The perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
In order to determine the perimeter and area of Felicia's playhouse, we must first analyze the provided diagram:
There are two rectangles and a triangle, therefore we must calculate the area of each shape, and then add the areas together to get the total area.
Area of Rectangle A = lw = 8ft x 10ft = 80ft²
Area of Rectangle B = lw = 4ft x 10ft = 40ft²
Area of Triangle C = (1/2)bh = (1/2)(8ft)(6ft) = 24ft²
Total Area = Area of Rectangle A + Area of Rectangle B + Area of Triangle C = 80ft² + 40ft² + 24ft² = 144ft²
To determine the perimeter, we must add up the lengths of all four sides of the rectangle and the three sides of the triangle.
P = 2l + 2w + a + b + c
P = 2(10ft) + 2(8ft) + 6ft + 10ft + 8ft
P = 20ft + 16ft + 6ft + 10ft + 8ft
P = 60ft
Therefore, the perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
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Question
Felicia created a floor plan for a playhouse, as shown below. 2 ft 23 ft 7 ft 8 ft 844 What will be the perimeter and area of Felicia's playhouse?
Can you show your work as well please and thank you!!!
Answer:
[tex]69.85in^2[/tex]
Step-by-step explanation:
To work out an area of a sector, the general formula is [tex]\pi r^2\times\frac{\theta}{360}[/tex] where theta [tex](\theta)[/tex] is the angle.
To work out the total angle of the shaded area:
[tex]360 - (143\times 2)\\= 360 - 286\\= 74[/tex]
Now we know the angle, we work out the area (To nearest hundredth, 2d.p.):
[tex]\pi\times(10.4in)^2\times\frac{74}{360}\\ = 69.85 in^2[/tex]
Hope this helps!!!
Find the y - intercept of the quadratic function f ( x ) = (x - 2.5)^2 + 0.25.
a. ( 0, 6.5 )
b. (0, - 0.25 )
c. (0, 0.25)
d. ( 0, - 6 )
( it is not c, i tried and got it wrong.)
to get the y-intercept we simply set x = 0 and solve for "y", knowing that the x-coordinate will be, well, 0.
[tex]f(x)=(x-2.5)^2+0.25\implies f(0)=(\stackrel{ x }{0}-2.5)^2+0.25 \\\\\\ f(0)=(-2.5)^2 + 0.25\implies f(0)=6.25+0.25\implies f(0)=6.5~\hfill \boxed{(0~~,~~6.5)}[/tex]
Suppose f(x) is continuous on [4,8] and −4≤f′(x)≤3 for all x in (4,8). Use the Mean Value Theorem to estimate f(8)−f(4).
The difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.
The Mean Value Theorem is a fundamental result in calculus that relates the average rate of change of a function over an interval to its instantaneous rate of change at some point within the interval. It states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists some c in (a,b) such that:
f'(c) = [f(b) - f(a)] / (b - a)
In this problem, we are given that f(x) is continuous on [4,8] and differentiable on (4,8), and we are asked to estimate f(8) - f(4) using the Mean Value Theorem.
To do this, we first apply the Mean Value Theorem to obtain an expression for f(8) - f(4) in terms of f'(c) for some c in (4,8):
f'(c) = [f(8) - f(4)] / (8 - 4)
Rearranging, we get:
f(8) - f(4) = f'(c) [tex]\times[/tex] 4
So we need to find an estimate for f'(c) to find an estimate for f(8) - f(4).
We are given that −4≤f′(x)≤3 for all x in (4,8), which means that f'(x) lies between -4 and 3 for all x in (4,8). Since c is also in (4,8), it follows that f'(c) is also between -4 and 3. Therefore, we can say that:
-4 ≤ f'(c) ≤ 3
Substituting this inequality into our expression for f(8) - f(4), we get:
-4 * 4 ≤ f(8) - f(4) ≤ 3 [tex]\times[/tex] 4
Simplifying, we get:
-16 ≤ f(8) - f(4) ≤ 12
This means that the difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.
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What transformation has changed the parent function f(x) = log2x to its new
appearance shown in the graph?
f(x + 3)
After answering the provided question, we can conclude that the graph of function f(x + 3) is identical to the graph of f(x), but 3 units to the left.
what is function?In mathematics, a function seems to be a link between two sets of numbers in which each individual of the first set (known as the realm) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form wherein every value of x generates a unique value of y.
The transformation that altered the parent function f(x) = log2x to its new look displayed in the graph is a three-unit horizontal shift to the left, represented by the function f(x + 3).
In other words, the graph of f(x + 3) is identical to the graph of f(x), but 3 units to the left.
In the graph, we can see that the entire curve has been moved three units to the left. The point (1, 0) on the original graph, for example, would now be situated at (-2, 0) on the modified graph. Thus, the original graph's point (8, 3) would now be situated at (5, 3) on the converted graph.
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help me my homeworks due soon
Answer:
Median is 9
mode is 10
range4:
4,8,10,14,14,23,65
2) 23, 16, 4, 10, 16, 65, 8
Mean_205 Median_23 Mode 1 Range
Answer:
For the second set of numbers, 23, 16, 4, 10, 16, 65, 8:
Mean: To find the mean, we add up all the numbers and divide by the total number of numbers:
(23 + 16 + 4 + 10 + 16 + 65 + 8) / 7 = 142 / 7 = 20.2857 (rounded to 4 decimal places)
Median: To find the median, we need to first arrange the numbers in order from smallest to largest:
4, 8, 10, 16, 16, 23, 65
There are an odd number of numbers (7), so the median is the middle number, which is 16.
Mode: The mode is the number that appears most frequently in the set. In this case, 16 appears twice, which is more than any other number, so the mode is 16.
Range: To find the range, we subtract the smallest number from the largest number:
65 - 4 = 61
So the mean is 20.2857, the median is 16, the mode is 16, and the range is 61.
Hope This Helps!
Solve the following equations: 3(y – 2) = 2(y – 1) – 3
Answer:
3(y-2)=2(y-1)-3
or, 3y-6 =2y-2-3
or, 3y-6 =2y-5
or 3y-2y =6-5
or y=1
hence, the value of y is 1
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trying to make a box without a top out of a square piece of cardboard by cutting off the corners and folding up the sides. your box must have a height of 3 cm and have a square base. how long do the sides of the piece of cardboard, x, have to be in order for the volume of the box to equal 48 cm3?
The sides of the piece of cardboard have to be 10 cm long in order for the volume of the box to equal 48 cm³
Let us assume that the dimension of the square piece of cardboard = m × m
If we cut a 3 cm square out of each corner, then each side of the square base will be (m - 6) cm.
The height of the box, when folded, will be 3 cm.
The volume of the box is:
V= (height) × (width) × (length)
V = 3 (m - 6) (m - 6)
V = 48 cm³
3(m² - 12m + 36) = 48
m² - 12m + 36 = 16
m² - 12m + 36 - 16 = 0
m² - 12m + 20 = 0
m² - 10m - 2m + 20 = 0
m(m - 10) - 2(m - 10) = 0
(m - 10)(m - 2) = 0
m = 10 OR m = 2
when m = 2, (m - 6) = -4 which is not possible.
So, the dimensions of the base of the box = 10 × 10
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Directions: The following is an axiomatic system. Answer each question as required. Axiom Set: Axiom 1: Each line is a set of three points Axiom 2: Each point is contained by two lines. Axiom 3: Two distinct lines intersect at exactly one point. Question: 1. What are the undefined terms in this axiom set? 2. Is the axiomatic system consistent? Why? Why not? State what specific property is the given axiomatic system.
Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It includes the study of points, lines, angles, curves, surfaces, and solids, and the relationships between them.
What is Euclidean geometry?Euclidean geometry is a type of geometry that is based on the work of the ancient Greek mathematician Euclid. It is a branch of mathematics that deals with the properties and relationships of points, lines, angles, and planes in two and three-dimensional space.
In the given question
The undefined terms in this axiom set are "line," "point," and "intersect."The axiomatic system is consistent. To see why, we can use the properties of the axioms to reason about the properties of the system. From Axiom 1, we know that every line is a set of three points, and from Axiom 2, we know that every point is contained by two lines. This means that every point is shared by exactly two lines. If we assume that two lines intersect at two distinct points, then those two points must belong to four distinct lines. But this contradicts Axiom 2, which states that each point is contained by exactly two lines. Therefore, two lines must intersect at exactly one point, which is stated in Axiom 3. Thus, the axioms are self-consistent and do not lead to any contradictions.The specific property of the given axiomatic system is the Euclidean geometry of two-dimensional space. The system specifies the basic properties of points and lines in this geometry, including how they intersect, and serves as a foundation for further geometric reasoning and deduction.
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Audrey has $440 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $259.52.
She buys 2 bicycle reflectors for $3.07 each and a pair of bike gloves for $29.12.
She plans to spend some or all of the money she has left to buy new biking outfits for $72.61 each.
Write and solve an inequality which can be used to determine oo, the number of outfits Audrey can purchase while staying within her budget.
The inequality is 76.26 - 72.61x ≥ 0 and the value of x is x ≤ 1.05. Audrey can purchase at most 1 biking outfit while staying within her budget.
What is inequality?A mathematical statement called an inequality compares two values, frequently by employing symbols. When there is an inequality, one value is either bigger than or less than the other, not necessarily equal to it. For instance, the inequality x > 5 asserts that x is bigger than, but not necessarily the same as, 5. Relationships between different numbers, such as the sum of money spent on shopping and the sum of money left in a budget, are sometimes described as having inequalities.
Let us suppose the number of outfits = x.
Given that, the total amount Audrey has is $440.
Now, the inequality can be written as:
40 - 259.52 - 2(3.07) - 29.12 - 72.61x ≥ 0
76.26 - 72.61x ≥ 0
-72.61x ≥ -76.26
x ≤ 1.05
Hence, Audrey can purchase at most 1 biking outfit while staying within her budget.
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Which of the following conditions could be used to prove both a||b and c||d?
In other words, if a vector v exists such that an is parallel to v, b is parallel expression to v, c is parallel to v, and d is parallel to v, we may conclude that both a||b and c||d exist.
What is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity
We need a condition that assures that an is parallel to b and c is parallel to d to verify both a||b and c||d.
If a and b are both parallel to the same vector, and c and d are both parallel to the same vector, this is one such condition.
In other words, if a vector v exists such that an is parallel to v, b is parallel to v, c is parallel to v, and d is parallel to v, we may conclude that both a||b and c||d exist.
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El año pasado, Hong abrió una cuenta de inversiones con $6600. Al final del año la cantidad en la cuenta había aumentado en dólares? ¿Cuánto dinero había en su cuenta al final del año?
Hong opened a money investment account with $6600, which increased by 7.5% by the end of the year. The final amount in the account was $7095.
Hong opened an money investment account with $6600. At the end of the year, the amount in the account had increased by 7.5%. To solve the problem, we can start by calculating the amount of the increase in Hong's account:
Increase = $6600 x 7.5% = $495
Then, we can add the increase to the initial amount to find the final amount:
Final amount = $6600 + $495 = $7095
Therefore, there was $7095 in Hong's account at the end of the year.
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I don't understand this please help :)
Which triangle congruence theorem can be used to prove the triangles are congruent?
a. SSS
b. SAS
c. AAS
d. ASA
Answer:
a. SSS
Step-by-step explanation:
Answer:
Step-by-step explanation:
qacfascffaafa
Give me a good explanation of how the "Brainliest users" daily rankings work pls. Do points from challenges count? What else counts for the ranking?
Answer:
Step-by-step explanation:
pretty hard to explain but if you do a bunch of questions and answer them correctly then you'll get points. Yes the points from challenges count, Nothing else counts for the ranking.
Quadrilateral JKLM is an isosceles trapezoid. Write each length or angle measure.
The measure of angles JKL, KJM and KRL are -51°, 105° and 51° respectively and the length of diagonal JL is 81 units.
What is a isosceles trapezoid?An isosceles trapezoid is a four-sided polygon with two opposite sides parallel and two other sides of equal length.
In Quadrilateral JKLM,
KR = 42 and JR = 39,
R being the midpoint of diagonal.
Also, angle KMJ = 27° and KML = 78°.
The measure of angle JKL is equal to the difference of given angles KMJ and KML.
Therefore,
Angle JKL = KML-KMJ
= 78°- 27°
= 51°
The measure of angle KJM is equal to the sum of given angles KMJ and KML.
Therefore,
Angle KJM = KMJ + KML
= 27° + 78°
= 105°
The measure of angle KRL is equal to the difference of given angles KML and KMJ.
Therefore,
Angle KRL = KML - KMJ
= 78° - 27°
= 51°
The length of Diagonal JL is equal to the sum of lengths of given sides KR and JR.
Therefore,
Length of JL = KR + JR
= 42 + 39
= 81
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A snack mix recipe calls for 2 1 /5 cups of dip and 1 /2 cup of chips. Alex wants to make the same recipe using 1 cup of chips. How many cups of dip will Alex need?
Answer: 4 2/5
Step-by-step explanation:
1 divided by 2 is 1/2, so if 1/2 times 2 equals one cup, then all we have to do is times 2 1/5 by two. 2 x 2 is 4, and 1/5 times 2 is 2/5. Add them together, and you get 4 2/5. Alex will need 4 2/5 cups of dip.
20% of 24 kg please help with this
Answer:
4.8kg
Step-by-step explanation:
Answer:
Step-by-step explanation:
24 / 5 = 4.8.
20% of 24 kg is 4.8kg
The make African elephant at the city zoo has a mass of 5450 kg. What is its mass in scientific notation
The mass in scientific notation is [tex]5.45 * 10^3 kg[/tex], this means that the mass of the African elephant is 5.45 multiplied by 1000,
To write the mass of the African elephant in scientific notation, we need to express it as a number between 1 and 10, multiplied by a power of 10. To do this, we can start by moving the decimal point in 5450 kg to the left until we have a number between 1 and 10. This gives us 5.45 kg.
Next, we need to determine the power of 10 that we multiplied by to get this number. To do this, we count the number of places we moved the decimal point, which is three places to the left. Therefore, the mass of the African elephant in scientific notation is:
[tex]5.45 * 10^3 kg[/tex]
This means that the mass of the African elephant is 5.45 multiplied by 1000, which is the same as 5450 kg in standard notation. Writing the mass in scientific notation makes it easier to work with very large or small numbers, as it simplifies the representation of the number and makes it more manageable.
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Find the derivative f
0
m(x) of the following function with respect to x:
fm(x) = Xm
n=1
n
x
· x
n
!2
The derivative of [tex]fm(x) = Xm * x^n / (2^{(n+1)})[/tex] with respect to x is [tex]fm'(x) = (Xm-1)x^{n(n+1)}/2^{(n+1)}[/tex].
We can start by using the power rule of differentiation. Taking the derivative of Xm with respect to x gives mXm-1.
Next, we need to find the derivative of the series n=1 n x · x n !2, which involves using the product and chain rules.
First, we can rewrite the series as:
[tex]x(1!/2) * x^{2(2!/2)} *x^{3(3!/2)} * ... * x^n(n!/2)[/tex]
Taking the derivative of each term in the series with respect to x, we get:
[tex]1/2x^{(1-1)} * 1/2x^{(2-1)} * 2/2x^{(3-1)} * ... * n/2x^{(n-1)}[/tex]
Simplifying each term, we get:
[tex]1/2x^{(0)} * 1/2x * 1/x * ... * n/2x^{(n-1)}[/tex]
Combining all the terms, we get:
[tex](1/2 + 1/4 + 2/6 + ... + n/2n) * x^{(-1)}[/tex]
To simplify the series 1/2 + 1/4 + 2/6 + ... + n/2n, we can factor out 1/2 and simplify the remaining terms:
1/2(1/1 + 1/2 + 1/3 + ... + 1/n)
This is the harmonic series, which does not have a closed-form solution. However, we can approximate it using the integral test:
∫(1 to n) 1/x dx = ln(n)
So, the harmonic series can be approximated as ln(n), and the derivative of the series can be written as:
[tex](1/2 ln(x) ) * x^{(-1)}[/tex]
Putting it all together, we get the derivative of fm(x) as:
[tex]f0m(x) = mXm-1 *(1/2 ln(x)) * x^{(-1)}[/tex]
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A circle has a diameter of 42 inches. What is the circumference of the circle. Use 22/7 for pi.
Answer:
132 in.
Step-by-step explanation:
C = πd
C = 22/7 × 42 in.
C = 132 in.
There are 60,094 people under the age of 14 years old
There are 212,468 people age between 15 and 64 years old
There are 42,362 people over the age of 65 years old
What is the Age Dependency Ratio as a decimal rounded to the Thousandths place?
the mayor of a town has proposed a plan for the construction of an adjoining bridge. a political study took a sample of 800 800 voters in the town and found that 59% 59 % of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 54% 54 % . determine the p-value of the test statistic. round your answer to four decimal places.
The p-value of the test statistic is 0.0000 (rounded off to four decimal places).
The p-value of the test statistic can be calculated by subtracting the area under the normal curve from the test statistic to infinity in the direction of the alternative hypothesis.
We are given that a political study has been carried out, taking a sample of 800 voters in the town. The sample shows that 59% of the residents favored construction. A political strategist wants to test the claim that the percentage of residents who favor construction is over 54%.
The hypothesis can be defined as follows:
Null hypothesis (H0): p ≤ 0.54, where p is the proportion of residents who favor the construction of the bridge.
Alternative hypothesis (Ha): p > 0.54, where p is the proportion of residents who favor the construction of the bridge.
To calculate the test statistic, we use the formula given below:
z = (p - P) / √[P(1-P) / n]
Here, P = 0.54, n = 800, p = 0.59
Putting these values in the above formula, we get:
z = (0.59 - 0.54) / √[0.54(1-0.54) / 800] = 5.06
To determine the p-value of the test statistic, we need to calculate the area under the normal curve from 5.06 to infinity in the direction of the alternative hypothesis. As the alternative hypothesis is one-tailed, we use the standard normal distribution table to find the corresponding area under the curve. The area can be calculated as:
P(Z > 5.06) = 0.00000035 (using the standard normal distribution table)
Therefore, the p-value of the test statistic is 0.0000 (rounded to four decimal places).
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Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. a rating of 0 means "not at all important" and a rating of 10 means "very important." here is a dot plot of their responses. a dot plot for the "importance of reducing pollution" where the numbers 2 through 10 are indicated. the data for the dot plot are as follows: scale 2, 1 dot scale 3, 1 dot scale 4, 1 dot scale 5, 2 dots scale 6, 2 dots scale 7, 2 dots scale 8, 5 dots scale 9, 5 dots scale 10, 6 dots explain why a rating of 6 is not a good description of the center of this data set.
A rating of 6 is not a good description of the center of this data set because the data is skewed to the right, with more students rating the importance of reducing pollution as 7, 8, 9, or 10.
A rating of 6 is not a good description of the center of this data set because the dot plot is skewed to the right. There are more dots to the right of 6 than to the left, indicating that there are more students who rated the importance of reducing pollution as 7, 8, 9, or 10 than those who rated it as 2, 3, 4, 5, or 6.
The center of a data set is typically measured by its mean, median, or mode. In this case, the median would be a better measure of the center than the mean or mode because the dot plot is skewed. The median would be the middle value when the data set is ordered from smallest to largest.
If we order the data set from smallest to largest, we get
2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10
The median of this data set is 9, which is higher than 6. Therefore, a rating of 6 is not a good description of the center of this data set.
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The steps to solve equation 5x−6+7=153x are shown. Which statement about the solution is true?
Therefore, the statement that is true is: "The solution to the equation is x = 0.1."
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions. It is made up of two sides: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equal sign (=). An equation indicates that the two expressions on either side of the equal sign have the same value. Equations can take different forms, depending on the types of expressions involved and the operations used.
Here,
However, we can solve the equation ourselves to find the solution and then check the options.
5x − 6 + 7 = 15x (Given equation)
Simplifying the left-hand side of the equation, we get:
5x + 1 = 15x
Subtracting 5x from both sides, we get:
1 = 10x
Dividing both sides by 10, we get:
x = 1/10
Now we can check each option to see which statement is true:
x = 0.1: This is true, as 1/10 is equal to 0.1.
x = -0.1: This is false, as we found that x = 0.1, not x = -0.1.
x = 10: This is false, as we found that x = 0.1, not x = 10.
The equation has no solution: This is false, as we found a solution for x, namely x = 0.1.
The solution to the equation is x = 1: This is false, as we found that x = 0.1, not x = 1.
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Complete question:
The steps to solve equation 5x−6+7=15x are shown. Which statement about the solution is true?
x = 0.1
x = -0.1
x = 10
The equation has no solution
The solution to the equation is x = 1
Find X, Y geometry y x 45
In triangle, value of x and y are 10,10 .
What does a triangle in math mean?
Three edges and three vertices make up the three sides of a triangle, which is a three-sided polygon in geometry. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles.
Triangle's angle sum property is what this characteristic is known as. Three edges and three vertices make up a triangle, which is a polygon. It is one of the fundamental geometric shapes. The symbol represents a triangle with the vertices A, B, and C. triangle with equal sides.
In triangle ,
sin45° = y/10√2
1/√2 = y/10√2
10√2 = √2y
y = 10
tan45° = x/y
1 = x /10
x = 10
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What is the area of this figure?
6 in
6 in
5 in
9 in
11 in
2 in
Write your answer using decimals, if necessary.
square inches
3 in
9 in
Answer:
116in2
Step-by-step explanation:
Top Rectangle Shape: 2in x 3in = 6in2
Middle Rectangle Shape: (9in+3in) x (9in-2in) = 84in2
Far Left Rectangle Shape: (9in-2in-5in) x (6in) = 12in2
Bottom Triangle Shape: [6in - (9in-5in-2in] x [(9in+3in-11in)+6in] x 1/2 = 14in2
Total: 6in2 + 84in2 + 12in2 + 14in2 = 116in2
*Recommend dividing shape to avoid trapezoids
What's the domain and range of the exponential growth function?
A. Domain: All real numbers; Range: All real numbers
B. Domain: x > –2; Range: y > –2
C. Domain: x < –2; Range: All real numbers
D. Domain: All real numbers; Range: y > –2
The closest answer choice is A. Domain: All real numbers; Range: All real numbers.
What are the domain and range?
The domain of a function is the set of all possible input values (often represented by x) for which the function is defined. The range of a function is the set of all possible output values (often represented by y) that the function can produce, based on its input values. In other words, the domain is the set of all valid inputs, and the range is the set of all possible outputs.
The domain and range of an exponential growth function depend on the specific equation of the function.
However, in general, an exponential growth function has a domain of all real numbers and a range of y > 0.
This is because an exponential growth function always has a positive output, and it can take any positive input value.
Therefore, the closest answer choice is A. Domain: All real numbers; Range: All real numbers.
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Consider this system of linear equations.
-2x - 5y = 12
3x - 4y = 5
Graph the system, and then mark its solution
Answer:
(-1, -2)
Step-by-step explanation:
a b and c are positive intergers a:b = 3:8 and b:c= 6:11 work out the smallest possible value of a b and c
Answer:
We can use ratios to set up a system of equations and solve for a, b, and c. Since a:b = 3:8, we can write:
a = 3x
b = 8x
Similarly, since b:c = 6:11, we can write:
b = 6y
c = 11y
Now we have two expressions for b, so we can set them equal to each other and solve for y:
8x = 6y
y = 4x/3
Substituting y back into the expression for c, we get:
c = 11y = 44x/3
To find the smallest possible values of a, b, and c, we want to choose values of x that are as small as possible while still being positive integers. Since x must be a multiple of 3 (because a = 3x is a multiple of 3), let's try x = 3. Then we get:
a = 3x = 9
b = 8x = 24
c = 44x/3 = 44
So the smallest possible values of a, b, and c are 9, 24, and 44, respectively.
Step-by-step explanation: