Given:
A rectangular pool with the following measures,
Perimeter
Length = x + 8
Width = x
Let's determine the measure of its dimensions:
[tex]\text{ Perimeter = 2L + 2W}[/tex][tex]\text{ = 2(x + 8) + 2(x)}[/tex][tex]\text{ 44 = 2x + 16 + 2x}[/tex][tex]\text{ 44 = 4x + 16}[/tex][tex]\text{ 44 - 16 = 4x}[/tex][tex]\text{ 28 = 4x}[/tex][tex]\text{ }\frac{28}{4}\text{ = }\frac{4x\text{ }}{4}[/tex][tex]\text{ 7 = x}[/tex]Let's now determine its dimensions,
Length = x + 8 = 7 + 8 = 15 ft.
Width = x = 7 ft.
Therefore, the dimension of the rectangular pool is Length = 15 ft. and Width =7 ft.
For my practice review, I need help to determine if these are functions or not.
Answer:
1: no
2: no
3: yes
4: no
5: yes
6: yes.
Step-by-step explanation:
Think of a vertical line sweeping across the graph from left to right. If ever this line crosses two points of the graph at the same time, it cannot be a function, since a function can only have max. 1 result per x value.
what is the answer for this pls answer
Answer: A
Step-by-step explanation: You merge the equations, -2x and 2x cancel out, 4y + 1y = 5y, and 12 + (-7) = 5
You'll be left with 5y = 5
Dividing both sides by 5 to isolate the y results in y = 1
> Use the drop-down menus to explain how Ken' can use the model to find the total weight of the baseballs. Click the arrows to choose an answer from each menu. To represent the weight of one baseball, 0.3 pounds, Ken should shade 3 Choose... To represent the weight of all of the baseballs, he should shade this amount 7 times. The shaded part of the model will represent the expression Choose... The total weight of the baseballs is 2.1 pounds. > My Progress All rights reserved These materials, or any portion thereof may not be reproduced or shared in any manner without expS ENCOME
To represent 0.3 pounds Ken should shade 3 columns
To represent the weight of all of the baseballs He should shade 7 times
The shaded part of this model will represent the expression 7 x 0.3 (7x 0.3 = 2.1)
The Total weight of the baseballs is 2.1 pounds
1) Gathering the data
7 baseballs each one weighs 0.3 pounds
7 x 0.3 = 2.1 ⇔2.1 : 0.3 = 7
Each tiny square corresponds to 0.01 of the block.
2.1 : 0.3 = 7
2) So the total weight (2.1) corresponds to 2 blocks and 0.1 blocks mean 1 column on the third block. Or, 2.1 = 7 x 0.3 Seven times three columns.
Examining the options:
3 ) We can answer each drop-down menu:
• To represent 0.3 pounds Ken should shade ,3 columns
,• To represent the weight of all of the baseballs He should shade ,7 ,times
,• The shaded part of this model will represent the expression ,7 x 0.3 ,(7x 0.3 = 2.1)
,• The Total weight of the baseballs is ,2.1 pounds
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". DRAW A TREE DIAGRAM IN YOUR NOTES AND USE IT TO HELP YOU SOLVE THIS PROBLEM. Find the probability that a person has the virus given that they have tested positive; i.e. find P(AIB). Give your answer as a decimal number and include at least 3 or more non-zero digits. P(AIB)=
In the tree, the first branch will be person has virus or person doesn't have the virus.
P(virus) = 1/300
P(not virus) = 299/300
Now,
Then we branch out from each option. These branches would be positive or negative.
If they have virus:
P(positive) = 0.8
P(negative) = 0.2
If don't have virus:
P(positive) = 0.1
P(negative) = 0.9
Now, solving the question of probability that a person has the virus given that they have tested positive:
We find:
P(A|B)
P(has virus | positive test) = P(positive and has virus) / P(positive test)
P(positive and has virus) = 4/5 * 1/300 = 4/1500
P(positive test) = 1/300 * 4/5 + 1/10 * 299/300
= (4/1500)+(299/3000)
=(8/3000) + (299/3000) = 307/3000
= 0.10233
So,
P(positive and has virus) / P(positive test) = 4/1500 divided by 299/3000 = 0.02675
Graph the parabola.y=1/4x^2-1Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button
This is basic parabola of the form:
[tex]y=ax^2-b[/tex]So, this one is shifted 1 units down.
The vertex is at (0, -1).
To take 2 points to the left of vertex, we find coordinates for x = -2 and x = -4.
To take 2 points to the right of vertex, we find coordinates for x = 2 and x = 4.
Let's find it:
[tex]\begin{gathered} \text{When x = -2,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(-2)^2^{}-1 \\ y=0 \\ When\text{ x = -4,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(-4)^2-1 \\ y=3 \\ \text{When x = 2,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(2)^2-1 \\ y=0 \\ \text{When x= 4,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(4)^2-1 \\ y=3 \end{gathered}[/tex]So, the 4 coordinates are:
(-2,0), (-4,3), (2,0), (4,3)
The graph:
Plot the image of point C under a reflection across line n.Click to add points
We can find the image of point C reflected across line n by finding the distance d (perpendicular) from point C to line n, and then placing point C', the image, at an equal and perpendicular distance d on the other side of the line.
We can graph this as:
Consider the line y=4x-5.Find the equation of the line that is perpendicular to this line and passes through the point (6. 4).Find the equation of the line that is parallel to this line and passes through the point (6, 4).Equation of perpendicular line: Equation of parallel line:
Solution
gradient = 4
Slope for Perpendicular = -1/4
Slope for Parallel = 4
Equation of perpendicular line:
[tex]\begin{gathered} y-4=-\frac{1}{4}(x-6) \\ \\ 4y-16=-x+6 \\ \\ 4y+x=22 \end{gathered}[/tex]Equation of parallel line:
[tex]\begin{gathered} y-4=4(x-6) \\ \\ y-4=4x-24 \\ \\ y=4x-20 \end{gathered}[/tex]I need help with 5 and 6. The exponent for part 5 if you can't see it well 2/3
5.
Given the equation to solve for x:
[tex]3(x+1)^{\frac{2}{3}}=12[/tex]The steps for the solution are as follows:
[tex]\begin{gathered} 3(x+1)^{\frac{2}{3}}=12 \\ \frac{3(x+1)^{\frac{2}{3}}}{3}=\frac{12}{3} \\ (x+1)^{\frac{2}{3}}=4 \\ \lbrack(x+1)^{\frac{2}{3}}\rbrack^{\frac{1}{2}}=(4)^{\frac{1}{2}} \\ \lbrack(x+1)^{\frac{1}{3}}\rbrack=\pm2 \\ \lbrack(x+1)^{\frac{1}{3}}\rbrack^3=(\pm2)^3 \\ x+1=\pm8 \end{gathered}[/tex]From the above equation, we have x + 1 = 8 and x + 1 = -8. These imply x = 7 and x = -9.
Check for extraneous solutions:
If x = 7, then the left-hand side of the equation is:
[tex]3(x+1)^{\frac{2}{3}}=3(7+1)^{\frac{2}{3}}=3(4)=12[/tex]Thus, the equation holds true at x = 7.
If x = -9, then the right-hand side of the equation is:
[tex]3(x+1)^{\frac{2}{3}}=3(-9+1)^{\frac{2}{3}}=3(4)=12[/tex]Thus, the equation holds true at x = -9.
There is no extraneous solution. The solutions of the given equation are x = 7 and x = -9.
6.
Given an equation to solve for x:
[tex]\sqrt[]{3x+2}-2\sqrt[]{x}=0[/tex]The steps of the solution are as follows:
[tex]\begin{gathered} \sqrt[]{3x+2}-2\sqrt[]{x}=0 \\ \sqrt[]{3x+2}=2\sqrt[]{x} \\ (\sqrt[]{3x+2})^2=(2\sqrt[]{x})^2 \\ 3x+2=4x \\ 2=4x-3x \\ 2=x \end{gathered}[/tex]Thus, the solution of the equation is x = 2.
Solve for x. -2x+5≤10
Answer:
x≥-2.5
Explanation:
Given the inequality:
[tex]-2x+5\le10[/tex]Step 1: Subtract 5 from both sides of the inequality
[tex]\begin{gathered} -2x+5-5\le10-5 \\ -2x\le5 \end{gathered}[/tex]Step 2: Divide both sides by -2.
Note: Since we divide by a negative number, the inequality sign is reversed.
[tex]\begin{gathered} -\frac{2x}{-2}\ge\frac{5}{-2} \\ x\ge-\frac{5}{2} \\ x\ge-2.5 \end{gathered}[/tex]The solution to the inequality is x≥-2.5.
Simplify the following expression(-2v)^4
We have
[tex]\mleft(-2v\mright)^4[/tex]In order to simplify this expression, we will use the next rule
[tex]\mleft(ab\mright)^m=a^mb^m[/tex]We use the rule and we simplify
[tex](-2)^4v^4=16v^4[/tex]which expression below has the same value as 9[tex] {9}^{6} [/tex]
Given data:
The given number is 9^6.
The given number can be written as,
[tex]9^6=9\times9\times9\times9\times9\times9[/tex]Thus, second option is correct.
Diagram 3 shows a piece of rectangularcardboard and an open box that is made from the cardboard.The box is made by cutting out four squares of equal size from the cornersof the cardboard then folding up the sides. Finda) the length in cm of sides of the squares to be cut out in order to get a box with largest volume.b) the minimum number of the boxes needed to fill with 5645 cm³ of pudding
SOLUTION:
Step 1:
In this question, we are given the following:
Diagram 3 shows a piece of rectangular cardboard and an open box that is made from the cardboard.
The box is made by cutting out four squares of equal size from the corners
of the cardboard then folding up the sides.
Find
a) the length in cm of sides of the squares to be cut out in order to get a box with the largest volume.
[tex]\begin{gathered} The\text{ volume of the rectangle would be expressed as:} \\ \text{V = ( 30-2x )(16-2x) ( x)} \\ Multiply\in g\text{ out, we have that:} \\ V=480x-92x^2+4x^3 \\ \text{Differentiating V with respect to x, we have that:} \\ \frac{dV}{dx}=480-184x+12x^2=0 \\ \text{Factorizing the quadratic equation, we have that:} \\ \text{x = 12 or x =}\frac{10}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{Differentiating again, we have that:} \\ \frac{d^2V}{dx^2\text{ }}\text{ = -184 + 24 x} \end{gathered}[/tex]To get the maximum, we need to substitute the values of :
[tex]\begin{gathered} x\text{ = 12, we have that:} \\ \frac{d^2V^{}}{dx^2\text{ }}\text{ = -184 + 24( 12) = }-184\text{ +288 = 104} \\ x=\frac{10}{3},\text{ we have that:} \\ \frac{d^2V}{dx^2}\text{ = -184 + 24 (}\frac{10}{3})\text{ = -184 +}\frac{240}{3}\text{ = - 184 + 80 = -104 }<0 \end{gathered}[/tex]At this stage, we can see that:
[tex]\begin{gathered} x\text{ =}\frac{10\text{ }}{3}cm\text{ is the length of the squares to be cut in order to get a box with } \\ \text{largest volume} \end{gathered}[/tex]b) Find the minimum number of the boxes needed to fill with 5645 cm³ of pudding
[tex]\begin{gathered} \text{From the equation,} \\ V=(30-2\text{x )(16-2x)(x)} \\ \text{put x =}\frac{10}{3}\text{ in the equation, we have that:} \\ V\text{ = \lbrack}30\text{ -2(}\frac{10}{3})\rbrack\text{ \lbrack 16-2(}\frac{10}{3}\rbrack\lbrack\frac{10}{3}\rbrack \\ V\text{ = ( 30 -}\frac{20}{3})\text{ ( 16 - }\frac{20}{3})(\frac{10}{3}) \\ V=725.93cm^3 \\ Now\text{, we asked to find the minimum number of boxes ne}eded^{} \\ to^{} \\ \text{fill with 5645cm}^{3\text{ }}\text{ of pudding.} \\ \text{Then, we ne}ed\text{ to do the following:} \end{gathered}[/tex]
Minimum number of boxes =
[tex]\begin{gathered} \frac{5645}{725.93} \\ =\text{ 7.78} \\ \approx\text{ 8} \end{gathered}[/tex]CONCLUSION:
A minimum of 8 boxes will be needed to fill with 5645 cm³ of pudding
A warren of bunnies is growing at 14% per month.a. Find the approximate doubling time.b. If the warren is currently at a population of 400 bunnies, use the approximate doubling time to find the size of the warren in 2 years.c. Find the exact doubling time. Round to 2 decimal places.d. If the warren is currently at a population of 400 bunnies, use the exact doubling time to find the size of the warren in 2 years. e. What is the relative error caused by using the approximate doubling time instead of the exact doubling time? Round to 2 decimal places.
If a warren of bunnies is growing at 14% per month then the approximate doubling time is 5 months.
A warren of bunnies is growing at 14% per month
r = 14% = 0.14
Let the initial population of bunnies be N
Then the final population of bunnies = 2N
N(1 + r)ˣ = 2N
here x is time in months
(1 + 0.14)ˣ = ln 2
x ln 0.14 = ln 2
x = 5.29 months
b) doubling time = 5months
number of cycle = 24/5
population = 400(2)²⁴/⁵
= 11143
c) exact doubling time is 5.29 months
Therefore, if a warren of bunnies is growing at 14% per month then the approximate doubling time is 5 months.
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What is - 4 - 2y= - x in standard form ?
The standard form is
[tex]Ax+By=C[/tex]We have
[tex]-4-2y=-x[/tex][tex]x-2y-4=0[/tex][tex]x-2y=4[/tex]The standard form is
[tex]x-2y=4[/tex]ANSWER
Lynette is covering shapes with wrapping paper to make a design for the school carnival how much paper and square feet will Lynette need to cover the figure shown below
The area of paper needed is;
[tex]7\frac{1}{2}ft^2[/tex]Here, we want to get the square feet of paper needed
What we have to do here is to get the area of the parallelogarm
Mathematically, that would be the product of the base of the parallelogram and its height
We have the base as 3 3/4 ft which is same 15/4 ft and the height as 2 ft
Thus, we have the area calculated as follows;
[tex]\frac{15}{4}\times\text{ 2 = }\frac{30}{4}\text{ = 7}\frac{1}{2}ft^2[/tex]Write the inequality statement in x describing the numbers [ 11, ∞)
The inequality [ 11, ∞) represents that value is more than or equal to 11. The interval can be expressed as,
[tex]x\ge11[/tex]In inequality, x is any variable.
So inequality statement in x is,
[tex]x\ge11[/tex]XIXIXI
Name:
amount paid (in dollars)
Movie Mania Tickets
ty
72
63
54
45
36
27
10 00
18
9
0
CINEMA
ADMIT ONE
12345
ADMIT ONE
nyum
Movie Ticket Sales
12345
2 4 6
8
# of tickets
72=6=12
X
10
Perfect Picture Tickets
Only $65.50 for 5 tickets!
65÷5=13
# of tickets
Date:
Fantastic Flicks Tickets
3
6
9
12
amount paid (in dollars)
38.25
76.50
114.75
153
Periods:
The Big Screen
Which movie theater is the cheapest?
Pertert Picture
Which movie theater is the most expensive?
Movie mania
What is the constant of proportionality (slope) of each option?
movie minin. = 12
Perfect Pictures (3
·Fantastic Flick5= 12.75
The Big screen= 12.90
Write an equation to represent all four options.
12345
CINEMA
ADMIT ONE
y = 12.90x
NEMA
ADMIT ONE
12345
12.75
1. The cheapest movie theatre is Fantastic Flicks.
2. The most expensive movie theatre is Movie Mania.
3. The slopes for the ticket prices for Movie Mania, Perfect Picture, The Big Screen, and Fantastic Flicks are 13.5, 13.1, 12.9, and 12.75.
4. The equation to represent all the four options is (y - 13.5x)*(y - 13.1x)*(y - 12.9x)*(y - 12.75x) = 0.
We have four movie theaters. The names of the movie theatres are Movie Mania, Perfect Picture, The Big Screen, and Fantastic Flicks. We need to calculate the slopes for each option. Let the slopes for Movie Mania, Perfect Picture, The Big Screen, and Fantastic Flicks be m1, m2, m3, and m4, respectively.
m1 = 27/2 = 13.5
m2 = 65.5/5 = 13.1
m3 = 12.9
m4 = 153/12 = 12.75
The equations for the price of tickets for each theatre are given below.
E1 : y = 13.5x
E2 : y = 13.1x
E3 : y = 12.9x
E4 : y = 12.75x
The theatre with the minimum slope is the cheapest. The theatre with the maximum slope is the most expensive.
The equation to represent all four options is the product of all the other equations.
(y - 13.5x)*(y - 13.1x)*(y - 12.9x)*(y - 12.75x) = 0
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Angles P and Q are supplementary and m
Given: P &Q are supplementary. Therefore P+Q = 180 degress
P = 180 - Q
If m
then m +30 = p
m + 30 = 180 - Q
m = 150 - Q
m - 150< -Q
m + 150 > Q
m>q = 150
a quadrilateral has vertices S (0,0) T (4,0) U (5,4) V (1,4). what is the most precise name for the quadrilateral
First, plot the points on a coordinate plane:
Notice that ST is parallel to VU, as well as SV is parallel to TU.
A quadrilateral whose opposite sides are parallel, is called a parallelogram.
Therefore, the most precise name for the quadrilateral is: parallelogram.
can someone help me find the valu of X &Y?
Given that the triangle ABC and DEF are similar, therefore its corresponding sides must be proportional,
[tex]\begin{gathered} \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF} \\ \frac{4}{6}=\frac{10}{y}=\frac{x}{12} \end{gathered}[/tex]Comparing the first and third terms,
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{12} \\ x=\frac{4}{6}\times12 \\ x=4\times2 \\ x=8 \end{gathered}[/tex]Comparing the first and second terms,
[tex]\begin{gathered} \frac{4}{6}=\frac{10}{y} \\ y=\frac{6}{4}\times10 \\ y=3\times5 \\ y=15 \end{gathered}[/tex]Thus, the values of 'x' and 'y' are 8 and 15, respectively.
Not a timed or graded assignment. Need a quick answer showing work. Please DRAW factor tree. Thank you so much.
ANSWER:
[tex]40\sqrt[]{7}m^3[/tex]STEP-BY-STEP EXPLANATION:
Using the following factor tree, we decompose the number 112 to be able to simplify, just like this:
Therefore, it would be:
[tex]\begin{gathered} 10\sqrt[]{2\cdot2\cdot2\cdot2\cdot7\cdot m^6} \\ 10\sqrt[]{2^4\cdot7\cdot m^{3\cdot2}} \\ 10\cdot2^2\cdot m^3\sqrt[]{7} \\ 10\cdot4\cdot m^3\sqrt[]{7}=40\sqrt[]{7}m^3 \end{gathered}[/tex]The original price of a riding lawn mower is $1250. Paul bought his for $1000. What percent was the discount?
we get that the percentage he paid was
[tex]\frac{1000}{1250}\cdot100=80\text{ \% }[/tex]so the percentage of discount is 20%
What is the value of x in the figure at the right? 60° (2x)°
The angle whose measure is 60° and the angle (2x)° are vertical angles, if two angles are vertical angles, then they are congruent, then we can express:
[tex]2x=60[/tex]From this expression, we can solve for x to get:
[tex]\begin{gathered} \frac{2x}{2}=\frac{60}{2} \\ x=30 \end{gathered}[/tex]Then, x equals 30
Enter the exponential function using t (for time) as the independent variable to model the situation. Then find the value of the function after the given amount of time. The value of a textbook is $65 and decreases at a rate of 14% per year for 13 years. The exponential function that models the situation is y =__After 13 years, the value of the textbook is $__
Please, give me some minutes to take over your question
_________________________________
Find the perimeter and area of a square with side 9 inches.
The perimeter (P) and area (A) of a square of sides a = 9 in, are given by:
[tex]\begin{gathered} P=4a=4\cdot(9in)=36in, \\ A=a^2=(9in)^2=81in^2. \end{gathered}[/tex]Answer
• Perimeter = 36 in
,• Area =, ,81 in²
Which function has the graph shown?O A. y = secx-1)O B. y = - secxO C. y = csexO D. y = csc(x) +1
We will have that the graph of the function shown belongs to:
[tex]y=csc(x)+1[/tex]This can be seeing as follows:
The mean annual salary at the company where Samuel works is $37,000, with standard deviation $4,000. Samuel's salary is $32,500. Based on the mean and standard deviation, is Samuel's salary abnormal compared to other salaries at this company? When choosing your answer, be careful to select the answer with the correct explanation. A. Samuel's salary falls within the standard deviation, so his salary is not abnormal compared to other salaries at this company. B. Samuel's salary falls outside the standard deviation, so his salary is abnormal compared to other salaries at this company. C. Samuel's salary falls within the standard deviation, so his salary is abnormal compared to other salaries at this company. D. Samuel's salary falls outside the standard deviation, so his salary is not abnormal compared to other salaries at this company?
Answer : Samuel salary falls within the standard deviation and his salary is not abnormal
The mean annual salary at the company where samuel works is $37, 000
The standard deviation is given as $4, 000
Samule's annual salary is $32, 500
Using the Z- score formula
[tex]\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \text{Where x = sample score} \\ \mu\text{ = mean} \\ \sigma\text{ = standard deviation} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = \$32, 500} \\ \mu\text{ = \$37, 000} \\ \sigma=\text{ \$ 4000} \\ z\text{ = }\frac{32,\text{ 500 - 37000}}{4000} \\ z\text{ = }\frac{-4500}{4000} \\ z\text{ = -1.125} \end{gathered}[/tex]Since, the value of Z- score is -1. 125, then, the salary is 1 standard deviation below the mean.
Therefore, Samuel salary falls within the standard deviation and his salary is not abnormal
Can you please help me out with a question
To determine the green rectangle, each side of the blue rectangle was multiplied by a determined scale factor k.
To determine the measure of x, the first step is to determine the scale factor.
The information that you have to use is the areas of both rectangles.
After dilation, the area of the resulting shape is equal to the area of the original shape multiplied by the square of the scale factor:
[tex]A_{\text{green}}=k^2A_{\text{blue}}[/tex]A.green=50 m²
A.blue= 72m²
[tex]50=72k^2[/tex]-Divide both sides by 72
[tex]\begin{gathered} \frac{50}{72}=\frac{72k^2}{72} \\ \frac{25}{36}=k^2 \end{gathered}[/tex]-Apply the square root to both sides of the equal sign:
[tex]\begin{gathered} \sqrt[]{\frac{25}{36}}=\sqrt[]{k^2} \\ \frac{5}{6}=k \end{gathered}[/tex]Now, to determine the value of x, multiply the length of the corresponding side on the blue rectangle by the scale factor:
[tex]\begin{gathered} x=\frac{5}{6}\cdot12 \\ x=10 \end{gathered}[/tex]The length of the side on the green triangle is 10m
Evaluate 2^5.32251016
32
Explanation:The given expression is:
2⁵
This means the product of 2 in 5 places
That is,
2⁵ = 2 x 2 x 2 x 2 x 2
2⁵ = 32
Write the polynomial function in standard form that has complex roots -2+i and -2-i
ANSWER
[tex]\text{ x}^2\text{ - 4x + 5}[/tex]EXPLANATION
Given information
The root of the polynomial function are -2 + i and -2- i
To find the standard form of the polynomial function, follow the steps below
Step 1: Express the root of the polynomial in terms of the factor
[tex]\begin{gathered} \text{ Given that the roots of the polynomial function are -2+i and -2 - i} \\ \text{ The factors of the above roots can be expressed as} \\ \text{ \lbrack x + \lparen-2 + i\rparen\rbrack and \lbrack x + \lparen-2 - i\rparen\rbrack} \end{gathered}[/tex]Step 2: Expand the factors of the polynomial in step 1
[tex]\begin{gathered} \text{ \lbrack x + \lparen-2 + i\rparen\rbrack \lbrack x +\lparen-2 -i\rparen\rbrack} \\ [x\text{ -2\rparen + i\rparen\rbrack \lbrack x -2\rparen - i\rparen\rbrack} \\ (x\text{ - 2\rparen}^2\text{ - i}^2 \\ (x\text{ - 2\rparen\lparen x - 2\rparen- i}^2 \\ x^2\text{ - 2x - 2x + 4 - i}^2 \\ x^2\text{ - 4x + 4 - i}^2 \\ \text{ Recall, that i}^2\text{ = -1} \\ \text{ x}^2\text{ - 4x + 4 - \lparen-1\rparen} \\ \text{ x}^2\text{ - 4x + 4 + 1} \\ \text{ x}^2\text{ - 4x + 5} \end{gathered}[/tex][tex]\text{ Hence, the polynomial function in standard form is x}^2\text{ - 4x + 5}[/tex]