The given functions f(x) = 3x + 6 and g(x) = (x+5)/3 are not inverses of each other, as their compositions of functions are not equal.
When we want to check if two functions are inverses of each other, we need to verify if composing the functions in both orders results in the input variable. In other words, we need to check if (f ∘ g)(x) = x and (g ∘ f)(x) = x, where f and g are the two functions.
For this problem, we have two functions:
f(x) = 3x + 6
g(x) = (x + 5)/3
Let's start by computing (f ∘ g)(x):
(f ∘ g)(x) = f(g(x)) = f((x + 5)/3) = 3((x + 5)/3) + 6
We can simplify this by canceling the 3's:
(f ∘ g)(x) = x + 5 + 6 = x + 11
Now let's compute (g ∘ f)(x):
(g ∘ f)(x) = g(f(x)) = g(3x + 6) = ((3x + 6) + 5)/3
Again, we can simplify this by canceling the 3's:
(g ∘ f)(x) = (3x + 11)/3
We can see that neither (f ∘ g)(x) nor (g ∘ f)(x) is equal to x, so we can conclude that the functions f(x) = 3x + 6 and g(x) = (x + 5)/3 are not inverses of each other.
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Can someone help me with this question i dont get it
Answer:
Step-by-step explanation:
The equation connects m and n.
Suppose n=1,
m=3/1=3.
If n=2,
m=3/2=1.5
If n=3,
m=3/3=1. This shows that as n increases, m decreases.
If m was equal to 1,
1=3/n
Thus n=3.
If m=2,
2=3/n
n=1.5
If m=3,
3=3/n
n=1.
This also shows that as m increases, n decreases.
Hope this helps :)
Answer:
When I increased n, m decreased.
When I increase m, n decreases
Step-by-step explanation:
Let's say that m is one and n is 3
1 = [tex]\frac{3}{3}[/tex] Us this as our base to compare increasing m and n.
Increase n to 6
[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]
When I increased n, m decreased.
Increase m to 3
3 = [tex]\frac{3}{1}[/tex]
When I increase m, n decreases
1. The distance d through which a stone falls from rest is proportional
to the square of the time taken t. If the stone falls 45 m in 3 seconds,
how far will it fall in 6 seconds? How long will it take to fall 20 m?
Answer:
In 6 seconds: 180 m
20 m: in 2 seconds
Step-by-step explanation:
y = distance
x = time
y is proportional to x:
y = kx
y is proportional to the square of x:
y = kx²
We are given: (3, 45)
45 = k × 3²
45 = 9k
k = 5
The equation is:
y = 5x²
When x = 6,
y = 5(6²)
y = 180
180 m in 6 seconds
When y = 20,
20 = 5x²
x² = 4
x = 2
2 seconds for 20 m
The three sides of a triangular fence have lengths 2x + 3, y − 6, and 4x − 3. What is the total perimeter?
2x + y − 6 feet
6x + y feet
6x + y + 6 feet
6x + y − 6 feet
A triangular fence having dimensions 2x + 3, y − 6, and 4x − 3, has a perimeter of Option D: 6x + y - 6 feet.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
A triangular fence has measurements -
a = (2x + 3) feet
b = (y - 6) feet
c = (4x - 3) feet
The formula for perimeter of a triangle is -
Perimeter = sum of all three sides
So the equation will be -
Perimeter = a + b + c
Substitute the values in the equation -
Perimeter = (2x + 3) + (y - 6) + (4x - 3)
Perimeter = 2x + 3 + y - 6 + 4x - 3
Perimeter = 6x + y - 6
Therefore, the value for perimeter is 6x + y - 6 feet.
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Once a month, the cafeteria has each student pick a card from a standard deck of cards. Students who pick an ace get a free lunch. Last month 26 of the 280 students won a free lunch. As a percent to the nearest tenth, what is the experimental probability of winning?
Last month 26 of the 280 students won a free lunch. The experimental probability of winning will be 13/140
Probability is the occurence of the events. Some of the events cannot be predicted with certainty. Probability of any event can be defined as P(A) , and there are many types of probability density functions.
Once a month, the cafeteria has each student pick a card from a standard deck of cards. From the deck of cards, each student has to pick a card for every one month.
Students who pick an ace get a free lunch
Given that,
Last month 26 of the 280 students won a free lunch and the percentage of winning is near to 9.2% approximately and it is very near to the 10%.
The experimental probability of winning is the ratio of number of possible outcomes to the total number of outcomes.
So, the experimental probability of winning is 26/280 = 13/140
Therefore, the experimental probability of winning is 13/140
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A wholesaler sells 1 kg of green tea leaves for $8 and 600 g of assam black tea leaves for $7.20. A tea merchant wants to mix these two types of tea leaves to form 100 kg of classic blend. Determine the amount of each type of tea leaves he should order from the wholesaler such that his cost price is $10/kg.
Answer:
50 kg of green tea leaves and 50 kg of assam black tea leaves.
Step-by-step explanation:
Let x kg be the amount of green tea and y kg be the amount of Assam tea.
x+y=100 (1) [mass]
price for 1 kg of assam tea= 7.20/600×1000g
= $12/kg
total cost= 100×10
= $1000
8x+12y= 1000 (2) [cost]
(1)×8: 8x+8y= 800 (3)
(2)-(3): (8x+12y)-(8x+8y)= 1000-800
4y= 200
y= 50 (4)
sub (4) into (1):
x+50= 100
x= 50
Heeeeeloepepepelelelelelelelelelloeoepeoepwp
Answer:
C) E = 118°; T = 118°
-----------------------------------
The given figure is a kite since it has two pairs of congruent sides as marked.
Its one pair of opposite angles are congruent. That is:
∠E ≅ ∠TSum of all interior angles of a quadrilateral is 360°:
m∠W + m∠E + m∠S + m∠T = 36029 + x + 95 + x = 3602x + 124 = 3602x = 360 - 1242x = 236x = 118Both the missing angles are 118°.
one card is randomly selected from a standard deck of 52 cards. what is the probability of randomly selecting a(n) jack or 4? enter your answer as a reduced fraction.
the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.
In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.
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Group 4: A drive in movie charges $15 per car, plus $2 per person as an
admission fee. The total charged for a car with x people is m(x) = 2x + 15.
How will the graph of this function change if the per car charge is changed
to $20 per car?
O
The line will shift vertically down by $5.
O The line will shift vertically up by $5.
O The line will shift horizontally left by $5.
O The line will shift horizontally right by $5.
Answer:
The graph of the function will shift vertically up by $5.
Step-by-step explanation:
The original function is m(x) = 2x + 15, where x is the number of people in the car. If the per car charge is changed to $20 per car, the new function becomes m(x) = 2x + 20, because the charge per car has increased by $5.
This means that the y-intercept of the new function is 20 instead of 15, which represents the minimum cost for a car, regardless of the number of people inside. So the graph of the new function will be shifted vertically up by $5 from the graph of the original function.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase
The formula to calculate the new value after an increase is to multiply the original value by the percentage of the increase.
The formula to calculate the new value after an increase is to multiply the original value by the percent of the increase. For example, if the original value is $100 and the increase is 10%, the new value would be $100 x 1.10 = $110. This formula can be applied to any original value and any percentage increase. It is useful for calculating the new value after applying a percentage increase, such as when calculating a pay raise or the cost of goods after a price increase. The formula can also be applied to calculate the new value after a percentage decrease, by multiplying the original value by 1 minus the percentage of the decrease.
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The complete question is
the formula for calculating the value after an increase by multiplying the original value by the percent for a new value is: value after increase by multiplying the original value by the percent for a new value?
Julieta is using the dot plots to compare two sets of data. Both plots use the same number line. What is the difference between the mean of each data set?
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Suppose that a motorboat is moving at ​ft/s when its motor suddenly​ quits, and that s later the boat has slowed to ​ft/s. assume that the resistance it encounters while coasting is proportional to its​ velocity, so that ​dv/dtkv. How far will the boat coast in​ all?
the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.
To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:
dv/dt = -k*v
where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.
We can solve this differential equation to obtain the velocity of the boat as a function of time:
v(t) = v(0) * e^(-k*t)
where "v(0)" is the initial velocity of the boat (40 ft/sec).
Using the given information, we can set up two equations:
v(10) = 20 (velocity after 10 sec)
v(0) = 40 (initial velocity)
Plugging these values into the equation, we get:
20 = 40 * e^(-10k)
Solving for "k", we get:
k = ln(2)/10
Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:
d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]
Plugging in the values, we get:
d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft
To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.
Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.
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Complete question is:
Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?
a millworker measures the width of a plank. the width is . what is the width in meters? write your answer as a decimal.
If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58
The width of the plank in decimeter = 15.8 dm
Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit
We have to find the width of the plank in meter
We know that,
1 decimeter = 0.1 meter
Convert the given decimeter to meter
15.8 decimeter = 15.8 × 0.1
Multiply the numbers
= 1.58 meters
Therefore, the width of the plank in meter is 1.58
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The given question in incomplete, the complete question is :
A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?
Daniel is working two summer jobs, making $8 per hour babysitting and making $15 per hour lifeguarding. In a given week, he can work a maximum of 18 total hours and must earn no less than $200. If Daniel worked 3 hours babysitting, determine the minimum number of whole hours lifeguarding that he must work to meet his requirements
The minimum number of hours life guarding that Daniel must work to meet his requirements = 12 hours
To the nearest whole number approximately:
If the digit following the decimal is less than 5, only the number preceding the decimal should remain unchanged.
Add one to the number before the decimal and eliminate the decimal part if the digit following the decimal is five or greater.
Given the information,
Babysitting pays Daniel $8 per hour, and life guarding pays him $15 per hour.
Daniel can only work a total of 18 hours per week and must make at least $200.
Daniel has been babysitting for three hours.
Daniel thus makes 3 x 8 = 24 dollars.
He has earned $200 - 24 = 176 dollars from the original $200.
Let's say Daniel was a lifeguard for m hours.
He therefore made m x 15 = 176.
15 × m = 176
m = 11.73
m ≈ 12 hours
So, the minimum number of whole hours = 12
This means, Daniel must work 12 hours lifeguarding to meet his requirements.
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Dani leaves her house at 08 00 she drives 63 miles to work she drives at an average speed of 27 miles per hour at what time does dani arrive at work
10:40 am
63 mile distance and 27 mph. starting from 8 am
63/27 => 2 (2/3) hours. 2/3 of an hour is also, 40 minutes.
so 8 am plus 2 hours and 40 minutes means 10:40 am
a Find: i the number of games played Goals 0 1 2 3 4 5 6 7 8
Frequency 6 11 5 11 4 0 2 0 1
ii the mode iii the median
iv the mean number of goals.
b Maha asked: ‘What is the average number of goals?’
Which would be the best average to use to answer this question? Give a reason for your answer.
1) The mean of the data is 4.45.
2) The mode of the data is 11.
3) The median of the data is 4.
What are the mean, mode, and median?The mean of the data is the ratio of the sum of the given data and the number of the count of the data.
The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.
Given data is 6 11 5 11 4 0 2 0 1.
The mean of the data is,
Mean = ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9
Mena = 4.45
Mode = 11
Median:- 0,0,1,2,4,5,6,11,11
Median = 4
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please help with this
Answer: the initial points is 30.
and per pair of shoes is 15.
Step-by-step explanation:
plssss helppppp
Factor the polynomial.
x³+3x²-x-3
Answer:
(x-1)(x+1)(x+3)
Step-by-step explanation:
[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]
the probability of successfully landing a plane using a flight simulator is given as 0.80. nine randomly and independently chosen student pilots are asked to try to fly the plane using the simulator. (a) what is the probability that all the student pilots successfully land the plane using the simulator? (b) what is the probability that none of the student pilots successfully lands the plane using the simulator? (c) what is the probability that exactly eight of the student pilots successfully land the plane using the simulator?
(a) The probability that all the student pilots successfully land the plane using the simulator is 43%
(b) The probability that none of the student pilots successfully lands the plane using the simulator is 0.0026%
(c) The probability that exactly eight of the student pilots successfully land the plane using the simulator is 30.1%
Probability is a measure of the likelihood of an event occurring.
(a) What is the probability that all the student pilots successfully land the plane using the simulator?
Probability of all pilots successfully landing
=> 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = 0.43 or 43%
So, the probability that all the student pilots successfully land the plane using the simulator is 0.43 or 43%.
(b) What is the probability that none of the student pilots successfully land the plane using the simulator?
The probability of each pilot failing to land the plane is 0.20. We can use the multiplication rule again to calculate the probability of none of the pilots successfully landing the plane.
Probability of all pilots failing to land = 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 = 0.000026 or 0.0026%
So, the probability that none of the student pilots successfully land the plane using the simulator is 0.0026% or 0.000026.
(c) What is the probability that exactly eight of the student pilots successfully land the plane using the simulator?
where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success in one trial, and nCk is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.
In this case, we have n=9, k=8, p=0.80, and (1-p)=0.20. So, the probability of exactly eight pilots successfully landing the plane is:
P(X=8) = 9C8 * 0.80^8 * 0.20^(9-8) = 0.301 or 30.1%
So, the probability that exactly eight of the student pilots successfully land the plane using the simulator is 0.301 or 30.1%.
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Need help fast!
Whats rhe radical aproximation of
7.07
7.21
7.93
Answer:
The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:
2.65
2.68
2.82
Step-by-step explanation:
Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:
Start by finding an approximate square root by making an educated guess or by using a calculator.
Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.
Refine the estimate by averaging the guess and the number divided by the guess.
Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.
Here's an example for 7.07:
An educated guess for the square root of 7.07 could be 2.7
Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.
To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.
Repeat steps 2 and 3 until the desired level of accuracy is achieved.
After several iterations, the square root of 7.07 is approximately equal to 2.65.
Similarly, you can find the approximate square roots of 7.21 and 7.93.
for the histogram on the right determine whether the mean is greater​ than, less​ than, or approximately equal to the median. justify your answer.
The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.
The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.
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If 10,000 is deposited into a savings account that pays 2. 3% annual interest, how much more would the
The account would contain 10,230.00 after 1 year.the amount in the account after 1 year, we can use the formula: [tex]P (1 + r/n)^nt[/tex]
To find the amount in the account after 1 year, we can use the formula:[tex]P (1 + r/n)^nt[/tex]
Where,
P = Principal Amount
r = Rate of Interest
n = Number of times the interest is compounded per year
t = Time in years
For this question,
P = 10,000
r = 2.3%
n = 1
t = 1
Therefore,
[tex]10,000 (1 + 0.023/1)^1*1\\10,000 (1.023)^1[/tex]
10,000 x 1.023
= 10,230.00
The complete question is:
If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account contain after 1 year?
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Can someone please help me with this aleks
The measure of <E= 60, <F= 95 and <G= 25 degree.
What is similarity?In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.
Given:
The two triangles are similar.
In triangle JKL using Angle Sum Property
<J + <K + <L = 180
95 + 60 + <K = 180
155 + <K = 180
<K = 180- 155
<K = 25 degree
Thus, the measure <E= 60
and, the measure <F= 95
and, the measure of <G= 25.
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write an expression for a triangle where side 1 is an unknown length . side 2 is twice side 1 and side 3 is 4 centimeters longer than side 1 .
Answer:
Let's call the length of side 1 "x". Then, the length of side 2 is 2x, and the length of side 3 is x + 4. So, the expression for the three sides of the triangle can be represented as:
x + 2x + (x + 4) = 3x + 4
This expression represents the sum of the lengths of all three sides of the triangle.
Step-by-step explanation:
Answer: x+2x+(4+x)
Step-by-step explanation:
since side one is unknown, we can substitute it with variable x, and side two is twice as much as side one so we do 2x, and side three is four cm longer than side one so we do 4+x at the end
write the equation for the given graphs. How do we find the "a" value?
The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11
How to determine the equations of the graphsFrom the question, we have the following parameters that can be used in our computation:
The graphs
The lines are absolute function graphs, and they can be represented as
y = a|x - h| + k
Where
Vertex = (h, k)
For the blue line, we have
(h, k) = (2, -5) and (x, y) = (0, -4)
So, we have
-4 = a|0 - 2| - 5
2a = 1
a = 1/2
So, the equation is y = 1/2|x - 2| + 5
For the red line, we have
(h, k) = (-2, 3) and (x, y) = (0, -11)
So, we have
-11 = a|0 + 2| + 3
2a = -14
a = -7
So, the equation is y = -7|x + 2| - 11
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Todd and Amani started savings accounts. Todd started with
$10 and deposits $4 each week. Amani started with $10 and
makes two $2 deposits each week. Complete the table. Will
Todd and Amani ever have the same amount in their
accounts? Why or why not? Write an equation to represen-
the total amount in each of their accounts at any
given time.
a) Since Todd and Amani started with the same initial deposit, they will never have the same amount in their accounts if they keep to their weekly savings plans because Todd's weekly savings are two times that of Amani.
b) An equation to represent the total amount in each of their accounts at any given time or weeks is as follows:
Todd, t = 10 + 4wAmani, a = 10 + 2w.What is an equation?An equation is a statement of equality or equivalence of two or more mathematical expressions.
Mathematical expressions combine values, variables, and numbers or constants without the equation symbol (=), which differentiates them from equations.
Todd Amani
Initial deposit in account $10 $10
Weekly deposits $4 $2
Let the number of weeks of deposits = w
Let the total deposit in Todd's account in w weeks = t
t = 10 + 4w
Let the total deposit in Amani's account in w weeks = a
a = 10 + 2w
For Todd's and Amani's account to be equal, 10 + 4w = 10 + 2w
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A store charges a restocking fee for any returned item based upon the item price. An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. If you return an item that has an original price of $180, how much is the restocking fee?
An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.
To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:
$200/$12 = $150/$9
We can simplify this proportion by dividing both sides by 3:
$200/$4 = $150/$3
Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:
$200 x $3 = $150 x $4
$600 = $600
This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.
In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.
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what's the slope on the coordinate plane
Answer: -1/3
Step-by-step explanation:
Slope = Rise/Run
Points: 0 of 1
A student wants to simulate 28 birthdays, but she does not have a calculator or software program available, so she makes up 28 numbers between 1 and 365
it okay to conduct the simulation this way? Why or why not?
Choose the correct answer below.
OA. Yes. People are capable of randomly making up numbers between two values.
OB. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
OC. No. Simulations must be performed with either a calculator or a statistical program.
OD. Yes. People are better at picking birth dates than computers, since they can base the numbers on the birth dates of people they know.
Save
From the given choices, we get:
No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
The correct option is D.
What is simulation?A computer experiment in which you can select a random sample from the given probability distributions is called a simulation.
Given:
A student wants to simulate 28 birthdays,
but she does not have a calculator or software program available,
so she makes up 28 numbers between 1 and 365.
By comparing with the definition:
From the given choices, we get,
D. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
Hence, D is the correct option.
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If 65% of a number is 208 and 15% ofthe same number is 48, find 80% of that number.
Answer:
256
Step-by-step explanation:
65% is 208
15% is 48
15% + 65% is 80%
So, just add 48 and 208 together:
48 + 208 = 256
Therefore, 80% of that number is 256.
Answer:
256
Step-by-step explanation:
We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.
a garden is in the shape of a rectangle with a perimeter of 18 meters. the length is 3 meters more than twice the width. find the length of the garden
The length of the garden which is in the shape of a rectangle with a perimeter of 18 meters and whose length is 3 meters more than twice the width, is 7 metres.
Let's name the width "w" and the length "l" of the rectangle.
We know from the problem description that the rectangle's perimeter is 18 metres, thus we can formulate an equation:
2l + 2w = 18
We also know that the length is 3 metres longer than the breadth, thus we can solve the following equation:
l = 2w + 3
We may plug the second equation into the first to remove the letter "l" and get an equation with only one variable:
2(2w + 3) + 2w = 18
When we simplify this equation, we get:
6w + 6 = 18
When we subtract 6 from both sides, we get:
6w = 12
When we divide both sides by 6, we get:
w = 2
We can use the second equation to get the length now that we know the width is 2 metres:
l = 2w + 3 = 2(2) + 3 = 7
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