The measurements in order of size, starting with the smallest are: 2.3 mm, 24 mm, 2.3 cm, 21 cm, and 0.2 m.
How to order sizes starting with the smallest?Given the measurements in the question;
2.3 cm, 24 mm, 0.2 m, 21 cm, 2.3 mm
To arrange the measurements in order of size, we need to convert them to a common unit of measurement.
We can convert all the measurements to meters, as it is the largest unit given.
Hence;
2.3 mm = 2.3 ÷ 1000 = 0.0023 m
24 mm = 24 ÷ 1000 = 0.024 m
21 cm = 21 ÷ 100 = 0.21 m
2.3 cm = 2.3 ÷ 100 = 0.023 m
0.2 m = 0.2 m
Now that all the measurements are in meters, we can compare them:
0.0023 m < 0.024 m < 0.023 m < 0.21 m < 0.2 m
Therefore, the measurements in order of size, starting with the smallest, are:
2.3 mm < 24 mm < 2.3 cm < 21 cm < 0.2 m
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How did the ticket sales for the spring play change? Complete the statement
Answer:
"The sales for the spring play (Increased) by (30) tickets"
Step-by-step explanation:
The opening night sales were 200, to 230 by closing night so it increased by 30.
I think of a number, treble it and take 6 from my answer. If the result is 18, find the number. My teacher says its 4 I say its eight whats the answer?
Answer: Let's work through the problem step by step:
"Treble it": If we call the unknown number "x", then "trebling" it means multiplying it by 3, so we have 3x.
"Take 6 from my answer": We subtract 6 from 3x, giving us 3x - 6.
"If the result is 18": We set 3x - 6 equal to 18 and solve for x.
So, we have:
3x - 6 = 18
Adding 6 to both sides:
3x = 24
Dividing both sides by 3:
x = 8
Therefore, the answer is 8.
Step-by-step explanation:
After how many years will the battery life of a cell phone be 2 hours? Rounds to the nearest tenth if necessary
To round to the nearest tenth, we can say that a cell phone's battery life is typically 2 hours after two years.
Generally speaking, the battery life of a cell phone will depend on the type of phone and usage habits. Most cell phones will last about 18-24 months before needing to be replaced.
The battery life of a cell phone is determined by a variety of factors, including battery capacity, phone usage habits, and battery age. We can, however, make certain assumptions and calculate how long it would take for a common mobile phone battery to decline to 2 hours of battery life.
Considering that a typical lithium-ion battery, which is often used in mobile phones, has a capacity of approximately 3,000 mAh when new and that its capacity drops by roughly 20% after 2-3 years of usage, we may estimate that the battery capacity would be around 2,400 mAh after 2-3 years.
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PLEASE HELP ME IM STRUGGLING AHHH
The total cost after tax to repair Deborah’s computer is represented by 0.08(73h) + 73h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of dollars Deborah has to pay in tax? Explain.
Answer:
0.073(73h)
Step-by-step explanation:
[tex]0.08(73h)+73h[/tex]
[tex]=\dfrac{73}{100}(73h)+73h[/tex]
[tex]=73\%(73h)+73h[/tex]
Since, it took 50h to repair the computer so, 0.073(73h) represents the amount of tax Deborah has to pay. Which is 73% of 73h.
WILL MARK BRAINLEIST!!!!
The last three problems in this set involve the Mean Value Theorem.
Let [a, b] = [0, 1] and let f(x) = x³. Find a number c = _______ such that
f(b) - f(a) = f'(c)(b − a).
Answer:
We have:
a = 0
b = 1
f(x) = x³
f'(x) = 3x²
Using the Mean Value Theorem, we have:
f(b) - f(a) = f'(c)(b - a)
Substituting the given values:
f(1) - f(0) = f'(c)(1 - 0)
Simplifying the left side of the equation:
1³ - 0³ = 1
Simplifying the right side of the equation:
f'(c) = 3c²
Therefore:
3c² = 1
Solving for c:
c² = 1/3
c = ±√(1/3)
Since c must be between 0 and 1, we have:
c = √(1/3)
Therefore, c = √(1/3).
I hope this helps!
What is 3 divided by the difference of 4 and a numb
er
The result of 3 divided by the difference of 4 and 2 is 1.5.
Formula:
3 / (4 - x)
Let's take the number x to be equal to 2.
Therefore, the calculation is 3 divided by the difference of 4 and 2, which is 3 / (4 - 2) or 3 / 2.
The answer is 1.5.
To explain further, when we divide the number 3 by the difference of 4 and 2, we are essentially dividing the number 3 by the result of subtracting 2 from 4. The result of subtracting 2 from 4 is 2. When we divide 3 by 2, the answer is 1.5.
Therefore, 3 divided by the difference of 4 and a number is equal to 1.5 when the number is equal to 2.
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Complete question:
What is 3 divided by the difference of 4 and a number?
Quadrilateral MNOP has vertices M(-2,4) N(-2,1) O(3,1) and P(3,4). what are the coordinates of the image of point P after a reflection across the X-axis??
After just a reflection along the [tex]X-axis[/tex], a quadrilateral [tex]MNOP[/tex] of position [tex]P[/tex] is [tex](3, -4)[/tex].
Describe the quadrilateral form.Four closed sides are making up a quadrilateral. Quadrilaterals are the following figures: Designed by Raphael. a four-sided figure. There is just one pair of parallel sides to the form, and there are no right angles.
With an example, define a quadrilateral.A closed form known as a quadrilateral is known to be have sides with various widths and lengths. It is a closed polygon in two dimensions with four vertices, four angles, and four sides. Some examples of a quadrilateral are a cohesion and coherence, parallelogram, rectangle, rhombus, square, and kite.
When a point is reflected across the [tex]X-axis[/tex], the [tex]X-[/tex]coordinate stays the same, but the [tex]Y-[/tex]coordinate is multiplied by [tex]-1[/tex].
So to find the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex], we keep the [tex]X-[/tex]coordinate of [tex]P[/tex] the same (which is 3) and multiply the [tex]Y-[/tex]coordinate by [tex]-1[/tex]
New [tex]Y-[/tex]coordinate of [tex]P = -1 * 4 = -4[/tex]
Therefore, the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex] is [tex](3, -4)[/tex].
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A global research study found that the majority of today's working women would prefer a better 'work-life balance' to an increased salary. One of the most important contributors to 'work-life balance' identified by the survey was 'flexibility' with 46% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 working women. (Round answers to four decimal places.) a) What is the probability that, in the sample, fewer than 50% say that having a flexible work schedule is either very important or extremely important to their career success? b) What is the probability that, in the sample, more than 43% say that having a flexible work schedule is either very important or extremely important to their career success?
z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192
a) The number of working women in the sample is 100. The majority of women prefer a better 'work-life balance' to a higher salary, according to a global research study. The majority in percentage is 50% or greater, which implies that 50% of 100 working women or more prefer a better work-life balance to an increased salary. If we assume that the null hypothesis is correct and the number of women who say having a flexible work schedule is important is exactly 50, the standard error for the sample can be calculated as follows:
σ = sqrt(p(1-p)/n)
σ = sqrt(0.50(1-0.50)/100)
σ = 0.05
P(x<50) can be calculated as follows:
z = (x - np) / σ
z = (50 - 100(0.50)) / 0.05
z = -20
P(z < -20) = 0
Therefore, the probability that fewer than 50% of the sample say that having a flexible work schedule is either very important or extremely important to their career success is 0.
b) The proportion of women who said having a flexible work schedule is very important or extremely important to their career success is more than 43%. That implies the number of women in the sample who say having a flexible work schedule is important is greater than 43.
P(x > 43) can be calculated as follows:
z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192
Therefore, the probability that more than 43% of the sample says having a flexible work schedule is very important or extremely important to their career success is 0.9192.
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i need a friend what is 234x 7364
Answer:
1,723,176
Step-by-step explanation:
By plugging this into a calculator, you will receive 1,723,176.
Answer: 234 x 7364 = 1,723,176
Problem 2 Suppose you observe a single realization of a binomial random variable,
X∼Bin(n,p), and you want to test the hypothesis H0 :p=0.5 against H1:p=0.8
. (a) Derive the likelihood ratio, assuming the realization of X equalsx. (b) Give a full description of the most powerful test between H0 and H1 at the significance level α=0.1. (c) Suppose n=20
and x=15. Does your test from part (b) at the significance level α=0.1 reject H0?
α = 0.1
Answer: (a) Suppose X ∼ Bin(n, p). The likelihood function isL(p) = [n!/x!(n − x)!] px (n−p)−x.Then, we get the likelihood ratio asLR = [L(p1)] / [L(p0)]=[p1^x * (1−p1)^(n−x)] / [p0^x * (1−p0)^(n−x)]Let X be a binomial random variable. We can write the likelihood function as L(p) = [nCx px(1−p)n−x] . (b) Most powerful test: To derive the most powerful test, we need to find the likelihood ratio as LR = (p1/p0)x(1−p1/1−p0)n−x. Accept H0 if LR < c and reject H0 if LR ≥ c for some constant c.LRc= (0.8/0.5)^15*(0.2/0.5)^5 / (0.8/0.5)^15*(0.2/0.5)^5= (8/5)^15 = 34.99We reject H0 if the LR ≥ 34.99. Accept H0 if the LR < 34.99. (c) Reject H0 if the LR ≥ 34.99.LR = (0.8/0.5)15*(0.2/0.5)5 = 20.96Since 20.96 < 34.99, we accept H0. Therefore, at α = 0.1, we do not reject H0.
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3x-2=7-6x
help pls???
Answer:
x=1
Step-by-step explanation:
3x-2=7-6x
3x-2 +2=7-6x +2
3x+6x=9-6x +6x
9x=9
x=1
Answer:
x = 1
Step-by-step explanation:
3x -2 = 7 -6x
9x - 2 = 7
9x = 9
x = 1
Let's check
3(1) -2 = 7 - 6(1)
3 - 2 = 7 - 6
1 = 1
So, x = 1 is the correct answer.
 find the difference between the perimeters of two circular planets if one has a radius of 16.8 CM and the other has a diameter of 16.8 CM 
Answer:
16.8π cm or 52.78 cm
Step-by-step explanation:
We are given the radius of one planet and the diameter of the other.
So, we have perimeter (circumference) of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
For the first planet with a radius of 16.8 cm, we can calculate its circumference as:
C1 = 2π(16.8) = 33.6π cm
For the second planet with a diameter of 16.8 cm, we can calculate its radius as half of the diameter:
r2 = d/2 = 16.8/2 = 8.4 cm
And then, we can calculate its circumference as:
C2 = 2π(8.4) = 16.8π cm
The difference between the perimeters of the two planets is:
C1 - C2 = (33.6π - 16.8π) cm
C1 - C2 = 16.8π cm
Therefore, the difference between the perimeters of the two planets is approximately 52.78cm, rounded to two decimal places.
A kite is graphed on a coordinate grid and then dilated by a scale factor of 4/3 with the center of dilation at (1, 1). Vertex A of the original kite is located at (6, 15) Write the ordered pair that represents the location of vertex A after the dilation.
The ordered pair that represents the location of vertex A after the dilation is (8, 20).
What is vertex?Vertex is a point in geometry that describes the location of a object in a two-dimensional or three-dimensional space. In two-dimensional space, it is a point where two lines, curves, or surfaces intersect. In three-dimensional space, it is the point where three planes intersect. In a graph, it is the point where two lines intersect.
Vertex A of the original kite is located at (6, 15).
The center of dilation is at (1, 1). To dilate the kite by a scale factor of 4/3, each point (x,y) of the kite must be multiplied by the scale factor, 4/3. In this case, vertex A will transform to (8, 20) after the dilation.
Therefore, the ordered pair that represents the location of vertex A after the dilation is (8, 20).
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irst, find the terms of the missing factor. 25 Now, write 125x-50y in factored form.
Answer:
25(5x - 2y)
Step-by-step explanation:
25 is the common factor for the equation. so the answer will be 25( 5x - 2y )
In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728?
A. 137,982
B. 142,398
C. 292,389
D. 392,097
In number 292,389 the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728.
What is a number?
A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations.
The value of a digit depends on its place value in a number. For example, the digit 3 in the number 143,728 has a value of 3 x 1,000 = 3,000 because it is in the thousands place.
Let's call the number we are looking for "x". We want to find a number where the value of the digit 3 is 10 times as great as the value of the digit 3 in 143,728.
The value of the digit 3 in x is 10 times the value of the digit 3 in 143,728, so we can set up the equation:
3 x place value of 3 in x = 10 x 3,000
Simplifying this equation, we get:
3 x place value of 3 in x = 30,000
Dividing both sides by 3, we get:
place value of 3 in x = 10,000
So the digit 3 in x must be in the ten thousands place. Now we can eliminate choices A and B, because they do not have a digit 3 in the ten thousands place.
Checking the remaining choices, we find that only choice C has a digit 3 in the ten thousands place, with a value of 3 x 10,000 = 30,000. Therefore, the answer is:
C. 292,389
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the sheet is a series of arcs of radius 10cm,each arc subtending 120° at it's centre. if there are 14 such arcs in one sheet, how wide would the sheet be if flattened out
The sheet would be approximately 93.13 cm wide if flattened out.
Describe Arc?The length of an arc is determined by the degree measure of the central angle that subtends the arc. For example, if a circle has a radius of 5 units and an arc has a central angle of 90 degrees, the length of the arc can be found using the formula:
arc length = (central angle / 360) x 2πr
where r is the radius of the circle. In this case, the length of the arc would be:
arc length = (90/360) x 2π(5) = 1.25π units
The length of each arc can be found using the formula:
length = (angle / 360) x 2πr
where angle is the central angle of the arc in degrees, r is the radius of the arc, and π is pi (approximately equal to 3.14).
In this case, the radius is 10 cm and the central angle is 120 degrees, so the length of each arc is:
length = (120/360) x 2π(10) = (1/3) x 20π = (20/3)π cm
There are 14 such arcs in one sheet, so the total length of the sheet when flattened out is:
total length = 14 x (20/3)π = (280/3)π cm
This is approximately equal to 93.13 cm if we use the approximation π ≈ 3.14.
Therefore, the sheet would be approximately 93.13 cm wide if flattened out.
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A softball coach has ordered softballs for two different leagues. The Junior League uses an 11-inch softball priced at $2.50 each. The Senior League uses a 12-inch softball priced at $3.50 each. The softball coach ordered a total of 120 softballs for $350.
The first step to solving a system of linear equations by substitution is to solve one of the equations for one of its variables. Solve the first equation in the system of equations that you selected above. Write the equation with an isolated variable as your response below.
The number of 11-inch softballs ordered is 70 and the number of 12-inch softballs ordered is 50.
How many of each size of softball was ordered?a + b = 120 equation 1
2.50a + 3.50b = 350 equation 2
Where:
a = number of 11-inch softballs ordered b = number of 12-inch softballs orderedThe substitution method would be used to determine the number of each size of softball ordered.
Make a the subject of the formula in equation 1:
a = 120 - b
Substitute for a in equation 2:
2.50(120 - b) + 3.50b = 350
300 - 2.5b + 3.50b = 350
Combine and add similar terms:
3.5b - 2.5b = 350 - 300
b = 50
Substitute for b in equation 1
a + 50 = 120
a = 120 - 50
a = 70
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The graph of f (x)=√x is transformed to create the
graph of g (x)= -2√x+6. Which of these describes a
transformation used to create the graph of g?
The transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.
The "-2" in the equation of g(x) reflects a vertical stretch by a factor of 2, which causes the graph to become narrower and steeper than f(x).
The "+6" in the equation of g(x) reflects a vertical shift upward by 6 units, which moves the entire graph of g(x) upward by 6 units.
Therefore, the transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.
Simplify the expression \( \sqrt{y^{2}-81} \) as much as possible after substituting \( 9 \sec x \) for \( y \).
The expression√{y²-81} can be simplifies to trigonometry as 9|tanx|.
If an algebraic expression has no like terms and no parenthesis, it is said to be in its simplest form. Use the Distributive Property to add or subtract the coefficients to combine like terms with variables. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
We start by substituting 9 sec x for y:
√{y²-81} = √{(9 sec x)²-81}
= √{81(sec²x) - 81}
= √{81(sec²x-1)}
= 9√{sec²x-1}
Using the trigonometric identity sec²x - 1 = tan²x, we can simplify further:
9√{sec²x-1} = 9√{tan²x}
= 9|tanx|
Therefore, the simplified expression is 9|tanx|.
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(Open Ended) Describe a general method for adding a decimal with two decimal places to a decimal with three decimal places. Give an example.
How would I answer this?
Answer:
I think you could just add a zero onto the end of the two digit decimal, assuming it's not a decimal that continuously repeats, but is just like 2.25 or something like that. So to add 3.184 to 2.25, you would ads a 0 to the 2.25, making it 2.250.
Sketch a graph that could represent each scenario below. Be sure to label the axes appropriately and then write a description of the graph. a. The height of a baseball thrown from centerfield to home plate in relation to the distance from the centerfield. b. The number of shoppers at the mall each hour during business hours on a given day. c. The temperature of a cup of coffee x minutes after being poured.
The function graph for each of the cases with the description of the graph is plotted.
Explain about the graphing of functions?You must choose x-values and insert those into the equation in order to graph a function. You will obtain a y-value if you enter those values in into equation. Your coordinates for such a single point are made up of your x-values and your y-values.a. The ratio of the height of such a baseball thrown across outfield to home plate to the distance from centerfield.
This, will a parabolic graph as shown.
b. The volume of people who visit the mall per hour during regular business hours on such a particular day.
Thus, this graph will be step wise function as the value of people visiting the mall varies with the time.
c. A cup of coffee's temperature x minutes after it has been poured.
This, will be decreasing graph as the temperature of the coffee will keep on decreasing.
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According to the 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino. A political party wants to know how much impact the Hispanic and Latino vote will have, so they wonder if that percentage has changed since then. They take a random sample of 853 adults in Oregon and ask, among other things, their race. 113 of the people surveyed were Hispanic or Latino. Can the political party conclude that the Hispanic proportion of the population has changed since 2010?
Do not provide links, improper answers, etc or I will report the answer!
Yes, the political party can conclude that the Hispanic proportion of the population has changed since 2010
Now, let's look at the given information. In 2010, the percentage of Hispanic or Latino people in Oregon was 11.7%. This means that out of every 100 people in Oregon, approximately 12 were Hispanic or Latino.
The political party conducted a survey of 853 adults in Oregon and found that 113 of them were Hispanic or Latino. To determine if the percentage of Hispanic or Latino people in Oregon has changed since 2010, we need to compare the survey results to the 2010 percentage.
To do this, we can calculate the percentage of Hispanic or Latino people in the survey by dividing the number of Hispanic or Latino people in the survey (113) by the total number of people surveyed (853), and then multiplying by 100. This gives us a percentage of approximately 13.2%.
Using this formula, we can estimate the margin of error for this survey to be approximately +/- 2.8%.
This means that the true percentage of Hispanic or Latino people in Oregon could be as low as 10.4% or as high as 15.6%, based on the survey results.
Since the margin of error includes the 2010 percentage of 11.7%, we cannot conclude that the Hispanic proportion of the population has definitively changed based on this survey alone.
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How can the area of this triangle be determined by forming a
rectangle?
Select from the drop-down menus to correctly complete the
statements
Copy and rotate the triangle and place it next to the existing
triangle to form a rectangle. The length of the rectangle is
Choose.
units. The width of the rectangle is
Choose.
units. The area of the rectangle IS
N
Choose..
square units
The area of the triangle is half the area of the rectangle, so the
area of the triangle is Choose.
square units.
The area of triangle will be 1/2*area of rectangle.
what exactly is a triangle?
A triangle is a geometric shape that consists of three line segments or sides, and three angles. Triangles are among the simplest and most fundamental shapes in geometry, and they are used in many fields of mathematics, science, engineering, and art.
The sum of the three interior angles of a triangle is always 180 degrees. The length of each side of the triangle is related to the size of the angles opposite to it, and to the length of the other sides, through various trigonometric functions.
Now,
The area of given triangle can be found by making a whole rectangle by making equal and parallel lines base and perpendicular.
let 1 box represent 1 unit if length
then area of rectangle=L*B
=5*4
=20 unit²
then, area of triangle=1/2*area of rectangle
=20/2
=10 unit²
hence,
The area of triangle will be 1/2*area of rectangle.
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HELP ME PLEASE THIS IS DUE TOMORROW
Answer:∠A = 9
Step-by-step explanation:In a Parallelogram opposite angles are always equal thus, 14x - 4 = 15x - 13.
Start by isolating the variable on one side of the equation. You can do this by subtracting 14x from both sides:
14x - 4 - 14x = 15x - 13 - 14x
Simplifying the left side gives:
-4 = x - 13
Now, isolate x by adding 13 to both sides:
-4 + 13 = x - 13 + 13
Simplifying the left side gives:
9 = x
Therefore, the solution to the equation 14x - 4 = 15x - 13 is x = 9
Using the nth term formula a + (n-1)d,
(i) Find the nth term of this arithmetic sequence 8, 11, 14, 17,20,...
(ii) Find the 50th term ?
Answer:
i) here a=8 d=3 nth term= 8+(n-1)3
ii)50th term= 8+49×3=155
Step-by-step explanation:
i hope you find it helpful
Step-by-step explanation:
hope you understood the answer
lines AB and CD are perpendicular to each other. If 3 measures (4x + 3)°, and 4 measures 43°, what is the value of x?
Step-by-step explanation:
4x+3+43=180
46+4x=180
4x=180-46
4x/4=134/4
X=33,5
Answer this ASAP, I will give the brainliest answer.
Given that y = 4 cm and θ = 38°, work out x rounded to 1 DP.
The diagram is not drawn accurately.
from S^OH
sinθ=opp/hyp
sin38°=x/4
cross multiply and make x the subject of the formulax=4sin38°
x=4×(0.61566147533)
x=(2.4626459013)
to 1dp
x=2.5cm
Please only help me if your going to give me the answer thanks
The area of the rectangular prism from the net is 209.8 square meters
Two B's = 30.4Two C's = 87.4How to determine the area of the rectangular prism from the netFrom the question, we have the following parameters that can be used in our computation:
The net of a rectangular prism
Start by calculating the areas of each labelled rectangle by multiplying tthe dimensions
So, we have
A = 2 * 11.5 * 4 = 92
Two B's
B = 2 * 3.8 * 4 = 30.4
Two C's
C = 2 * 3.8 * 11.5 = 87.4
Add the individual areas to get the net area
Area = 92 + 30.4 + 87.4
Evaluate the sum
Area = 209.8
Hence, the total area is 209.8 square meters
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Does anyone know how to solve this similar polygons question?
The length of the corresponding side of the larger polygon is 5/4.
What is polygon?
A polygon is a two-dimensional shape that is formed by connecting a sequence of straight lines (called sides or edges) end-to-end to form a closed loop. The term "poly" means "many," and "gon" means "angle," so a polygon literally means "many angles."
Polygons can have any number of sides, from three (a triangle) to infinity. The most common polygons are the quadrilateral (four sides), pentagon (five sides), hexagon (six sides), heptagon (seven sides), octagon (eight sides), nonagon (nine sides), and decagon (ten sides).
Let's assume that the smaller polygon has n sides and the larger polygon has m sides. Since the polygons are similar, their corresponding sides are proportional. Therefore, we can set up the following proportion:
n/m = 4/x
where x is the length of the corresponding side of the larger polygon.
We also know that the perimeter of the smaller polygon is 20, so each of its sides has length 20/n. Similarly, the perimeter of the larger polygon is 28, so each of its sides has length 28/m.
Since the polygons are similar, their corresponding sides are proportional, so we can set up another proportion:
(20/n) / (28/m) = 4/x
Simplifying this expression, we get:
20m = 28nx
Dividing both sides by 4, we get:
5m = 7nx
Substituting n/m = 4/x, we get:
5m = 28x
Solving for x, we get:
x = (5m)/28
Now, we need to find the value of m. The perimeter of the smaller polygon is 20, so the sum of its sides is 20. Since each side has length 20/n, we can write:
20 = (20/n)*n
Simplifying, we get:
n = 4
The perimeter of the larger polygon is 28, so the sum of its sides is 28. Since each side has length 28/m, we can write:
28 = (28/m)*m
Simplifying, we get:
m = 7
Now, we can substitute the value of m into the expression for x that we derived earlier:
x = (5m)/28 = (5*7)/28 = 5/4
Therefore, the length of the corresponding side of the larger polygon is 5/4.
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Which equation has x = 8 as its only solution?
O 3(2x + 1) + 5 = 4x + 2x + 8
O 2(x+3) = (6x - 4)
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○ −3x+8 = x − 3x+6−½(2x − 4)
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○ − (6x + 4) = 2x − 4
The equation −6x + 4 = -4 has x = 8 as its only solution, which can be verified using the substitution property of equality.
The equation that has x = 8 as its only solution is − (6x + 4) = 2x − 4. To solve this equation, we first need to move all the terms with x to one side and all the constants to the other side. To do this, we can first subtract 2x from both sides, giving us −6x − 4 = −4. We then need to subtract 4 from both sides, giving us −6x = −8. Finally, we need to divide both sides by −6 to get x = 8.
To check if this is the only solution, we can use the substitution property of equality. This property states that if two expressions are equal, then replacing one with the other should still make the equation equal. Therefore, if we substitute x = 8 into the original equation, we should get 0 = 0. To do this, we plug 8 into the equation and get − (6(8) + 4) = 2(8) − 4, which simplifies to −52 = 8 − 4, which is equal to 0 = 0. Since the equation still holds true, x = 8 is the only solution.
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