The quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3) is; y = 0.2x² - 2.2x + 2
How to write the standard form of the quadratic equation?
The standard form of a quadratic equation is;
y = ax² + bx + c
where a, b and c are constants
Thus, for the coordinate (10,0), we have;
0 = a(10)² + b(10) + c
100a + 10b + c = 0 -----(1)
For the coordinate (1,0), we have;
0 = a(1)² + b(1) + c
a + b + c = 0 -----(2)
For the coordinate (4,3), we have;
3 = a(4)² + b(1) + c
16a + b + c = 3 ------(3)
Using online simultaneous equation, we have;
a = 0.2 and b = -2.2 and c = 2
The quadratic function is;
y = 0.2x² - 2.2x + 2
Read more about Quadratic Equations at; https://brainly.com/question/25841119
#SPJ1
A seasoning blend is 4\%4%4, percent onion powder, by mass. How much pure onion powder should they include in a 72\,\text{g}72g72, start text, g, end text bottle to make the final blend have 20\ , percent onion powder? khan academy
They need to put 14.4 grams of onion powder in each bottle.
Given,
The quantity of onion powder in a seasoning blend = 4%
We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;
How much is a percentage?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."
Here,
Let x be the seasoning blend.
Now, 4% of 72=20% of x
⇒ 0.04×72=0.2×x
⇒ 0.2x=2.88
⇒ x=2.88/0.2
⇒ x=14.4 g
Therefore, a container should contain 14.4 grams of onion powder.
Learn more about quantity of onion powder here;
https://brainly.com/question/29332582
#SPJ4
If I’m doing fractions on a number line how do I do thirds
Answer:
Step-by-step explanation:
it would be devided into 3 sections so the thing would look like this
When 10 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
The positive solution is 5.
given,
When 10 is subtracted from a number's square, the result is three times the number.
let x be the number
according to given statement the quadratic equation will be
[tex]x^2-10=3x\\\\x^2-3x-10\\\\x^2+2x-5x-10=0\\\\x(x+2)-5(x+2)=0\\\\(x-5)(x+2)=0\\\\x=5\ or\ -2[/tex]
Thus, the positive solution is 5.
To learn more about quadratic equations refer here
https://brainly.com/question/26090334
#SPJ4
Please help i really need it only number 4
Answer:
(2) 11
Step-by-step explanation:
You want the area of the triangle with vertices (1, 3), (3, -1), and (-2, -2).
Pick's theoremPick's theorem says the area of a figure drawn on a grid can be found by counting the grid points on the boundary (b) and the interior grid points (i). Then the area is ...
A = (b/2) +i -1
This figure has a boundary grid point at (2, 1) in addition to the three vertices. So, b = 4.
There are 10 interior grid points, a number that can be arrived at by counting them. The numbers in each row, starting from the bottom, are 4, 3, 2, 1.
Then the area is ...
A = (4/2) +10 -1 = 11
The area of the triangle is 11 square units.
From CoordinatesThe area can be computed from the coordinates by the formula ...
A = 1/2|x1(y2 -y3) +x2(y3 -y1) +x3(y1 -y2)|
A = 1/2|1(-1 -(-2)) +3(-2 -3) +(-2)(3 -(-1))| = 1/2|1 -15 -8| = 11
The area is 11 square units.
Using geometryThe triangle can be bounded by a square 5 units on a side. The triangle area is smaller than the square area by the sum of the three triangles cut from the corners of the square. Clockwise from left, those triangle areas are ...
1/2(5·3) +1/2(4·2) +1/2(1·5) = 1/2(15 +8 +5) = 14
Then the area of the triangle of interest is ...
5² -14 = 11
The area of the triangle is 11 square units.
Using trigonometryThe angle the bottom edge makes with the horizontal is ...
arctan(1/5) ≈ 11.3099°
and the length of that edge is ...
5/cos(11.3099°) ≈ 5.099
The angle the left side makes with the horizontal is ...
arctan(5/3) ≈ 59.0362°
and the length of that edge is ...
3/cos(59.0362°) ≈ 5.831
The area of the triangle with sides 'a' and 'b' and angle C between them is ...
Area = 1/2(ab·sin(C)) = 1/2(5.099·5.831·sin(59.0362° -11.3099°)) = 11
The area of the triangle is 11 square units.
__
Additional comment
Side lengths could also be determined using the Pythagorean theorem, and the angle between any two of them could be found using the Law of Cosines.
Heron's formula could be used to find the area from the three side lengths.
Given two rectangular ducts with equal cross-sectional area but different aspect ratios (width/height) of 2 and 4 which will have the greater frictional losses? Explain your answer
The frictional loss will be greater for aspect ratio of 2 as friction will be more when the height of the duct is higher compared to the increase in width.
In a straight duct with constant cross sectional area , the velocity of the water is changed. The change in static pressure is the frictional loss .
In the duct the energy is constant. Therefore when water moves upwards with the increase in height the frictional loss or the pressure loss will be more more.
When width increases there will be less pressure, So frictional loss will be increased with height.
Let the width and height be a and b respectively.
now area = ab
and a\b =2
or, a = 2b
again a\b = 4 or, a = 4b
if ab is constant then the height for the aspect ratio of 4 is greater.
Therefore there will be more frictional loss for the increased height.
To learn more about frictional loss visit:
https://brainly.com/question/27829571
#SPJ4
35+6x-2=13x+12 solve for x
Answer:
x = 3
Step-by-step explanation:
Solve for x:
35 + 6x - 2 = 13x + 12
Simplifying on the left side:
33 + 6x = 13x + 12
Subtracting 33 on both sides:
6x = 13x - 21
Subtracting 13x on both sides:
-7x = -21
Dividing by -7 on both sides:
x = 3
100x100x325x1773x3.44554x34444x6i78754x23324
Answer:
1.097174699×10^²⁶
Step-by-step explanation:
100×100×325×1773×3.44554×34444×6878755×23324=
1.097174699×10^²⁶
A satellite flies 136640136640 miles in 17. 817. 08 hours. How many miles has it flown in 9. 879. 87 hours?.
If a satellite flies 136640 miles in 17.8 hours then in 9.87 hours the satellite flows down to 75766.6 miles
Given that:
A satellite flies 136640 miles in 17.8 hours
We will find the unit rate first,
Unit rate = 136640/17.8
Unit rate = 7676.40 miles per hour.
Miles flown in 9.87 hours,
Miles flown = 7676.40 × 9.87
Miles flown = 75766.6 miles
Hence Miles flown in 9.87 hours is 75766.6 miles
Learn more about Unit rate here:
brainly.com/question/19493296
#SPJ4
11. MARINE BIOLOGY Killer whales usually swim at a
rate of 3.2-9.7 kilometers per hour, though they can travel
up to 48.4 kilometers per hour. Suppose a migrating killer
whale is swimming at an average rate of 4.5 kilometers per
hour. The distance d the whale has traveled in t hours can
be predicted by the equation d = 4.5t.
a. Graph the equation.
b. Use the graph to predict the time it takes the killer
whale to travel 30 kilometers.
The graph of linear function d = 4.5t and the time to cover 30km is 6.67s
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here;
m = slopeb = y-interceptThe linear function given in the question is;
d = 4.5t
a) The graph of the function d = 4.5t is attached below.
b) The time it takes to cover 30km will be
d = 4.5t
30 = 4.5t
t = 30 / 4.5
t = 6.67 s
The time it takes to cover a distance of 30km is 6.67s
Learn more on linear function here;
https://brainly.com/question/15602982
#SPJ1
M is the midpoint of AC. A is (3, -9) and C is (-5, 16). Solve for the following
Answer:
[tex]M=\left(-1, \dfrac{7}{2} \right)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given endpoints:
A (3, -9)C (-5, 16)Substitute the given points in the midpoint formula:
[tex]\implies M=\left(\dfrac{x_C+x_A}{2}, \dfrac{y_C+y_A}{2} \right)[/tex]
[tex]\implies M=\left(\dfrac{-5+3}{2}, \dfrac{16+(-9)}{2} \right)[/tex]
[tex]\implies M=\left(\dfrac{-2}{2}, \dfrac{7}{2} \right)[/tex]
[tex]\implies M=\left(-1, \dfrac{7}{2} \right)[/tex]
the mass of a bag of flour is 7kg 500g. Joyce repacks the flour into 12 small packs of equal mass. What is the mass in kilograms of each small pack of flour
Answer:
I'm pretty sure it's 0.625kg
Step-by-step explanation:
There are 1000g in 1kg so 7kg would be 7000g plus 500g which is 7500g.
7500g divided by 12 is 625g. Divide by 1000 to get kg and you get 0.625kg.
Hope this helps!
you toss a fair coin 9 times. find the probability of no more than 8 heads given that at least one toss resulted in heads.
The probability of no more than 8 heads given that at least one toss resulted in heads will be 511/512.
What is probability ?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
A coin has two possibility, either head or tail.
So, there will be 2 possible outcomes when a coin is tossed.
hence, Total no. of outcomes (T) = 2^9. = 512
Now, Probability of getting one tail = 1/2^9 = 1/512
and, Probability of getting at most 8 heads
= 1 - Probability of getting one tail
= 1 - 1/512
= 511/512.
Learn more about Probability from the link given below:
https://brainly.com/question/13604758
#SPJ4
Find an expression that produces a quotation of 9 R15 . Write the expression in the box
Pls help me :,)
The numerical will be equal to 159 ÷ 16 and the polynomial will be (9x +15)/x.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
In comparison to the divisor, the dividend will be 15 times greater. It seems that you are free to select any divisor. It must be more than 15 if the divisor is totally numerical.
Numerical:
Divisor = 16,
so we have,
(9×16 +15) ÷ 16
= 159 ÷ 16
Polynomial:
The simplest divisor we can have is a single variable: x.
(9x +15)/x
To know more about Expression:
https://brainly.com/question/14083225
#SPJ1
john drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. what was his average speed for the whole journey?
The average speed of John for the whole journey is 54km/h.
What is the average speed?Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.
Speed is the rate of movement of something at a specific time.
Average speed refers to the average speed over the course of a journey.
So, the average speed will be:
Distance = speed x time
d₁ = v₁ x t₁
d₁ = 50 x 3
d₁ = 150 km
d₂ = v₂ x t₂
d₂ = 60 x 2
d₂ = 120 km
So,
D = d₁ + d₂
D = 150 + 120
D = 270 km
Utilizing the S formula:
S = D/ T
S = 270 / 5
S = 54 km/hr
S = 54km/hr
Therefore, the average speed of John for the whole journey is 54km/h.
Know more about the average speed here:
https://brainly.com/question/4931057
#SPJ4
how many 1/4 lbs are in 80 lbs
Answer:
640 1/4 lbs
Step-by-step explanation:
Product filling weights are normally distributed with a mean of 350 grams and a standard deviation of 10 grams. a. Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30. b. What happens to the control limits as the sample size is increased? c. What happens when a Type I error is made? d. What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30? f. What is the advantage of increasing the sample size for control chart purposes? What error probability is reduced as the sample size is increased?
The control limits for the x chart for a sample of size 10,
a-Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30
UCL = 359.48
LCL = 340.51
b. What happens to the control limits as the sample size is increased
The control limits for the x chart for a sample of size 20,
UCL = 356.71
LCL = 343.29
c-What happens when a Type I error is made
The control limits for the x chart for a sample of size 30,
UCL = 355.47
d- What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30
LCL = 344.52
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event.
The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
Probability generally refers to the degree to which something is likely to occur.
This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
To learn more about probability visit: https://brainly.com/question/11234923
#SPJ4
the faces of each of two fair dice are numbered 1, 2, 3, 5, 7, and 8. when the two dice are tossed, what is the probability that their sum will be an even number?
The probability that the sum will be an even number on the toss of two dice is 5/9 .
In the question ,
it is given that ,
the numbers on the faces of the dice are 1, 2, 3, 5, 7, and 8 .
the probability of getting an odd number first is = 4/6 = 2/3,
the probability of getting an even number first is = 2/6 = 1/3,
To get an even, we must get either 2 odds or 2 evens.
The probability of getting 2 odds is 4/6 × 4/6 = 16/36 .
The probability of getting 2 evens is 2/6 × 2/6 = 4/36.
If we add them together,
we get ,
= 16/36 + 4/36
= 20/36
= 10/18 = 5/9
Therefore , the required probability is 5/9 .
Learn more about Probability here
https://brainly.com/question/14986190
#SPJ4
in a class of 45 student there are 12 girls what is the percentage of girls in the class?
The percentage of girls in a class are 26.67%.
What is percentage?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Given:
In a class of 45 student there are 12 girls.
We have to find the percentage of girls in the class.
Percentage of girls = (number of girls / Total number of students ) x 100
= (12 / 45) x 100
Percentage of girls = 26.6666
Percentage of girls ≈ 26.67
Hence, the percentage of girls in a class are 26.67%.
To know more about percentage, click on the link
https://brainly.com/question/24877689
#SPJ4
Express the triple integral f(x, y, z)dV as an iterated integral in cylindrical coordinates for the given function f and solid region E
Evaluate the iterated integral.
f(x, y, z) = xy ZA 256-x-y? -y E == x + y ? 0
The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.
The iterated integral in cylindrical coordinates is given by:
∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz
Evaluating the integral yields:
∫∫∫f(ρ, θ, z)dV = 256π∫zdz
= 256πz²
= 256π(256 - x - y)²
learn more about integral here
https://brainly.com/question/22008756
#SPJ4
What is the value of x?
Enter your answer in the box.
x =[ ]
Answer:
(2x+2)=(3x-52)
2x+2=3x-52
2x-3x=-52-2
-x=-54
x=54
Can someone help me with this??
Step-by-step explanation:
H is the plan
F is the side
A is the plan
hope it helps.. please mark brainliest
What is the approximate speed of sound in the experimental medium ( speed = frequency X wavelength )
The speed will be calculated by the formula by the product of frequency and wavelength.
What is the speed of sound?The speed of sound is the distance travelled by a sound wave per unit of time as it propagates through an elastic medium. At 20 degrees Celsius, the speed of sound in air is approximately 343 metres per second or one kilometre in 2.91 seconds or one mile in 4.69 seconds.
Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
The speed of the sound will be calculated by the multiplication of frequency and wavelength.
To know more about the speed of sound follow
https://brainly.com/question/16012426
#SPJ1
11. BC
5/4y-1
B
A
7/3y-2
C
Answer:
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:
All the sides have equal lengths. Set the two sides equal to each other and solve for y
[tex]\frac{5}{4}[/tex]y + 1 = [tex]\frac{7}{3}[/tex]y -2 I am going to clear the fractions by multiplying through by 12
[tex](\frac{12}{1})[/tex][tex]\frac{5}{4}[/tex] y + (12)(-1) = [tex](\frac{12}{1})[/tex][tex]\frac{7}{3}[/tex] y - (12)2
15y - 12 = 28y - 24 Subtract 15y from both sides
-12 = 13y - 24 Add 24 to both sides
12 = 13y Divide both sides by 13
[tex]\frac{12}{13}[/tex] = y
Plug 12/13 into the expression for either side to find the length of BC. All the sides have the same length
[tex]\frac{7}{3}[/tex][tex](\frac{12}{13})[/tex] - 2
[tex]\frac{28}{13}[/tex] - [tex]\frac{26}{13}[/tex] = [tex]\frac{2}{13}[/tex]
which test should be used to determine if a difference exists between the proportion of all ucf and usf students who prefer to use hand sanitizer?
the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
When there are multiple alternatives accessible, hypothesis testing is utilised. To decide whether to accept or reject the null hypothesis, the z test is performed in the mean, which determines the t value. This value is then compared with the p value. The alternate explanation in this case is mu, which is represented. For P1 and P2, the 90% confidence interval is (- 0.0765, 0.02646).
Hence, the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%
Learn more about z test, by the following link.
brainly.com/question/17144617
#SPJ4
Please help me with explanation
Answer:
[tex]5c+\frac{9-8c}{24}[/tex]
Step-by-step explanation:
Simplify
[tex]5c+\frac{1*(\frac{3}{4}-\frac{2c}{3} )}{2}[/tex]
[tex]5c+\frac{9-8c}{24}[/tex]
an architect is making a floor plan for a rectangular gymnasium. if the gymnasium is 80 feet long and 60 feet wide, what will the distance be between opposite corners?
In the gym, there are 100 feet between the opposing corners.
Given,
The length of the rectangular gymnasium = 80 feet
The width of the rectangular gymnasium = 60 feet
We have to find the distance between opposite corners of the gymnasium;
Here,
The distance between opposite corners of the gymnasium is the diagonal of the rectangle;
Diagonal of rectangle = [tex]\sqrt{width^{2} + length^{2} }[/tex]
Then,
Diagonal = [tex]\sqrt{80^{2} +60^{2} }[/tex]
Diagonal = [tex]\sqrt{6400+3600}[/tex]
Diagonal = √10000
Diagonal = 100 feet
That is,
The distance between the opposite corners if the gymnasium is 100 feet.
Learn more about diagonal of rectangle here;
https://brainly.com/question/22530917
#SPJ4
If the bond angle between two adjacent hybrid orbitals is 180°, which is the hybridization?.
If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization is sp hybridization , it forms linear molecules with an angle of 180°.
Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.
In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.
The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:
To learn more about hybridization
brainly.com/question/16305420
#SPJ4
Bro please help and tell me how to do this with the steps!
For ΔDEF , Length of shorter side = 6, Length of medium side = 8 , Length of longer side = 12.
For ΔGHI , Length of shorter side = 9, Length of medium side = 12 , Length of longer side = 18.
For ΔJKL , Length of shorter side = 3/2, Length of medium side = 2 , Length of longer side = 3.
What are Similar Triangles ?
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.
In the given figure below, two triangles ΔABC and ΔXYZ are similar only if,
i) ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
ii) AB/XY = BC/YZ = AC/XZ (Similar triangles proportions)
Hence, if the above-mentioned conditions are satisfied, then we can say that ΔABC ~ ΔXYZ
It is interesting to know that if the corresponding angles of two triangles are equal, then such triangles are known as equiangular triangles. For two equiangular triangles we can state the Basic Proportionality Theorem (better known as Thales Theorem) as follows:
For two equiangular triangles, the ratio of any two corresponding sides is always the same
Given that ,
For ΔABC , Length of shorter side = 3, Length of medium side = 4 , Length of longer side = 6.
Now,
For ΔDEF ,
Scale Factor = 2
Length of shorter side = 2*3 = 6, Length of medium side =2*4 = 8 , Length of longer side =2*6 = 12.
For ΔGHI ,
Scale Factor = 3
Length of shorter side = 3*3 = 9, Length of medium side =3*4 = 12 , Length of longer side =3*6= 18.
For ΔJKL ,
Scale Factor = 1/2
Length of shorter side =3*1/2 = 3/2, Length of medium side =4*1/2= 2 , Length of longer side =6*1/2= 3.
Learn more about Similar Triangles at :
https://brainly.com/question/14285697
#SPJ1
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
The no of student ticket, x = 30
The no of adult ticket, y = 37
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.
The drama club is selling tickets to their play to raise money for the show's expenses.
Let the student ticket be represented as x and adult ticket as y
Cost of student ticket,x = $7
Cost of adult ticket,y = $9
The total number of tickets, x + y = 67 ... (1)
There was a total of $543 in revenue from the sale of 67 total tickets.
7x + 9y = 543 ...(2)
Multiplying eq(1) by 7, we get
7x + 7y = 469 ...(3)
Subtract eq (3) from (2), we get
2y = 74
y = 37, sub in eq (1)
x = 30
The no of student ticket, x = 30
The no of adult ticket, y = 37
To learn more about equation from the given link
https://brainly.com/question/15833335
#SPJ1
Answer: Let s= the number of student tickets sold Let
Let a=the number of adult tickets sold
7s+9a=543
s+a=67
Step-by-step explanation:
1. this question concerns the group z26 under addition modulo 26. a) list the elements of this group. b) is this group cyclic? c) is 16 a generator of this group? what about 5?
The element of this group is {0, 1, 2, 3, ...., 25}, this group is a cyclic group, and 16 is not a generator for this group but 5 is a generator for this group.
How to find element of group under addition modulo?
[tex]Z_{26}[/tex] ≡ Group of integers under addition modulo 26
addition modulo is all addition of integer in ordinary way than remove integral multiple. For example, addition modulo a+mb is a+b than remove all integral multiple m and the result is lower than m (residue).
a) The elements of this group is all the integers remainder after mod 26. So,
x = k (mod 26) where 0 ≤ k < 26
or we can write each of them as {0, 1, 2, ..., 23, 24, 25}
b) Cyclic group is a group that is generated by 1 element. Since, the group is integers under addition modulo with all integers can be generated by adding 1 repeatedly, so the group [tex]Z_{26}[/tex] is cyclic group.
c) As 1 ∈ [tex]Z_{26}[/tex] but there is no m ∈ N such that [tex]16^m[/tex] = 1, but for [tex]5^m[/tex] is
{0, 5, 10, 15, 20, 25, 4, 9, 14, 19, 24, 3, 8, 13, 18, 23, 2, 7, 12, 17, 22, 1, 6, 11, 16, 21}
or in simply way, we can say there is m ∈ N for [tex]5^m[/tex] = 1. So, 16 is not generator of this group, but 5 is generator of this group.
Thus, the number of {0, 1, 2, 3, ...., 25} is the element for this group, cyclic group is a type of this group, and 5 is a generator for this group but 16 is not a generator for this group.
Learn more about cyclic group here:
brainly.com/question/28875300
#SPJ4