch of the question.
The measure of CFE is 81 degrees.
Suppose elephant poaching reduces an initial animal population of 25,000 animals by 15% each year. 1. Find the rate of change.2. How many animals will be left in 10 years?
Answers
Answer
Initial animal population, P₀ = 25,000
1. Rate of change = 15% = 0.15
2. Animal left in 10 years?
To calculate the animals left in 10 years, we use the formula:
P(t) = P₀ (1 - r)^t in t years
t = 10, P₀ = 25,000, r = 15% = 0.15)
P₍₁₀₎ = 25000 (1 - 0.15)¹⁰
P₍₁₀₎ = 25000 (0.85)¹⁰
P₍₁₀₎ = 25000 (0.1969)
P₍₁₀₎ = 4922.50
Therefore, 4922.50 animals will be left in 10 years.
Find f(-4) and f(3) for the following funxripnf(x)=3x
Answers
Given the function:
[tex]f(x)=3x[/tex]• You need to substitute this value of "x" into the function:
[tex]x=-4[/tex]And then evaluate, in order to find:
[tex]f(-4)[/tex]You get:
[tex]f(-4)=3(-4)[/tex][tex]f(-4)=-12[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]• Substitute this value of "x" into the function:
[tex]x=3[/tex]Then:
[tex]f(3)=3(3)[/tex]Evaluate, in order to find:
[tex]f(3)[/tex]You get:
[tex]f(3)=9[/tex]Hence, the answer is:
[tex]\begin{gathered} f(-4)=-12 \\ f(3)=9 \end{gathered}[/tex]D is the midpoint of AC, BA ≅BC and ∠EDA ≅ ∠FDC. Prove ΔAED ≅ ΔCFD
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We are asked to prove that triangles AED and CFD are congruent. To do that we will prove that we can use the ASA (Angle Side Angle) rule of congruency.
First, we are given that D is a midpoint of segment AC, therefore:
[tex]\bar{AD}=\bar{AC}[/tex]Also, we are given that:
[tex]\bar{BA}=\bar{BC}[/tex]This means that triangle ABC is an isosceles triangle and therefore, its base angles are equal. This means that:
[tex]\angle BAC=\angle BCA[/tex]And, since we are given that angles EDA and FDC are equal, then by ASA we can conclude that:
[tex]\Delta AED\cong\Delta CFD[/tex]Function f is defined by f(x) = 2x – 7 and g is defined by g(x) = 5*
Answers
Answer
f(3) = -1, f(2) = -3, f(1) = -5, f(0) = -7, f(-1) = -9
g(3) = 125, g(2) = 25, g(1) = 5, g(0) = 1, g(-1) = 0.2
Step-by-step explanation:
Given the following functions
f(x) =2x - 7
g(x) = 5^x
find f(3), f(2), f(1), f(0), and f(-1)
for the first function
f(x) = 2x - 7
f(3) means substitute x = 3 into the function
f(3) = 2(3) - 7
f(3) = 6 - 7
f(3) =-1
f(2), let x = 2
f(2) = 2(2) - 7
f(2) = 4 - 7
f(2) =-3
f(1) = 2(1) - 7
f(1) = 2 - 7
f(1) =-5
f(0) = 2(0) - 7
f(0) =0 - 7
f(0) = -7
f(-1) = 2(-1) - 7
f(-1) = -2 - 7
f(-1) = -9
g(x) = 5^x
find g(3), g(2), g(1), g(0), and g(-1)
g(3), substitute x = 3
g(3) = 5^3
g(3) = 5 x 5 x 5
g(3) = 125
g(2) = 5^2
g(2) = 5 x 5
g(2) = 25
g(1) = 5^1
g(1) = 5
g(0) = 5^0
any number raised to the power of zero = 1
g(0) = 1
g(-1) = 5^-1
g(-1) = 1/5
g(-1) = 0.2
Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13
Answers
13.
Given:
AB = 3x - 8, BC = x + 4
A, B and C are collinear
B is a midpoint of AC
Since B is the midpoint, we can write:
[tex]\text{length of AB = Length of BC}[/tex]Hence, we have:
[tex]3x\text{ - 8 = x + 4}[/tex]Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]Hence, the length of AB is:
[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]Answer:
The length of AB is 10 unit
A graph has age (weeks) on the x-axis, and height (inches) on the y-axis. Points are grouped closely together. One point is outside of the cluster. Which statement is true? There is no relationship between the height of the plant and its age. Although the outlier is an extreme value, it should be included in the interpretation. By excluding the outlier, a better description can be given for the data set
Answers
Answer:
Step-by-step explanation:
The answer is C
Answer:All three 1. to compare groups, not individuals2. to lessen the influence of outliers3. to clearly see trends
Explanation:edge 2022
Allison earned a score of 150 on Exam A that had a mean of 100 and a standard deviation of 25. She is about to take Exam B that has a mean of 200 and a standard deviation of 40. How well must Allison score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
Answers
Allison must score 280 on Exam B to do equivalently well as she did on Exam A
Explanations:Note that:
[tex]\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \text{where }\mu\text{ represents the mean} \\ \sigma\text{ represents the standard deviation} \end{gathered}[/tex][tex]\begin{gathered} \text{For Exam A:} \\ x\text{ = 150} \\ \mu\text{ = 100} \\ \sigma\text{ = 25} \\ z-\text{score = }\frac{150-100}{25} \\ z-\text{score = 2} \end{gathered}[/tex]Since we want Allison to perform similarly in Exam A and Exam B, their z-scores will be the same
Therefore for exam B:
[tex]\begin{gathered} \mu\text{ = 200} \\ \sigma\text{ = 40} \\ z-\text{score = 2} \\ z-\text{score = }\frac{x-\mu}{\sigma} \\ 2\text{ = }\frac{x-200}{40} \\ 2(40)\text{ = x - 200} \\ 80\text{ = x - 200} \\ 80\text{ + 200 = x} \\ x\text{ = 280} \end{gathered}[/tex]Allison must score 280 on Exam B to do equivalently well as she did on Exam A
The width of a rectangle measures (8u - 2v) centimeters, and its length meas(5u +9v) centimeters. Which expression represents the perimeter, in centimof the rectangle?
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The perimeter of a rectangle is given by two times the length plus two times the width, so we have:
[tex]\begin{gathered} P=2L+2W\\ \\ P=2(5u+9v)+2(8u-2v)\\ \\ P=10u+18v+16u-4v\\ \\ P=26u+14v \end{gathered}[/tex]Therefore the perimeter's expression is 26u + 14v
Triangle FGH is similar to triangle IJK. Find the measure of side JK. Round youranswer to the nearest tenth if necessary.
Answers
Let x be the measure of JK so we get that
[tex]\frac{23}{5}=\frac{x}{3.5}\rightarrow x=3.5\cdot\frac{23}{5}=16.1[/tex]Can you please help me with 44Please use all 3 forms such as :up/down, as_,_ and limits
Answers
Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]The x-intercepts of the given polynomial are
[tex]x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}[/tex]Substitute x=0 in h(x) to find y-intercepts.
[tex]\text{ y-intercepts =}(-1)^3(3)^2=-9[/tex][tex]\lim _{x\to-\infty}h(x)=\lim _{x\to-\infty}(x-1)^3(x+3)^2=-\infty[/tex][tex]as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty[/tex][tex]\lim _{x\to\infty}h(x)=\lim _{x\to\infty}(x-1)^3(x+3)^2=\infty[/tex][tex]as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty[/tex]The graph of the given polynomial h(x) is
The degree of the polynomial is 6=even and the leading coefficient=1=positive.
Both ends of the graph point up.
End behaviour is
up/up.
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
Answers
The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
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