Answers
Given:
• Degree of polynomial = 3
,• Zeros of the polynomial: 2, 3 - 2i
Let's find the polynomial.
Since the polynomail is of degree 3, it's highest exponent will be 3.
Equate the zeros to zero:
x = 2
Subtract 2 from both sides:
x - 2 = 2 - 2
x - 2 = 0
x = (3 - 2i)
Since this root is a complex conjugate, we have the other complex root: (3 + 2i)
Hence, we have:
(x - (3 - 2i)) and (x - (3 + 2i)).
Therefore, to write the function, we have:
[tex]f(x)=(x-2)(x-(3-2i))(x-(3+2i))[/tex]Now, simplify the expression:
[tex]\begin{gathered} f(x)=(x-2)(x-3+2i)(x-3-2i) \\ \\ f(x)=x(x-3+2i)-2(x-3+2i)(x-3-2i) \\ \\ f(x)=x^2-3x+2ix-2x+6-4i(x-3-2i) \\ \\ f(x)=x^2-5x+2ix-4i+6(x-3-2i) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} f(x)=x(x^2-5x+2ix-4i+6)-3(x^2-5x+2ix-4i+6)-2i(x^2-5x+2ix-4i+6) \\ \\ f(x)=x^3-5x^2+2ix^2-4ix+6x-3x^2+15x-6ix+12i-18-2ix^2+10ix-4i^2x-8-12i^{} \end{gathered}[/tex]Combine like terms:
[tex]\begin{gathered} f(x)=x^3-5x^2-3x^2-4ix-6ix+10ix+2ix^2-2ix^2+6x+15x+12i-12i-8-16 \\ \\ f(x)=x^3-8x^2+25x-26 \end{gathered}[/tex]ANSWER:
[tex]f(x)=x^3-8x^2+25x-26[/tex]Related Questions
Dee, Sarah, Brett, and Betsy are splitting their dinner bill. After the tip, the total is $30.08. How muchdoes each owe if they split the bill four ways?
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The four individuals Dee, Sarah, Brett and Betsy split their dinner bill four ways, which means its divided into four parts. Hence, after splitting, each person owes;
[tex]\begin{gathered} \text{Per person=}\frac{Total}{4} \\ \text{Per person=}\frac{30.08}{4} \\ \text{Per person=7.52} \end{gathered}[/tex]This shows that when paying the bill, each of the four individuals will have to pay $7.52
Ex5: The half-life of a certain radioactive isotope is 1430 years. If 24 grams are present now, howmuch will be present in 500 years?
Answers
For the given situation:
[tex]\begin{gathered} A_0=24g \\ h=1430 \\ t=500 \\ \\ A=24(\frac{1}{2})^{\frac{500}{1430}} \\ \\ A=24(\frac{1}{2})^{\frac{50}{143}} \\ \\ A\approx18.83g \end{gathered}[/tex]Then, after 500 years there will be approxiomately 18.83 grams of the radioactive isotope1. Find all real solutions to each equation. (a) x(2x − 5) = 1
Answers
Use the distributive property to expand the parenthesis:
[tex]x(2x-5)=2x^2-5x[/tex]Then:
[tex]undefined[/tex]What is the volume of the cone rounded to the nearest tenth? The diagram is not drawn to scale. The height of the cone is 19 yd.A) 2646.3 yd^3B) 1462.4 yd^3C) 1039.0 yd^3D) 975.0 yd^3
Answers
Answer:
To find the volume of the cone rounded to the nearest tenth
we have that,
Volume of the cone (V) is,
[tex]\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height of the cone.
Given that,
r=7 yd
h=19 yd
Substitute the values we get,
[tex]V=\frac{1}{3}\pi(7)^2\times19[/tex]we get,
[tex]V=\frac{931}{3}\pi[/tex]we know that pi is approximately equal to 3.14, Substitute the value we get,
[tex]V=\frac{931}{3}(3.14)[/tex]we get,
[tex]V=974.446\approx975\text{ yd}^3[/tex]Answer is: Option D:
[tex]\begin{equation*} 975\text{ yd}^3 \end{equation*}[/tex]Solve by using a proportion. Round answers to the nearest hundredth if necessary. 1. You jog 3.6 miles in 30 minutes. At that rate, how long will it take you to jog 4.8 miles? 2. You earn $33 in 8 hours. At that rate, how much would you earn in 5 hours?
Answers
EXPLANATION
Let's see the facts:
rate ---> 3.6 miles / 30 minutes
The unit rate is:
Unit rate = 0.12 miles/minute
Now, dividing the needed 4.8 miles by the unit rate will give us our desired number:
Time= 4.8 miles/ 0.12miles/minute = 40 minutes
The answer is 40 minutes.
decide whether circumference or area would be needed to calculate the total number of equally sized tiles on a circular floor and explain your reasoning
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The total number of equally-sized tiles on a circular floor.
Here, we are covering the region or the total space occupied by all the tiles on the floor.
Hence, the area is calculated.
on a horizontal line segment, point A is located at 21, point b is located at 66. point p is a point that divides segment ab in a ratio of 3:2 from a to b where is point p located
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We have a one-dimensional horizontal line segment. Three points are indicated on the line as follows:
In the above sketch we have first denoted a reference point at the extreme left hand as ( Ref = 0 ). This is classified as the origin. The point ( A ) is located on the same line and is at a distance of ( 21 units ) from Reference ( Ref ). The point ( B ) is located on the same line and is at a distance of ( 66 units ) from Reference ( Ref ).
The point is located on the line segment ( AB ) in such a way that it given as ratio of length of line segment ( AB ). The ratio of point ( P ) from point ( A ) and from ( P ) to ( B ) is given as:
[tex]\textcolor{#FF7968}{\frac{AP}{PB}}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{3}{2}\ldots}\text{\textcolor{#FF7968}{ Eq1}}[/tex]The length of line segment ( AB ) can be calculated as follows:
[tex]\begin{gathered} AB\text{ = OB - OA } \\ AB\text{ = ( 66 ) - ( 21 ) } \\ \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = 45 units}} \end{gathered}[/tex]We can form a relation for the line segment ( AB ) in terms of segments related to point ( P ) as follows:
[tex]\begin{gathered} \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = AP + PB }}\textcolor{#FF7968}{\ldots}\text{\textcolor{#FF7968}{ Eq2}} \\ \end{gathered}[/tex]We were given a ratio of line segments as ( Eq1 ) and we developed an equation relating the entire line segment ( AB ) in terms two smaller line segments as ( Eq2 ).
We have two equation that we can solve simultaneously:
[tex]\begin{gathered} \textcolor{#FF7968}{\frac{AP}{PB}}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{\frac{3}{2\text{ }}\ldots}\text{\textcolor{#FF7968}{ Eq1}} \\ \textcolor{#FF7968}{AB}\text{\textcolor{#FF7968}{ = AP + PB }}\textcolor{#FF7968}{\ldots Eq2} \end{gathered}[/tex]Step 1: Use Eq1 and express AP in terms of PB.
[tex]AP\text{ = }\frac{3}{2}\cdot PB[/tex]Step 2: Substitute ( AP ) in terms of ( PB ) into Eq2
[tex]AB\text{ = }\frac{3}{2}\cdot PB\text{ + PB}[/tex]We already determined the length of the line segment ( AB ). Substitute the value in the above expression and solve for ( PB ).
Step 3: Solve for PB
[tex]\begin{gathered} 45\text{ = }\frac{5}{2}\cdot PB \\ \textcolor{#FF7968}{PB}\text{\textcolor{#FF7968}{ = 18 units}} \end{gathered}[/tex]Step 4: Solve for AP
[tex]\begin{gathered} AP\text{ = }\frac{3}{2}\cdot\text{ ( 18 )} \\ \textcolor{#FF7968}{AP}\text{\textcolor{#FF7968}{ = 27 units}} \end{gathered}[/tex]Step 5: Locate the point ( P )
All the points on the line segment are located with respect to the Reference of origin ( Ref = 0 ). We will also express the position of point ( P ).
Taking a look at point ( P ) in the diagram given initially we can augment two line segments ( OA and AP ) as follows:
[tex]\begin{gathered} OP\text{ = OA + AP} \\ OP\text{ = 21 + 27} \\ \textcolor{#FF7968}{OP}\text{\textcolor{#FF7968}{ = 48 units}} \end{gathered}[/tex]The point ( P ) is located at.
Answer:
[tex]\textcolor{#FF7968}{48}\text{\textcolor{#FF7968}{ }}[/tex]
C. In which of the two functions is it possible to have negative output?
Answers
It is possible to have a negative output on:
[tex]y=a|x|[/tex]Since a can take possitive values and negative ones, and since it isn't inside the absolute value barrs.
perpendicular lines homework
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I just need to know if You just have to tell me if the circles are open or closed.
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Solution
- The solution is given below:
[tex]\begin{gathered} y-2<-5 \\ y-2>5 \\ \\ \text{ Add 2 to both sides} \\ \\ y<-5+2 \\ y<-3 \\ \\ y-2>5 \\ y>5+2 \\ y>7 \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} y<-3 \\ or \\ y>7 \end{gathered}[/tex]- Thus, the plot is:
1/10+1/2=____ options 3/5
Answers
we are given the sum of the following fractions:
[tex]\frac{1}{10}+\frac{1}{2}[/tex]To sum these fractions we may multiply the numerator and denominator of the second fraction by 5, like this:
[tex]\frac{1}{10}+\frac{5}{10}[/tex]Since now they have the same denominator we can add the numerators and leave the same denominator, like this:
[tex]\frac{1}{10}+\frac{5}{10}=\frac{1+5}{10}=\frac{6}{10}[/tex]Now we can simplify the resulting fraction by dividing the numerator and denominator by 2:
[tex]\frac{6}{10}=\frac{3}{5}[/tex]Therefore, the sum of the two fractions is 3/5
For p(2) = 7 + 10x - 12x^2 - 10x^3 + 2x^4 + 3x^5, use synthetic substitution to evaluate
Answers
Answer:
p(-3) = -428
Explanations:Given the polynomial function expressed as:
[tex]p(x)=7+10x-12x^2-10x^3+2x^4+3x^5[/tex]Determine the value of p(-3)
[tex]\begin{gathered} p(-3)=7+10(-3)-12(-3)_^2-10(-3)^3+2(-3)^4+3(-3)^5 \\ p(-3)=7-30-12(9)-10(-27)+2(81)+3(-243) \\ p(-3)=-23-108+270+162-729 \\ p(-3)=-428 \end{gathered}[/tex]Hence the value of p(-3) is -428
Identify the vertex and axis of symmetry of the quadratic equation. Then, sketch the graph f(x) = (x + 2)² - 1
Answers
Answer
Vertex = (-2, -1)
Axis of symmetry: x = -2
The graph of the function is presented below
Explanation
The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.
The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.
To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.
(df/dx) = 0
f(x) = (x + 2)² - 1
f(x) = x² + 4x + 4 - 1
f(x) = x² + 4x + 3
At the vertex, (df/dx) = 0
(df/dx) = 2x + 4
2x + 4 = 0
2x = -4
Divide both sides by 2
(2x/2) = (-4/2)
x = -2
We can then obtain the corresponding y-coordinate of the vertex
f(x) = (x + 2)² - 1
f(-2) = (-2 + 2)² - 1
f(-2) = 0² - 1
f(-2) = -1
So, the vertex is given as
Vertex = (-2, -1)
Although, one can obtain the vertex from the form in which that equation is given, the general form is that
f(x) = (x - x₁)² + y₁
Comparing that with
f(x) = (x + 2)² - 1
we see that,
x₁ = -2, y₁ = -1
So, Vertex: (-2, -1)
Then, the axis of symmetry will be at the point of the vertex.
Axis of symmetry: x = -2
And for the graph, we just need to obtain a couple of points on the line to sketch that.
when x = 0
f(x) = (x + 2)² - 1
f(0) = (0 + 2)² - 1
f(0) = 4 - 1 = 3
(0, 3)
when y = 0
x = -3 and x = -1
So,
(-3, 0) and (-1, 0)
(-2, -1), (0, 3), (-3, 0) and (-1, 0)
So, with these points, we can sketch the graph.
The graph of this function is presented under answer above.
Hope this Helps!!!
Suppose that the probability that you will win a contest is 0.0002, what is theprobability that you will not win the contest? Leave your answer as a decimal and donot round or estimate your answer.
Answers
Answer:
0.9998
Explanation:
The probability that you will not win the contest can be calculated as 1 less the probability that you will win a contest, so
1 - 0.0002 = 0.9998
Therefore, the answer is 0.9998
A grocery store sells sliced cheddar cheese by weight. The relationship between the amount of cheddar cheese in pounds, and the time in dollars of cheddar cheese in pounds, x, and the total cost in dollars of the sliced cheddra cheese, y, is represented by a graph drawn in the xy-planeIf the point (8, 44) lies on the graph, what does the point (8, 44) indicate?
Answers
Remember that the pair of coordinates
[tex](x,y)[/tex]of a point that lies on the graph of the function tells us the x-value and the
y-value related to that value.
Therefore, the point
[tex](8,44)[/tex]Represents that 8 pounds of cheddar cheese cost $44 in total (y represents the total cost, not the cost per pound)
(Correct answer is option B)
3. f(x) = |-3x - 1|3. For this function, findeach of the following:a. f(-1)b. f(0)c. f(3)
Answers
Given the absolute function;
[tex]f(x)=|-3x-1|[/tex](a)
[tex]\begin{gathered} f(-1)=|-3x-1| \\ f(-1)=|-3(-1)-1| \\ f(-1)=|3-1| \\ f(-1)=|2| \\ f(-1)=2 \end{gathered}[/tex](b)
[tex]\begin{gathered} f(0)=|-3(0)-1| \\ f(0)=|0-1| \\ f(0)=|-1| \end{gathered}[/tex]Here, we recall the absolute rule that;
[tex]|-a|=a[/tex]Thus, we have;
[tex]f(0)=|-1|=1[/tex](c)
[tex]\begin{gathered} f(3)=|-3(3)-1| \\ f(3)=|-9-1| \\ f(3)=|-10| \\ f(3)=10 \end{gathered}[/tex]A simple random sample from a population with a normal distribution of 98 body temperatures has x=98.20°F and s=0.61°F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Click the icon to view the table of Chi-Square critical values. °F
Answers
from the question;
we are to construct 99% confidence interval. this can be done using
[tex]\bar{}x\text{ }\pm\text{ z}(\frac{s}{\sqrt[]{n}})[/tex]where,
[tex]\bar{x}\text{ = }98.20,\text{ s = 0.61, n = 98 z= 2.576}[/tex]inserting values
[tex]\begin{gathered} 98.20\text{ }\pm2.576\text{ }\frac{0.61}{\sqrt[]{98}} \\ 98.20\text{ }\pm\text{ 2.576}\times0.0616 \\ =\text{ 98.20 }\pm\text{ }0.159 \\ =98.20\text{ + }0.159\text{ or 98.20 - 0.159} \\ =\text{ 98.359 0r 98.041} \end{gathered}[/tex]therefore the 99% confident inter vale is between 98.041 to 98.359
y varies inversely as x. y=12 when x=7. Find y when x=2
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We write as an inverse proportion first then make an equation by multiplying by k:
[tex]y=\frac{k}{x}\Rightarrow k=x\times y[/tex]Find the value of k:
[tex]k=7\times12=84[/tex]Then, when x = 2, y is:
[tex]y=\frac{84}{2}=42[/tex]Answer: y = 42
208 x 26 using long multiplication
Answers
Answer:
2 0 8
× 2 6
+ 1 2 4 8
+ 4 1 6
= 5 4 0 8
The Answer of 208 × 26 Is 5.408
Explanation.= 208 × 26
= (208 × 6) + (208 × 20)
= 1.248 + 4.160
= 5.408
__________________
Class: Elementary School
Lesson: Multiplication
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:CyberPresents}}}}[/tex]
Lines a and b intersect do that the measure angle 1 is 85°. If angle 2 is complement to angle 1, what's the measure for angle 2?
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if the angles are complementary, then the sum of the angles is 90°
[tex]\begin{gathered} 85+m\angle2=90 \\ m\angle2=90-85=5 \end{gathered}[/tex]so the measure of the angle 2 is 5°
Writing an Equation Assume that the ball rebounds the same percentage on each bounce. Using the initial drop height and the height after the first bounce, find the common ratio,r.Note: Round r to three decimal places. Use this formula:common ratio = height on first bounce/initial heightheight on first bounce = 54 in Dropped from 72in (6 feet)
Answers
The common ratio = 0.750 (3 decimal places)
Explanation:
Initial drop height = 72 inches
Height after the first bounce = 54 inches
common ratio = r = height on first bounce/initial height
r = 54/72
r = 0.75
The common ratio = 0.750 (3 decimal places)
find the equation of the circle with the given center and radius:center (-1,-6), and radius = 6
Answers
ANSWER:
[tex](x+1)^2+(y+6)^2=36^{}[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where (h, k) is the center and r is the radius } \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} (x-(-1))^2+(y-(-6))^2=6^2 \\ (x+1)^2+(y+6)^2=36^{} \end{gathered}[/tex]I need help to solve by using the information provided to write the equation of each circle! Thanks
Answers
Explanation
For the first question
We are asked to write the equation of the circle given that
[tex]\begin{gathered} center:(13,-13) \\ Radius:4 \end{gathered}[/tex]The equation of a circle is of the form
[tex](x-a)^2+(y-b)^2=r^2[/tex]In our case
[tex]\begin{gathered} a=13 \\ b=-13 \\ r=4 \end{gathered}[/tex]Substituting the values
[tex](x-13)^2+(y+13)^2=4^2[/tex]For the second question
Given that
[tex](18,-13)\text{ and \lparen4,-3\rparen}[/tex]We will have to get the midpoints (center) first
[tex]\frac{18+4}{2},\frac{-13-3}{2}=\frac{22}{2},\frac{-16}{2}=(11,-8)[/tex]Next, we will find the radius
Using the points (4,-3) and (11,-8)
[tex]undefined[/tex]! WHAT IS 3 3/8 - 1 3/4=
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The given expression is
[tex]3\frac{3}{8}-1\frac{3}{4}[/tex][tex]\text{Use a}\frac{b}{c}=\frac{a\times c+b}{c}\text{.}[/tex][tex]3\frac{3}{8}-1\frac{3}{4}=\frac{3\times8+4}{8}-\frac{1\times4+3}{4}[/tex][tex]=\frac{28}{8}-\frac{7}{4}[/tex]LCM of 8 and 4 is 8, making the denominator 8.
[tex]=\frac{28}{8}-\frac{7\times2}{4\times2}[/tex][tex]=\frac{28}{8}-\frac{14}{8}[/tex][tex]=\frac{28-14}{8}[/tex][tex]=\frac{14}{8}[/tex][tex]=\frac{2\times7}{2\times4}[/tex][tex]=\frac{7}{4}[/tex][tex]=\frac{1\times4+3}{4}[/tex][tex]=1\frac{3}{4}[/tex]Hence the answer is
[tex]3\frac{3}{8}-1\frac{3}{4}=1\frac{3}{4}[/tex]−3x−6+(−1) i need help with this ine
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Recall that the order of operations is a rule that tells the correct sequence of steps for evaluating a math expression, this order is: Parentheses, Exponents, Multiplications and Divisions (from left to right), Addition and Subtraction (from left to right).
Simplifying the parentheses in the given expression we get:
[tex]-3\times-6-1.[/tex]Simplifying multiplications in the above result we get:
[tex]18-1.[/tex]Finally, simplifying subtractions in the above result we get:
[tex]17.[/tex]Answer:
[tex]-3\times-6+(-1)=17.[/tex]inserted a picture of the question, can you just answer the question and not ask a lot of questions yes i’m following
Answers
Step-by-step explanation:
A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,
so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.
[tex]\frac{360}{9}=40[/tex]Therefore the degrees will a nonagon have rotational symmetry
Hene the correct answer is Option B
I'm trying to solve this problem. I went wrong somwhere.
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which of the equation below could be the equation of this parabola
Answers
We have a parabola with the vertex at (0,0).
If we write the equation in vertex form, we have:
[tex]\begin{gathered} \text{Vertex}\longrightarrow(h,k) \\ f(x)=a(x-h)^2+k \\ f(x)=a(x-0)^2+0=ax^2 \end{gathered}[/tex]We have to find the value of the parameter a.
As the parabola is concave down, we already know that a<0.
As a<0 and y=a*x^2, the only option that satisfies this condition is y=-1/2*x^2.
Answer: y=-(1/2)*x^2 [Option C]
What is the area of the composite figure?o 52.5 cm^2o 60 cm^2o 40 cm^265 cm^2
Answers
we have that
The area of the composite figure is equal to the area of a rectangle plus the area of a right triangle
so
step 1
Find out the area of the rectangle
A=L*W
A=8*5
A=40 cm2
step 2
Find out the area of the right triangle
A=(1/2)(b)(h)
where
b=8-(2+1)=8-3=5 cm
h=5 cm
A=(1/2)(5)(5)
A=12.5 cm2
therefore
the total area is
A=40+12.5=52.5 cm2
52.5 cm2The graph shows the function f(x) = |x – h| + k. What is the value of h?
h = –3.5
h = –1.5
h = 1.5
h = 3.5
Answers
F(x)=|x+1.5|-3.5
Hope this helps I could not put it into better detail due to device problems
