Answer:
[tex]\textsf{A)} \quad \cos 2 \theta=\dfrac{9}{25}[/tex]
[tex]\textsf{B)} \quad \sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]
Step-by-step explanation:
Given:
[tex]\sin \theta=\dfrac{2\sqrt{2}}{5},\quad \dfrac{\pi}{2} < \theta < \pi[/tex]
[tex]\hrulefill[/tex]
Part ATo determine the exact value of cos 2θ, we can use the Cosine Double-Angle formula:
[tex]\large\boxed{\cos^2\theta = 1 - 2 \sin^2 \theta}[/tex]
Substitute the given value of sin θ into the formula:
[tex]\begin{aligned}\cos 2 \theta&=1-2\left(\dfrac{2\sqrt{2}}{5}\right)^2\\\\\cos 2 \theta&=1-2\left(\dfrac{8}{25}\right)\\\\\cos 2 \theta&=\dfrac{25}{25}-\dfrac{16}{25}\\\\\cos 2 \theta&=\dfrac{9}{25}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part BTo determine the exact value of sin (θ/2), we can use the half-angle formula for sine:
[tex]\large\boxed{\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\cos \theta}{2}}}[/tex]
First, find the value of cos θ by substituting the given value of sin θ into the trigonometric identity sin²θ + cos²θ = 1:
[tex]\begin{aligned}\left(\dfrac{2\sqrt{2}}{5}\right)^2+\cos^2\theta&=1\\\\\dfrac{8}{25}+\cos^2\theta&=1\\\\\cos^2\theta&=1-\dfrac{8}{25}\\\\\cos^2\theta&=\dfrac{17}{25}\\\\\cos\theta&=\pm \sqrt{\dfrac{17}{25}}\\\\\cos\theta&=\pm \dfrac{\sqrt{17}}{5}\end{aligned}[/tex]
As cos θ is negative on the interval π/2 < θ < π, we take the negative square root. Therefore:
[tex]\cos\theta&=-\dfrac{\sqrt{17}}{5}[/tex]
Now, substitute the found value of cos θ into the half-angle formula:
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\left(-\dfrac{\sqrt{17}}{5}\right)}{2}}[/tex]
Therefore:
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5}{5}+\dfrac{\sqrt{17}}{5}}{2}}[/tex]
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5+\sqrt{17}}{5}}{2}}[/tex]
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]
As sin θ is positive on the interval π/2 < θ < π, we take the positive square root. Therefore:
[tex]\sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]
Graphing systems
Y= -1/4x + 3
Y=3/4x -1
The point P = (12,-9) on the circle x² + y² =2 is also on the terminal side of an angle 0 in standard position. Find sin 0, cos 0, tan, csc 0, sec 0, and cot 0
The values are:
Sin Ф = 4/5
Cos Ф = -3/5
Tan Ф = -4/3
Cosec Ф = 5/4
Sec Ф = -5/3
Cot Ф = -3/4
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
The point P = (12,-9) on the circle x² + y² =2 is also on the terminal side of an angle Ф.
This means,
Base = -9
Perpendicular = 12
Applying Pythagorean theorem.
Hypotenuse² = Base² + Perpendicular²
Hypotenuse² = (-9)² + 12²
Hypotenuse² = 81 + 144
Hypotenuse² = 225
Hypotenuse = √225 = 15
Hypotenuse = 15
Now,
Sin Ф = Perpendicular / Hypotenuse = 12/15 = 4/5
Cos Ф = Base / Hypotenuse = -9/15 = -3/5
Tan Ф = Perpendicular / Base = -12/9 = -4/3
Cosec Ф = Hypotenuse / Perpendicular = 15/12 = 5/4
Sec Ф = Hypotenuse / Base = -15/9 = -5/3
Cot Ф = Base / Perpendicular = -9/12 = -3/4
Thus,
The values are given above.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ1
How long would Joey need to invest his $300 at 4% annual interest if he wants to end up with $400? Assume simple interest, I = PRT and round to the nearest tenth of a year.
Answer:
1 year
Step-by-step explanation:
the equation to find simple interest
A = P (1 + rt)
so plug in yore numbers
400=300(1+0.4*t)
400=300+120t
120=120t
1=t
The two equations shown below represent different functions. Function P: y = + 2 Function Q: y = + 2 Identify each function as linear or nonlinear. State a reason why each function is linear or nonlinear
The functions are classified as follows:
Function P: nonlinear, as the variable x is in the denominator.Function Q: linear, as the variable x has an exponent of 1 in the numerator.How to model a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
Hence the conditions needed for a function to be a linear function are given as follows:
Variable x is present only on the numerator.The highest exponent of assumed by the variable x is of 1.Missing InformationThe functions are given as follows:
P: y = 3/x + 2.Q: y = 3x + 2.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
what question was asked and answered in order to gather the information presented on this graph? b. who was asked the question? c. how many people answered the question? d. verify the percentages, 1.59%, 17.46%, and 25.4%. e. are the percentages reported in this graph likely to be representative of all people? explain why or why not.
The graph presents information gathered through a survey or questionnaire, and the information is presented as a percentage to show the proportion of participants who answered in a particular way.
Percentage is a mathematical concept that represents a proportion of a whole as a fraction of 100. It is used to express how much of a whole something is and is commonly used in statistics and data analysis.
The bar graph shows three different percentages: 1.59%, 17.46%, and 25.4%. To verify these percentages, we need to know the total number of participants who answered the question and the number of participants who answered in a particular way.
If 100 participants answered the question, then 1.59% would represent 1.59 participants, 17.46% would represent 17.46 participants, and 25.4% would represent 25.4 participants.
It is important to consider whether the percentages reported in this graph are likely to be representative of all people.
This will depend on a number of factors, including the sample size, the method used to select participants, and the representativeness of the sample in relation to the population as a whole.
If the sample size is small, or if the participants were selected in a biased way, then the percentages may not be representative of all people.
If, however, the sample size is large and the participants were selected randomly, then the percentages may be representative of the population as a whole.
To know more about percentage here.
https://brainly.com/question/13729841
#SPJ4
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony X sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have?
Sue=?
Tony=?
Find the volume of the solid obtained by rotating the region bounded by the curves y=x^2, x=5, and y=0 about the x-axis
The volume of the solid given by rotating the region bounded by the curves y = x^2, x = 5, and y = 0 about the x-axis is 625π.
What is formula for the volume of a region bounded by the curves?When the region bounded above by the graph of f, below by the x-axis, and on the sides by x = a and x = b is rotated about the x-axis, the volume V of the generated solid is given by V = ∫ab π [f(x)]^2 dx. We can also find solids by revolving curves about the y-axis.
What is the formula to find volume of a solid object?Whereas the basic formula for the area of a rectangular shape is length * width, the basic formula for volume is length * width * height. How we refer to the different dimensions does not change the calculation. We may, for example, use depth instead of height.
In this case, the bounds of integration are from 0 to 5. The radius function is going to be:
r (x) = x^2
Now, substitute the value into the formula for the disk method:
V = π * ∫ba * [r(x)]^2 * dx
So, in this case it will be:
V = π * ∫5 0 * [x^2]^2 * dx
= π * ∫5 0 * x^4 * dx
= π * x^5 / 5 ∣ 5 0
= π * ((x^5 / 5) – (0 / 5))
= 625π
Hence, the volume of the solid is 625π.
Learn more volume of solid at: https://brainly.com/question/10841592
#SPJ4
2x-7/4 - (1-x/6)=17
Find the value of x in this given problem
Will Mark Brainlist!
Solve for x on the diagram below
Answer:
x = 50
Step-by-step explanation:
50 + 2x = 150
2x = 100
x = 50
Need assistance on this
The population after 1, 2, and 3 years are 2800, 3920, and 5488.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
y = 2000 x [tex](1.4)^x[/tex]
Now,
For x = 1,
y = 2000 x 1.4
y = 2800
For x = 1,
y = 2000 x 1.4²
y = 3920
For x = 1,
y = 2000 x
y = 2000 x 1.4³
y = 5488
Thus,
After 1, 2, and 3 years the populations are 2800, 3920, and 5488.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
7 engineering students are lined up to give presentations at a hiring fair. one person demands to be either first or last. in how many ways can these students line up? (enter an integer.)
The Answer is 1440 There are two possibilities for the person who demands to be either first or last: they can be first in line, or they can be last in line.
The problem is asking for the number of ways 7 engineering students can line up for presentations at a hiring fair, where one person demands to be either the first or last in line.
If they are first in line, then there are 6 students left to line up. The number of ways to line up 6 students is 6!, which is 720.
If they are last in line, then there are also 6 students left to line up, and the number of ways to line up 6 students is 6! or 720.
So, the total number of ways to line up the 7 students is 720 + 720 = 1440.
Therefore, the answer to the question is 1440.
To know more about Permutations
https://brainly.com/question/1216161
#SPJ4
it 6-2: MathXL for School: Additional Practice
Find the values of x and y in parallelogram PQRS.
PT=y, TR=2x+1, QT=5y, TS=7x+11
x=and y=
P
T
R
S
The value of x and y for the parallelogram PQRS is 2 and 5 respectively.
What is parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.
The qualities of a parallelogram are shared by the shapes of a square and a rectangle.
PT=y, TR=2x+1, QT=45y, TS=7x+11
The diagonals of a parallelogram bisect each other:
So, PT = TR and QT = TS
Thus, the system of equation is:
y = 2x+1
5y = 7x+11
Multiply the first equation by 5:
5y = 10x+5
Set the two equations as equal:
10x + 5 = 7x + 11
Subtract 7x from each side.
10x + 5 -7x = 7x + 11 -7x
3x + 5 = 11
Subtract 5 from both sides:
3x + 5 - 5 = 11 - 5
3x = 6
x = 2
Now solve for y:
y = 2x+1
y =2(2)+1
y =5
Hence, the value of x and y for the parallelogram PQRS is 2 and 5 respectively.
Learn more about parallelogram here:
https://brainly.com/question/29147156
#SPJ1
what would be the answer?
As per the above given question the reflection of m∠O=112°.
What is reflection?A process of introspection or self-examination is reflection. It entails reflecting critically on one's thoughts, feelings, and experiences in order to comprehend oneself better. Self-awareness and insight can be developed through reflection, which can result in personal development and change.
In a larger sense, reflection also refers to the bouncing back of light, sound, or other waves from a surface and is employed in many disciplines, including arithmetic, computer science, and optics. The capacity of a computer program to review and alter its own structure and behavior at runtime is known as reflection in computer programming.
According to question:
Here are given m∠G=61 m∠f=7
From angle sum property of triangle, we get in ΔGFA
m∠G+m∠F+m∠O=180°
⇒61+7+m∠O=180
⇒68+m∠O=180
Therefore m∠O=180-68=112
To know more about Reflection visit:
https://brainly.com/question/30270479
#SPJ1
An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year.(a) How many loads can be expected to occur during a 2-year period?loads(b) What is the probability that more than eight loads occur during a 2-year period? (Round your answer to three decimal places.)(c) How long must a time period be so that the probability of no loads occurring during that period is at most 0.2? (Round your answer to four decimal places.)yr
So, during a two-year period, we may anticipate 0.8 loads. As a result, the likelihood of more than 8 loads occurring in a 2-year period is 0.001. As a result, a time period of at least 2.303 years is necessary to assure that the likelihood of no loads occuring is at most 0.2.
What is Poisson distribution?A discrete probability distribution is a Poisson distribution. It expresses the likelihood of an event occurring a specific number of times (k) during a certain time or space period. The mean number of occurrences, (lambda), is the solitary parameter in the Poisson distribution.
Here,
a) The expected number of loads during a 2-year period can be calculated using the Poisson distribution formula:
E[X] = λt, where λ is the average rate of occurrences (mean time between occurrences) and t is the time period.
E[X] = λ * 2 years = 0.4 year^-1 * 2 years = 0.8 loads
So, we can expect 0.8 loads to occur during a 2-year period.
b) The probability that more than 8 loads occur during a 2-year period can be calculated using the cumulative distribution function of the Poisson distribution:
P(X > 8) = 1 - P(X <= 8)
We can use a Poisson distribution calculator or table to find the cumulative distribution function for P(X <= 8) and subtract it from 1 to find P(X > 8).
P(X > 8) = 1 - P(X <= 8) = 1 - 0.999 = 0.001
So, the probability that more than 8 loads occur during a 2-year period is 0.001.
c) To find the time period in which the probability of no loads occurring is at most 0.2, we can find the value of t such that P(X = 0) <= 0.2.
P(X = 0) = e^-λt
Setting P(X = 0) <= 0.2 and solving for t, we get:
0.2 >= e^-λt
ln(0.2) >= -λt
-ln(0.2) / λ >= t
Substituting λ = 0.4 year^-1, we get:
-ln(0.2) / 0.4 >= t
t >= (-ln(0.2) / 0.4) years = 2.303 years
So, we can expect 0.8 loads to occur during a 2-year period. So, the probability that more than 8 loads occur during a 2-year period is 0.001. So, a time period of 2.303 years or longer is required to ensure that the probability of no loads occurring is at most 0.2.
To know more about Poisson distribution,
https://brainly.com/question/17280826
#SPJ4
Write in a single Power: 25 x 5 x 125=
Answer: 5^6
Step-by-step explanation:
First, you have to simplify the numbers so that all of them share the same base. For this problem, the base for all of these numbers would be 5. So now the equation looks like this:
5^2 * 5^1 * 5^3
Next we have to turn all of these numbers into one. Whenever you multiply the numbers, all you have to do is add the exponents together. So now it will look like this:
5^(2+1+3)
Add the numbers up and you get your answer.
5^6
Find the average cost function if cost and revenue are given by C(x) = 146 +8.9x and R(x) = 4x -0.06x²
Elisa and her friend are dividing a 34-ounce bag of pretzels. Elisa
shares her portion equally with her two sisters. Which fraction
represents the amount of pretzels, in pounds, each person receives?
A. 17/48 lb
B. 2 1/8 lb.
c. 11 1/3 lb.
D. 1/2 lb.
Amount of pretzel each person receives is 17/16 lb.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Total weight of the bag of pretzels = 34 ounce
Elisa shares this among her two sisters equally.
Share of pretzels each sister gets = 34 / 2 = 17 ounces
We need this amount in pounds.
We know that,
16 ounce = 1 lb.
17 ounces = 17/16 lb.
Hence the amount of pretzels each get is 17/16 lb.
Learn more about Fractions here :
https://brainly.com/question/10354322
#SPJ1
Directions: Based on the information given in the following problem, compute the gross pay.
Hours worked: 51
Overtime hours worked: 11
Regular rate of pay: $7.35 per hour
Round your answers to two decimal places.
gross pay: $
The gross pay is $496.68.
SolutionTo calculate the gross pay, you need to calculate the total pay for the regular hours worked and the overtime hours worked separately, and then add them together.
Regular hours worked: 51 hoursRegular rate of pay: $7.35 per hourTotal pay for regular hours: 51 hours x $7.35/hour = $375.35
Overtime hours worked: 11 hours
Overtime rate of pay: 1.5 times the regular rate of pay, or $7.35 x 1.5 = $11.03
Total pay for overtime hours: 11 hours x $11.03/hour = $121.33
Gross pay: $375.35 + $121.33 = $496.68
So the gross pay is $496.68.
Learn more about multiplying here : brainly.com/question/28768606
#SPJ1
Solve the equation -3/2x+4=-4 by graphing. Drag the two points on each of the lines to create the graph. Enter the solution to the equation in the blank.
The solution to the equation is x = 16/3
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
-3/2x+4=-4
The above equation is a linear equation
A linear equation is represented as
y = mx + c
Where
slope = m
y-intercept = c
Next, we graph the equation
See attachment for the graph
From the graph, we can see that the solution is
x = 16/3
Read more about equation at
https://brainly.com/question/2972832
#SPJ1
You and your sister are saving money from your allowances. You have $25 and you save $3 each week. Your sister has $40 and she saves $2 each week.
In
weeks, you and your sister will have the same amount of money; and at the time, you both will have
Answer:
c below
Step-by-step explanation:
you: 25 +$3 /week * x weeks
sis: 40 + 2/week * x weeks
they have to equal to each other
so 25 + 3x = 40 +2x
move x around & simplify
so x = 15
total 25+3*15 = 25+45 = 70
HELP DUE IN 30MINSS!!!!!!!!!!!!!!
What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 8 yards
8π yards
4π yards
64π yards
25.12π yards
The circumference of the circle in terms of π is 8π yards.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Perimeter refers to the total outside length of an object,
here, we have,
the diameter of the circle = 8yrd
the circumference of the circle in terms of π
=π * 8
= π8 yrd.
Hence, The circumference of the circle in terms of π is 8π yards.
Learn more about perimeter here:
brainly.com/question/397857
#SPJ1
Is 707 greater or less than 6391÷10 9/7
Answer: yes
Step-by-step explanation:
Manny says he should multiply the first equation in the system of equations below by 3 and the second equation by 2, then add to eliminate x. Is there a more efficient way to solve this system? Explain your answer.
−2x+y=15
3x+4y=−12
A. No, there isn't a more efficient way to solve this system.
B. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate y, then solve for x.
C. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate x, then solve for y.
D. Yes, a more efficient way is to multiply the first equation by 4
add to eliminate y, then solve for x.
Step-by-step explanation:
A,No, there isn't a more efficient way to solve this system.
B.Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.
C.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate y, then solve for x.
D.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate x, then solve for y.
What values of n makes the equation true?
The value of n that makes the equation true is 0.
What is an exponent?In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;
bⁿ
Where:
the variables b and n represent numerical values or an algebraic expression.
By applying the property of exponents based on the law of indices for powers and division, we have the following:
Expression = 85^n/85^6 = 85^{-6}.
Expression = 85^{n - 6} = 85^{-6}
Since the powers both have a common base, we have:
n - 6 = -6
n = 6 - 6
n = 0.
Check:
85^0/85^6 = 85^{-6}
1/85^6 = 85^{-6}
Read more on exponent here: brainly.com/question/9524319
#SPJ1
Find the slope of the line represented by the data below
The slope of the line represented by the given data is; 1
How to find the slope between two coordinates?
The slope of a line is defined as the rate of change of y divided by the rate of change of x.
Thus, the formula to find the slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
Taking the last two coordinates gives us;
m = (16 - 13)/(7 - 3)
m = 3/3
m = 1
Read more about slope between coordinates at; https://brainly.com/question/3493733
#SPJ1
according to the national health statistics report, a sample of 360 one-year old boys in the u.s. had a mean weight of 25lbs. assume the population standard deviation is lbs., let the confidence level be 92%. a) the standard error [ select ] b) the margin of error e
given information are :- test mean () = 25.5 populace sd () = 5.3 example size (n) = 360 a).z critical value for 95% confidence level,
both followed tests be:- the 95% confidence interval for the mean load of every one of the one-year-old child young men in the US.
To get a 95% confidence interval, we should incorporate the focal 90% of the probability of the normal distribution. On the off chance that we incorporate the focal 90%, we leave out a sum of α = 10% in the two tails, or 5% in each tail, of the normal distribution.
To catch the focal 95%, we should go out 1.645 "standard deviations" on one or the other side of the determined example mean. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the middle, an area of 0.05 in the extreme left tail, and an area of 0.05 in the extreme right tail.
to know more about confidence interval click here:
https://brainly.com/question/15712887
#SPJ4
The complete question is:
According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3 pounds.
a. Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in the United States
b. Should this confidence interval be used to estimate the mean weight of all one-year old babies in the United States? Explain.
c. Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is less than 28 pounds?
Evaluate: (16/81)1/2
Answer:
Decimal0.395062
Step-by-step explanation:
16
(18)(1)
2
32/81
Answer:
The value of (16/81)^1/2 is 4/9.
Step-by-step explanation:
What is the expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
= the square root of 16/81
=4/9.
The value of (16/81)^1/2 is 4/9.
g seven people are in an elevator which stops at ten floors. (a) in how many ways can they get off the elevator ? (a) 710 (b) 107 (c) (10)7 (d) 10 7 ?
There are 107 different methods to disembark.
When you mention "no two folks exit on the same floor," I suppose you mean that each of the seven people exits the elevator on a different floor.
The first person can exit the elevator on any of the building's 10 levels, followed by the second person on any of the other 9 floors, and so on.
The total number of ways in which the 7 people can exit the elevator from different floors is 10P7 ways.
The first person, as well as the second, third, and other people, can exit from any of the ten floors, thus we take this into consideration when calculating the overall number of exits. Therefore, there are 107 different methods to disembark.
Know more about Lift problem
https://brainly.com/question/22048837
#SPJ4
The sides of a regular hexagon are equal in length. The perimeter of the hexagon is at most 24 inches. Find the possible side lengths of the hexagon. Let the lengths of the sides be x.
Answer:
[tex]0 < \text{x} \le 4[/tex]
If x is an integer, then x is any value in the set {1,2,3,4}
======================================================
Work Shown:
x = length of each side
6x = perimeter of the regular hexagon
The perimeter must be greater than 0.
Also, the perimeter must be less than or equal to 24. This is because of the phrasing "perimeter is at most 24 inches".
In other words, the perimeter is between 0 and 24, excluding 0 and including 24.
[tex]0 < \text{ perimeter } \le 24\\\\0 < 6\text{x} \le 24\\\\0/6 < 6\text{x}/6 \le 24/6\\\\0 < \text{x} \le 4\\\\[/tex]
If x is an integer, then x can be any value in the set {1,2,3,4}
Examples:
The side length x = 2 leads to a perimeter 6x = 6*2 = 12 inches. This shows why x = 2 is in the set shown above.The side length x = 5 leads to a perimeter 6x = 6*5 = 30 inches. This shows why x = 5 (and larger) is not in the set shown above.Which line represents the function y = 1/2x + 3?
Line q.
Line t.
Line s
Line r.
Which one?
The line that represents the function y = 1/2x + 3 is line r.
Which line Which line represents the function y = 1/2x + 3?Here we can see some graphed lines, and we want to see which one of these represents the linear function:
f(x) = (1/2)*x + 3
First, we can see that the slope is positive, which means that the line goes upwards (when reading from left to right).
And we can see that the y-intercept is 3, then the line should intercept the y-axis at y = 3.
With that we can conclude that the correct line is r.
Learn more about linear functions at:
https://brainly.com/question/1884491
#SPJ1