The sum of the series:
1 - 2/3 + 4/9 - 8/27+16/81 - 32/243 + .... = 2/3
All geometric sequences have a starting term a and a common ratio r.
The common ratio r is the number that the terms of the sequence are multiplied to find the next term, hence the name "ratio". All terms in the sequence are the same, hence the name "common".
The common ratios here are the numbers multiplied by 2/3 to get −4/9
and the numbers multiplied by−4/9 to get 8/27.
2/3⋅ 2/3 = [tex]\frac{2*2}{3*3 }[/tex] = 4/9 .
2/3 × (-2/3) = -4/9
The infinite sum of the geometric series can only be found in a specific case: r lies between −1 and 1.
When r is between these values, adding the series will converge - close on both sides - to a certain number.
Otherwise the sum diverges - further apart - i.e. there is no specific value that the series approaches. is in This means that an infinite series can be computed as the number to which the series converges.
This calculation is done using the formula
S∞ = a₁ − r.
a, the first term of the sequence is 2/3.
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The label on a \frac{1}{3}
3
1
-pound bag of seeds states that it will cover an area of 56 square feet. How many square feet do the seeds cover per pound?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
The number of square feet that the seed cover per pound is given as follows:
168 square feet per pound.
How to obtain the number of square feet that the seed covers per pound?The number of square feet that the seed covers per pound is obtained applying the proportions in the context of this problem.
The term proportion is used because the number of square feet that the seed covers per pound is given by the division of the total area by the number of pounds in the bag.
The parameters for this problem are given as follows:
Weight: 1/3 pound.Area: 56 square feet.Hence the number of square feet that the seed cover per pound is calculated as follows:
56/(1/3) = 56 x 3 = 168 square feet per pound.
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Evaluate the line integral, where C is the given curve.∫C xyds, C:x = t^2,y = 2t, 0 ≤ t ≤ 3
On solving the provided question, we can say that integral = [tex]\int\limits^a_b \,[/tex]t√9 + 16t² dt = [tex]\int\limits^a_b \,[/tex]√9 + 16t² d (9 + 16t²)
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.
integral
Curves, x = t³ or,
= 3t²
y = t⁴ or,
= 4t³
Now, the line integral along C will be:
→ = [tex]\int\limits^a_b \,[/tex]√(3t²)² + (4t³)² dt
= [tex]\int\limits^a_b \,[/tex]√9t⁴ + 16t⁶ dt
= [tex]\int\limits^a_b \,[/tex]√9 + 16t² dt
= [tex]\int\limits^a_b \,[/tex]√9 + 16t² dt
= [tex]\int\limits^a_b \,[/tex]t√9 + 16t² dt
= [tex]\int\limits^a_b \,[/tex]√9 + 16t² d (9 + 16t²)
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after a gymnastics meet, each gymnast shook hands once with every gymnast on every team (except herself). afterwards, a coach came down and only shook hands with each gymnast from her own team. there were a total of $281$ handshakes. what is the fewest number of handshakes the coach could have participated in?
So, the coach could have participated in at least 14 handshakes.
The total number of handshakes is the sum of the handshakes between gymnasts from different teams and the handshakes between gymnasts from the same team and the coach.
The coach shakes hands with each gymnast from her own team, so the number of handshakes between the coach and gymnasts is equal to the number of gymnasts on the team.
Let's assume the number of gymnasts on a team is x. And the number of teams is y. So the number of handshakes between gymnasts from different teams is x*(x-1)*y/2.
Given the total number of handshakes is 281, we know that:
x*(x-1)*y/2 + x = 281
In order to get the minimum number of handshakes the coach could have participated in, we can assume the maximum number of gymnasts on a team, which is x = 14.
So the equation becomes:
1413y/2 + 14 = 281
So we can find the value of y by solving this equation:
y = (281-14)/(13/2) = 17
Therefore, with x = 14 and y = 17, the minimum number of handshakes the coach could have participated in is 14, which is the number of gymnasts on the team.
So the coach could have participated in at least 14 handshakes.
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Function g is a transformation of the parent function f(x)=x2. The graph of f is reflected across the x-axis and then translated left 4 units and down 2 units to form the graph of g. Write the equation for g in the form y=ax2+bx+c.
The equation of g(x), after the translations, is given as follows:
g(x) = x² + 8x + 14.
What are the translation rules?There are four translation rules that can be applied to a function, and they are listed as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
f(x) = x².
The translations, along with their effects, are given as follows:
Left 4 units: x -> x + 4.Down 2 units: y -> y - 2.Hence the function g(x) is defined as follows:
g(x) = (x + 4)² - 2
g(x) = x² + 8x + 16 - 2
g(x) = x² + 8x + 14.
Which is in the standard form as is desired for this problem.
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Simplify to 5c + 3p,
The variable and the number come in one team.
We call that a(n)
Answer:
3(5/3c+p)
Step-by-step explanation:
5c+3p=3(5/3c+p)
lanie has decided to add strength training to her exercise program. her trainer suggests that she add weight lifting for 5 minutes during her routine for the first week. each week thereafter, she is to increase the weight lifting time by 2 minutes. a) which formula represents this sequential increase in weight lifting time?
23 minutes she will be devoting to weightlifting in week 10.
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Formula represent the sequential increase in weight lifting time is :
f (n) = 2n + 5
f (n) = 2n + 5
f (10-1) = 2(10-1) + 5
f(9) = 2(9)
f(9) = 18
f(9) = 23
Therefore,23 minutes she will be devoting to weightlifting in week 10.
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Does 1 only have 1-factor?
1 is the only number that is neither prime nor composite number. 1 is the only factor of 1. One is the only number that has only 1 factor.
The factor of 1: 1 Negative Factor of 1: -1Prime Factorization of 1: As 1 has no prime factors, it cannot be prime factorized.Sum of Factors of 1: 1The number 1 is known as a unit. 1 is neither a prime nor composite number and has no prime factors.This means we cannot find factors of 1 and the prime factorization of 1 is not possible.Explore factors using illustrations and interactive example
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4
Complete each congruency statement, and name the rule used.
If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "CanNot Be Determined" in place of the rule.
Chapter Reference
b
M is the midpoint of
CI
△CAM ≅ △____ by ____
A
M
I
C
Answer:
△C AM ≅△
By rule
△TAN ≅ △LEF, by the SSS congruence theorem.
What is the SSS congruence theorem?The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.
From the triangles given by the image presented at the end of the answer, the congruent sides are given as follows:
NT and LE.TA and EF.AN and FL.(the congruence of each side is represented by the |, || and ||| notations).
As the three sides are congruent, we have that triangles TAN and LEF are congruent by the Side - Side - Side congruence theorem.
Missing InformationThe two triangles are given by the image presented at the end of the answer.
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What are the 4 types of computer system components?
The 4 types of computer system components are Input devices, Output devices, Memory and Central Processing Unit (CPU).
To give input and instructions to the computer for processing, input devices are employed. These items, which also go by the name of peripheral devices, include the mouse, keyboard, microphone, scanner, etc.
Monitors and printers are examples of output devices that are used to display the outcomes of the instructions that the computer has processed.
The main part of a computer that processes data is called a CPU (Central Processing Unit). The mother board, registers, buses, and other subcomponents of the CPU are used to carry out processing operations. Memory, another crucial computer component, is used by the CPU to temporarily or permanently store the instructions.
Then, there are further types of memory, including RAM, ROM, and supplementary storage devices. Together, these parts carry out the numerous instructions provided by the user.
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Help would be greatly appreciated!
Items 3-4. AABC and
ACDE are shown.
3. What is m/BAC?
4. What is m/CDE?
three circles of radii 5, 6, and 9 cm are mutually tangent. find the shaded area enclosed between the circles. (round your answer to two decimal places.)
The shaded area between three mutually tangent circles of radii 5, 6, and 9 cm is 0.23 cm².
The three circles are mutually tangent which means that the distance between the centers of any two circles is equal to the sum of the radii of those circles.
Let's call the center of the largest circle C1, the center of the middle circle C2, and the center of the smallest circle C3.
Therefore, the distance between C1 and C2 is 9 cm + 6 cm = 15 cm, the distance between C2 and C3 is 6 cm + 5 cm = 11 cm and the distance between C1 and C3 is 9 cm + 5 cm = 14 cm. So semi-perimeter is
s = ( 15+11+14)/ 2 = 40/2 = 20
Area of triangle C1C2C3 is
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]A = \sqrt{20 (20-15)(20-11)(20-14)}[/tex]
A ≈ 73.48 cm²
Now we can use the area of a sector formula which is
(n/360)πr²
where n is degree subtended by the sector, to find the shaded area.
Area of the sector of C1 = (cos⁻¹(7.5/14)/360)π9² = 40.72 cm²
Area of the sector of C2 = (cos⁻¹(5.5/15)/360)π6² = 21.52 cm²
Area of the sector of C3 = (cos⁻¹(7/11)/360)π5² = 11.01 cm²
The shaded area enclosed between the circles is the sum of the above three area of sector subtracted from the area of triangle C1C2C3:
Shaded area = 73.48 - 40.72 -21.52 - 11.01 = 0.23 cm²
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___ units of measure.
Of all the total units of measurements, the seven base units are given above.
What are the units of measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given are the units of measurements.
The seven SI base units, which are comprised of:
Length - meter (m)Time - second (s)Amount of substance - mole (mole)Electric current - ampere (A)Temperature - kelvin (K)Luminous intensity - candela (cd)Mass - kilogram (kg)Therefore, of all the total units of measurements, the seven base units are given above.
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The roots of the equation x^2+bx+c=0 are -4 and 2. Find b
Answer:
The value of b in the equation x^2+bx+c=0 can be found using the quadratic formula. The quadratic formula states that the roots of the equation are given by:
x = (-b ± √(b^2 - 4ac))/2a
Where a = 1, since the coefficient of x^2 is 1, b = b and c = c.
Step-by-step explanation:
Given that the roots of the equation are -4 and 2, we can substitute these values for x into the equation and solve for b.
For the first root of -4, we get:
1x^2 + bx + c = (1)(-4)^2 + b(-4) + c = 0
This simplifies to:
16 - 4b + c = 0
For the second root of 2, we get:
1x^2 + bx + c = (1)(2)^2 + b(2) + c = 0
This simplifies to:
4 + 2b + c = 0
Now we have two equations with two unknowns, we can use the substitution method to find the value of b.
By equating the two equation we get:
16 - 4b + c = 4 + 2b + c
We can simplify it as:
12 - 2b = 0
therefore b = 6
In summary, the value of b in the equation x^2+bx+c=0 is 6 when the roots of the equation are -4 and 2.
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The grain silo pictured above has a radius of 1.7 m. How much paint is required to
completely cover the sides and top of the grain silo once?
* a grain silo has a cylinder shape
The estimated amount of paint needed for the grain silo is 103.61 m².
How to estimate the necessary paint to cover the grain siloThe cylinder and the conical lid are the two components that make up the figure. As a result, we solve for the total surface area of the cylinder and the cone and add.
TSA for cylinder = 2πr (h + r), for h = 6.2 m and r = 1.7 m.
= 2π * 1.7 (6.2 + 1.7)
= 84.38
TSA for cone = πr (l + r), for l = slant height = 1.9 m and r = 1.7,
resulting in a value = π * 1.7 (1.9 + 1.7) = 19.23
TSA for the cone plus TSA for the cylinder equals how much paint is needed.
how much paint needed = 84.38 + 19.23
how much paint needed = 103.61 m²
The volume of paint to be used depends on the thickness of the painting.
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a person is standing 10 feet away from a street light that is 22 feet tall. how long is his shadow if he is 6 feet tall? enter the exact value of the answer.
Length of the person's shadow is 3.75 feet.
Consider triangle as shown, segment DE represent the person standing, A represent the location of light, 22 feet away from ground, BC. The shadow's length would be the length of CE.
In triangle ABC and triangle DEC, ∠C is common, and ∠CBA = ∠CED = 90°. So by AA criterion, the triangles are similar. Thus
BC/ CE = AB/ DE
(BE + CE)/CE = AB/ DE
1 + BE/CE = AB/ DE
1 + 10/CE = 22/6
10/CE = 16/6 = 8/3
CE = (10 × 3)/8
CE = 3.75
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Flu is spreading exponentially at a school. The number of new flu patients can be modeled using the
equation F=10e^0. 12d, where d represents the number of days since 10 students had the flu.
(a) How many days will it take for the number of new flu patients to equal 50? Determine your answer
algebraically using the natural logarithm. Round your answer to the nearest day
If the number of flu patients at the school is modelled by the equation [tex]F=10e^{0. 12d}[/tex] , then the number of days that it will take for the number of patients to reach 50 is 13 days .
The Exponential Growth equation is given as : [tex]F=10e^{0. 12d}[/tex] ;
We have to find How many days will it take for the number of new flu patients to equal 50 .
So , we substitute the value [tex]F=50[/tex] in the model equation ;
we get ;
⇒ [tex]50 = 10e^{0. 12d}[/tex] ;
dividing both side by 10 ,
we have ;
⇒ [tex]5=e^{0. 12d}[/tex] ;
taking [tex]\ln[/tex] on both sides ,
⇒ [tex]\ln 5 = 0.12d(\ln e)[/tex] ,....we know that [tex]\ln e = 1[/tex] ;
⇒[tex]d= \frac{\ln 5}{0.12}[/tex] ⇒ 13.41198 ;
≈ 13 days .
Therefore , it will take 13 days for the number of patients to reach 50 .
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Juanita makes $30 an hour at work. She has to take time off work to purchase her dress, so each hour away from work costs her $30 in lost income. Assume that returning to work takes Juanita the same amount of time as getting to a store and that it takes her 30 minutes to shop. As you answer the following questions, ignore the cost of gasoline and depreciation of her car when traveling.
On solving the provided question, we can say that bye equation, The total cost will be: [tex]= $75 + $60 = $135[/tex]
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
from the data provided
opportunity cost of time will be $144.
opportunity cost oftown will be -
[tex]= 1.5 × 30 = $45.[/tex]
The total cost will be:
= $45 + $86 = $131
[tex]= 2.5 × 30 = $75[/tex]
The total cost will be:
[tex]= $75 + $60 = $135[/tex]
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How many polynomials are there having 4 and 2?
4 and 2 have only one polynomial, which is [tex]x^2-6x+8[/tex]
If a polynomial has two real zeros, then it will be a Quadratic polynomial. A quadratic polynomial is a polynomial that has a degree of two. Zeros of a Quadratic polynomial can be found by two methods, 1. Splitting the middle term 2. Quadratic formula. In this question, zeros are given for this we will use the reverse of splitting the middle term.
4 and 2 are two zeros of a polynomial. It can be represented as:
[tex]x=4\\x=2[/tex]
therefore,
[tex]x-4=0\\x-2=0[/tex]
The Above Linear polynomials are a simplified form of a quadratic polynomial. When multiplying both equations, we get:
[tex](x-4)(x-2)=0[/tex]
[tex]=x^2-2x-4x+8[/tex]
[tex]=x^2-6x+8[/tex]
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It takes Logan 3/10 of an hour to complete 1 lap.
How many laps will he complete 2/3 of an hour.
Answer:
20/9 laps
Step-by-step explanation:
convert everything to minutes to make things a little easier
3/10 of an hour = 1/10 of an hour (6 minutes) * 3 = 18 minutes
2/3 of an hour = 1/3 of an hour (20 minutes) * 2 = 40 minutes
18 minutes = 1 lap
40 minutes = ? laps
multiply the first equation by 40/18 to get 40 minutes on the left sides
40 minutes = 40/18 laps = 20/9 laps
7. Given the diagram below, what is the length of side x?
Answer:
x = 19.425
Step-by-step explanation:
x = (asin(B)) / (sin(B))
x = (21sin(61∘)) / (sin(71∘))
x = 19.425 cm
If a quadratic equation [tex]ax^{2} + bx + c = 0[/tex] has equal roots , then the value of b , is :
(a) ± 2√ac
(b) √ac
(c) 4ac
(d) -√ac
If a quadratic equation ax² + bx + c = 0, has equal roots , then the value of b , is : (a) ± 2√ac
How to Interpret Quadratic Formula?The general form of a quadratic equation is;
ax² + bx + c = 0
The quadratic formula used to solve this quadratic equation is;
x = [-b ± √(b² - 4ac)]/2a
The quadratic equation ax² + bx + c = 0 has equal roots if its discriminant b² - 4ac = 0.
Thus;
b² = 4ac
b = ±√4ac
b = ±2√ac
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suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. a high school teacher working at an inner city high school is concerned about the time students spend working at after school jobs. she randomly selects 15 of her students and calculates their average work hours to be 14.3 hours per week. identify the population and sample.
suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. So, the number of people selected from the public for a research is known as a sample.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
For the given details the correct matching will be:
Parameter - 17 hrs per week
Population - All high-school-aged teens in the US
Statistic - 14.4 hours per week
Sample - 15 students
Population is everything that is taken into account for an experiment since parameters reflect population characteristics and statistics state sample parameters.
The number of people selected from the public for a research is known as a sample.
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8. 4. G.SRT.3 For what value of x is AABC ~ADEF?.
The value of x which makes ΔABC congruent to ΔDEF is 12.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
ΔABC is congruent to ΔDEF
This means,
∠A = ∠D ____(1)
∠B = ∠E ____(2)
∠C = ∠F _____(3)
Now,
From (1),
42 = 4x - 6
42 + 6 = 4x
48 = 4x
x = 48/4
x = 12
From (2),
7x + 10 = 94
7x = 94 - 10
7x = 84
x = 12
Thus,
The value of x is 12.
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are the equations (2d) / (d/r1) + (d/r2) and r1t1 + r2t2 / t1 +t2 equal or not equal?
both the equation both equations are similar and they may or may not be equivalent.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Given equation (2d) / (d/r1) + (d/r2)
and (r1t1 + r2t2) / (t1 +t2)
Taking LCM: 2d/(dr2) (dr1) / r1r2
The product 2r1r2/ r1+r2
So both the equation equations are similar and they may or may not be equivalent.
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coco flips a penny, a nickel, and a quarter. each coin is fair. what is the probability that at least one of the coins comes up heads/
When four coins are flipped at once, there is probability a 1/4 chance that the penny and nickel will both come up heads.
As per the data given in the above question are as bellow,
The data provided are as ,
As stated in the query,
Four coins are flipped simultaneously.
Flipping a coin might result in either a head or a tail.
Total results equal 2
For each coin, there is a one-in-two chance of obtaining a head.
likelihood of finding heads on both penny and nickel coins
= ( 1 / 2 ) × ( 1 / 2 )
= ( 1 / 4 )
As a result, 1 / 4 represents the likelihood of finding heads on both the penny and nickel.
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Jessica is measuring two line segments. The first line segment is 30 cm long while the second line segment is 500 mm long. How long are the two line segments together?A. 80 cmB. 25 cmC. 47 cmD. 49 cm
The length of the two line segments together is 80 cm
Step 1: Convert 500mm into cm.
We know that the value of 1mm is equal to 0.1 cm.
Then, 500mm will be 500mm*0.1 = 50 cm.
Therefore, the second line segment is 50 cm long.
Step 2: Calculate total length.
Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.
Now, the total length is
L = L1 + L2
Substitute the values L1= 30 cm and L2= 50 cm in L = L1 + L2.
Hence, the length of the two line segments together is 80 cm
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10001000 students took a test and the scores are normally distributed, with a mean of 7676 and standard deviation of 55. approximately how many students scored between 8181 and 8686?
The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.
How is this calculated?z1 = (8181-7676)/55 = 1.89
z2 = (8686-7676)/55 = 3.04
Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.
What is the difference between a standard normal distribution and a non-standard normal distribution?A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.
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In manufacturing, systematic sampling could be used to determine if the machines are operating correctly. Which of the following best describes this type of sampling
According to the given information Every 10th product in the line is selected.
How does systematic sampling work?Systematic sampling is a probabilistic strategy that includes selecting people from the general population at predetermined intervals, such as each 15th people on a list of the population. If the community is set up in a random order, this can replicate the benefits of simple random sampling.
Why is sampling a systematic process?Biased sample sizes and subpar survey results are reduced by systematic sampling. If there is a low chance that data will be manipulated: Data validity may be compromised if researchers rearrange a data set. The best strategy for surveys when there is little likelihood of data manipulation is systematic sampling.
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Which of the following is NOT a value in the 5-number summary? Choose the correct answer below. O Mean O Median O Minimum
Mean is NOT a value in the 5-number summary among the given options..
What is 5-number summary?In descriptive studies or during the first exploration of a big data set, a five-number summary is very helpful. The maximum and lowest values, the median, the lower and upper quartiles, and the most extreme values in the data set make up a summary.
Comparisons may be made between five summaries of numbers. We shall see that two sets with comparable means and standard deviations may have summaries of five numbers that are substantially different. A normal probability plot, often known as a box and whiskers graph, can be used to quickly compare two five-number summaries.
5-number summary consists of : Min, Q₁, Median, Q₃, and Max
Thus, mean is not a value in the 5-number summary
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The complete question is as follows:
How do you find the domain and range of a linear line?
A graph when plotted, we get a straight line and it is called linear graph. Linear graph is a graph of linear function.
Domain refers to all the possible input values, it is the values in the x-axis of the graph. A range means all the output values, when each domain is used in a function. It is the y-axis values.
To determine the domain identify all the X- coordinates in the linear function graph. To determine the range, identify all Y-coordinates in the functions graph. The domain and range are usually represented as a set of values.
If the domain have values from 0-6, it is represented as {0<x<4}
If the range is values between -1 to 10, then it is represented as {-1<x<10}.
Lets consider the linear function y= 3x, the domain is between 0 and 10, and range above are,
Function y= 3x
Domain 0 1 2 3 4 5 6 7 8 9 10
Range 0 3 6 9 12 15 18 21 24 27 30
So domain is the X-coordinates, and range the Y-coordinates.
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